id int64 1 14M | domain stringclasses 6
values | topic stringclasses 23
values | subtopic stringclasses 37
values | difficulty int64 1 8 | unit_type stringclasses 3
values | title stringlengths 14 86 | content stringlengths 203 553 | key_equations stringclasses 23
values | prerequisites stringclasses 29
values | learning_objective stringclasses 37
values |
|---|---|---|---|---|---|---|---|---|---|---|
5,701 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 11.51 m, speed 18.34 m/s | An object moves in a circle of radius 11.51 m at constant speed 18.34 m/s. The centripetal acceleration has magnitude a_c = v² / r = 29.22 m/s² and is directed toward the center of the circle. The corresponding centripetal force is supplied by whatever agent constrains the motion (tension, gravity, friction, etc.). | a_c = v^2 / r; F_c = m v^2 / r | newton_second_law | Calculate centripetal acceleration and identify the force providing it. |
5,702 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 35.07 m, speed 36.55 m/s | An object moves in a circle of radius 35.07 m at constant speed 36.55 m/s. The centripetal acceleration has magnitude a_c = v² / r = 38.1 m/s² and is directed toward the center of the circle. The corresponding centripetal force is supplied by whatever agent constrains the motion (tension, gravity, friction, etc.). | a_c = v^2 / r; F_c = m v^2 / r | newton_second_law | Calculate centripetal acceleration and identify the force providing it. |
5,703 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 5.167 m, speed 6.429 m/s | An object moves in a circle of radius 5.167 m at constant speed 6.429 m/s. The centripetal acceleration has magnitude a_c = v² / r = 8 m/s² and is directed toward the center of the circle. The corresponding centripetal force is supplied by whatever agent constrains the motion (tension, gravity, friction, etc.). | a_c = v^2 / r; F_c = m v^2 / r | newton_second_law | Calculate centripetal acceleration and identify the force providing it. |
5,704 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 37.04 m, speed 37.92 m/s | An object moves in a circle of radius 37.04 m at constant speed 37.92 m/s. The centripetal acceleration has magnitude a_c = v² / r = 38.82 m/s² and is directed toward the center of the circle. The corresponding centripetal force is supplied by whatever agent constrains the motion (tension, gravity, friction, etc.). | a_c = v^2 / r; F_c = m v^2 / r | newton_second_law | Calculate centripetal acceleration and identify the force providing it. |
5,705 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 28.18 m, speed 18.09 m/s | An object moves in a circle of radius 28.18 m at constant speed 18.09 m/s. The centripetal acceleration has magnitude a_c = v² / r = 11.61 m/s² and is directed toward the center of the circle. The corresponding centripetal force is supplied by whatever agent constrains the motion (tension, gravity, friction, etc.). | a_c = v^2 / r; F_c = m v^2 / r | newton_second_law | Calculate centripetal acceleration and identify the force providing it. |
5,706 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 18.4 m, speed 28.26 m/s | An object moves in a circle of radius 18.4 m at constant speed 28.26 m/s. The centripetal acceleration has magnitude a_c = v² / r = 43.4 m/s² and is directed toward the center of the circle. The corresponding centripetal force is supplied by whatever agent constrains the motion (tension, gravity, friction, etc.). | a_c = v^2 / r; F_c = m v^2 / r | newton_second_law | Calculate centripetal acceleration and identify the force providing it. |
5,707 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 1.125 m, speed 21.48 m/s | An object moves in a circle of radius 1.125 m at constant speed 21.48 m/s. The centripetal acceleration has magnitude a_c = v² / r = 410.3 m/s² and is directed toward the center of the circle. The corresponding centripetal force is supplied by whatever agent constrains the motion (tension, gravity, friction, etc.). | a_c = v^2 / r; F_c = m v^2 / r | newton_second_law | Calculate centripetal acceleration and identify the force providing it. |
5,708 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 34.72 m, speed 25.76 m/s | An object moves in a circle of radius 34.72 m at constant speed 25.76 m/s. The centripetal acceleration has magnitude a_c = v² / r = 19.11 m/s² and is directed toward the center of the circle. The corresponding centripetal force is supplied by whatever agent constrains the motion (tension, gravity, friction, etc.). | a_c = v^2 / r; F_c = m v^2 / r | newton_second_law | Calculate centripetal acceleration and identify the force providing it. |
5,709 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 5.406 m, speed 19.47 m/s | An object moves in a circle of radius 5.406 m at constant speed 19.47 m/s. The centripetal acceleration has magnitude a_c = v² / r = 70.14 m/s² and is directed toward the center of the circle. The corresponding centripetal force is supplied by whatever agent constrains the motion (tension, gravity, friction, etc.). | a_c = v^2 / r; F_c = m v^2 / r | newton_second_law | Calculate centripetal acceleration and identify the force providing it. |
5,710 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 14.02 m, speed 22.73 m/s | An object moves in a circle of radius 14.02 m at constant speed 22.73 m/s. The centripetal acceleration has magnitude a_c = v² / r = 36.87 m/s² and is directed toward the center of the circle. The corresponding centripetal force is supplied by whatever agent constrains the motion (tension, gravity, friction, etc.). | a_c = v^2 / r; F_c = m v^2 / r | newton_second_law | Calculate centripetal acceleration and identify the force providing it. |
5,711 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 21.17 m, speed 3.542 m/s | An object moves in a circle of radius 21.17 m at constant speed 3.542 m/s. The centripetal acceleration has magnitude a_c = v² / r = 0.5926 m/s² and is directed toward the center of the circle. The corresponding centripetal force is supplied by whatever agent constrains the motion (tension, gravity, friction, etc.). | a_c = v^2 / r; F_c = m v^2 / r | newton_second_law | Calculate centripetal acceleration and identify the force providing it. |
5,712 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 13.21 m, speed 38 m/s | An object moves in a circle of radius 13.21 m at constant speed 38 m/s. The centripetal acceleration has magnitude a_c = v² / r = 109.3 m/s² and is directed toward the center of the circle. The corresponding centripetal force is supplied by whatever agent constrains the motion (tension, gravity, friction, etc.). | a_c = v^2 / r; F_c = m v^2 / r | newton_second_law | Calculate centripetal acceleration and identify the force providing it. |
5,713 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 17.95 m, speed 16.65 m/s | An object moves in a circle of radius 17.95 m at constant speed 16.65 m/s. The centripetal acceleration has magnitude a_c = v² / r = 15.45 m/s² and is directed toward the center of the circle. The corresponding centripetal force is supplied by whatever agent constrains the motion (tension, gravity, friction, etc.). | a_c = v^2 / r; F_c = m v^2 / r | newton_second_law | Calculate centripetal acceleration and identify the force providing it. |
5,714 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 45.97 m, speed 36.36 m/s | An object moves in a circle of radius 45.97 m at constant speed 36.36 m/s. The centripetal acceleration has magnitude a_c = v² / r = 28.75 m/s² and is directed toward the center of the circle. The corresponding centripetal force is supplied by whatever agent constrains the motion (tension, gravity, friction, etc.). | a_c = v^2 / r; F_c = m v^2 / r | newton_second_law | Calculate centripetal acceleration and identify the force providing it. |
5,715 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 43.79 m, speed 5.719 m/s | An object moves in a circle of radius 43.79 m at constant speed 5.719 m/s. The centripetal acceleration has magnitude a_c = v² / r = 0.747 m/s² and is directed toward the center of the circle. The corresponding centripetal force is supplied by whatever agent constrains the motion (tension, gravity, friction, etc.). | a_c = v^2 / r; F_c = m v^2 / r | newton_second_law | Calculate centripetal acceleration and identify the force providing it. |
5,716 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 8.184 m, speed 23.25 m/s | An object moves in a circle of radius 8.184 m at constant speed 23.25 m/s. The centripetal acceleration has magnitude a_c = v² / r = 66.03 m/s² and is directed toward the center of the circle. The corresponding centripetal force is supplied by whatever agent constrains the motion (tension, gravity, friction, etc.). | a_c = v^2 / r; F_c = m v^2 / r | newton_second_law | Calculate centripetal acceleration and identify the force providing it. |
5,717 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 33.27 m, speed 18.4 m/s | An object moves in a circle of radius 33.27 m at constant speed 18.4 m/s. The centripetal acceleration has magnitude a_c = v² / r = 10.18 m/s² and is directed toward the center of the circle. The corresponding centripetal force is supplied by whatever agent constrains the motion (tension, gravity, friction, etc.). | a_c = v^2 / r; F_c = m v^2 / r | newton_second_law | Calculate centripetal acceleration and identify the force providing it. |
5,718 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 49.83 m, speed 15.56 m/s | An object moves in a circle of radius 49.83 m at constant speed 15.56 m/s. The centripetal acceleration has magnitude a_c = v² / r = 4.859 m/s² and is directed toward the center of the circle. The corresponding centripetal force is supplied by whatever agent constrains the motion (tension, gravity, friction, etc.). | a_c = v^2 / r; F_c = m v^2 / r | newton_second_law | Calculate centripetal acceleration and identify the force providing it. |
5,719 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 13.22 m, speed 3.606 m/s | An object moves in a circle of radius 13.22 m at constant speed 3.606 m/s. The centripetal acceleration has magnitude a_c = v² / r = 0.9833 m/s² and is directed toward the center of the circle. The corresponding centripetal force is supplied by whatever agent constrains the motion (tension, gravity, friction, etc.). | a_c = v^2 / r; F_c = m v^2 / r | newton_second_law | Calculate centripetal acceleration and identify the force providing it. |
5,720 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 39.52 m, speed 8.235 m/s | An object moves in a circle of radius 39.52 m at constant speed 8.235 m/s. The centripetal acceleration has magnitude a_c = v² / r = 1.716 m/s² and is directed toward the center of the circle. The corresponding centripetal force is supplied by whatever agent constrains the motion (tension, gravity, friction, etc.). | a_c = v^2 / r; F_c = m v^2 / r | newton_second_law | Calculate centripetal acceleration and identify the force providing it. |
5,721 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 20.72 m, speed 22.83 m/s | An object moves in a circle of radius 20.72 m at constant speed 22.83 m/s. The centripetal acceleration has magnitude a_c = v² / r = 25.15 m/s² and is directed toward the center of the circle. The corresponding centripetal force is supplied by whatever agent constrains the motion (tension, gravity, friction, etc.). | a_c = v^2 / r; F_c = m v^2 / r | newton_second_law | Calculate centripetal acceleration and identify the force providing it. |
5,722 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 11.69 m, speed 6.748 m/s | An object moves in a circle of radius 11.69 m at constant speed 6.748 m/s. The centripetal acceleration has magnitude a_c = v² / r = 3.896 m/s² and is directed toward the center of the circle. The corresponding centripetal force is supplied by whatever agent constrains the motion (tension, gravity, friction, etc.). | a_c = v^2 / r; F_c = m v^2 / r | newton_second_law | Calculate centripetal acceleration and identify the force providing it. |
5,723 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 6.747 m, speed 28.36 m/s | An object moves in a circle of radius 6.747 m at constant speed 28.36 m/s. The centripetal acceleration has magnitude a_c = v² / r = 119.2 m/s² and is directed toward the center of the circle. The corresponding centripetal force is supplied by whatever agent constrains the motion (tension, gravity, friction, etc.). | a_c = v^2 / r; F_c = m v^2 / r | newton_second_law | Calculate centripetal acceleration and identify the force providing it. |
5,724 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 0.6586 m, speed 3.34 m/s | An object moves in a circle of radius 0.6586 m at constant speed 3.34 m/s. The centripetal acceleration has magnitude a_c = v² / r = 16.94 m/s² and is directed toward the center of the circle. The corresponding centripetal force is supplied by whatever agent constrains the motion (tension, gravity, friction, etc.). | a_c = v^2 / r; F_c = m v^2 / r | newton_second_law | Calculate centripetal acceleration and identify the force providing it. |
5,725 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 39.43 m, speed 5.397 m/s | An object moves in a circle of radius 39.43 m at constant speed 5.397 m/s. The centripetal acceleration has magnitude a_c = v² / r = 0.7389 m/s² and is directed toward the center of the circle. The corresponding centripetal force is supplied by whatever agent constrains the motion (tension, gravity, friction, etc.). | a_c = v^2 / r; F_c = m v^2 / r | newton_second_law | Calculate centripetal acceleration and identify the force providing it. |
5,726 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 33.33 m, speed 23.84 m/s | An object moves in a circle of radius 33.33 m at constant speed 23.84 m/s. The centripetal acceleration has magnitude a_c = v² / r = 17.05 m/s² and is directed toward the center of the circle. The corresponding centripetal force is supplied by whatever agent constrains the motion (tension, gravity, friction, etc.). | a_c = v^2 / r; F_c = m v^2 / r | newton_second_law | Calculate centripetal acceleration and identify the force providing it. |
5,727 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 0.542 m, speed 35.34 m/s | An object moves in a circle of radius 0.542 m at constant speed 35.34 m/s. The centripetal acceleration has magnitude a_c = v² / r = 2304 m/s² and is directed toward the center of the circle. The corresponding centripetal force is supplied by whatever agent constrains the motion (tension, gravity, friction, etc.). | a_c = v^2 / r; F_c = m v^2 / r | newton_second_law | Calculate centripetal acceleration and identify the force providing it. |
5,728 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 6.939 m, speed 36.91 m/s | An object moves in a circle of radius 6.939 m at constant speed 36.91 m/s. The centripetal acceleration has magnitude a_c = v² / r = 196.3 m/s² and is directed toward the center of the circle. The corresponding centripetal force is supplied by whatever agent constrains the motion (tension, gravity, friction, etc.). | a_c = v^2 / r; F_c = m v^2 / r | newton_second_law | Calculate centripetal acceleration and identify the force providing it. |
5,729 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 43.04 m, speed 32.25 m/s | An object moves in a circle of radius 43.04 m at constant speed 32.25 m/s. The centripetal acceleration has magnitude a_c = v² / r = 24.16 m/s² and is directed toward the center of the circle. The corresponding centripetal force is supplied by whatever agent constrains the motion (tension, gravity, friction, etc.). | a_c = v^2 / r; F_c = m v^2 / r | newton_second_law | Calculate centripetal acceleration and identify the force providing it. |
5,730 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 9.514 m, speed 19.52 m/s | An object moves in a circle of radius 9.514 m at constant speed 19.52 m/s. The centripetal acceleration has magnitude a_c = v² / r = 40.03 m/s² and is directed toward the center of the circle. The corresponding centripetal force is supplied by whatever agent constrains the motion (tension, gravity, friction, etc.). | a_c = v^2 / r; F_c = m v^2 / r | newton_second_law | Calculate centripetal acceleration and identify the force providing it. |
5,731 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 23.99 m, speed 4.863 m/s | An object moves in a circle of radius 23.99 m at constant speed 4.863 m/s. The centripetal acceleration has magnitude a_c = v² / r = 0.9858 m/s² and is directed toward the center of the circle. The corresponding centripetal force is supplied by whatever agent constrains the motion (tension, gravity, friction, etc.). | a_c = v^2 / r; F_c = m v^2 / r | newton_second_law | Calculate centripetal acceleration and identify the force providing it. |
5,732 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 19.45 m, speed 25.7 m/s | An object moves in a circle of radius 19.45 m at constant speed 25.7 m/s. The centripetal acceleration has magnitude a_c = v² / r = 33.96 m/s² and is directed toward the center of the circle. The corresponding centripetal force is supplied by whatever agent constrains the motion (tension, gravity, friction, etc.). | a_c = v^2 / r; F_c = m v^2 / r | newton_second_law | Calculate centripetal acceleration and identify the force providing it. |
5,733 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 27.12 m, speed 32.35 m/s | An object moves in a circle of radius 27.12 m at constant speed 32.35 m/s. The centripetal acceleration has magnitude a_c = v² / r = 38.6 m/s² and is directed toward the center of the circle. The corresponding centripetal force is supplied by whatever agent constrains the motion (tension, gravity, friction, etc.). | a_c = v^2 / r; F_c = m v^2 / r | newton_second_law | Calculate centripetal acceleration and identify the force providing it. |
5,734 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 7.391 m, speed 5.951 m/s | An object moves in a circle of radius 7.391 m at constant speed 5.951 m/s. The centripetal acceleration has magnitude a_c = v² / r = 4.792 m/s² and is directed toward the center of the circle. The corresponding centripetal force is supplied by whatever agent constrains the motion (tension, gravity, friction, etc.). | a_c = v^2 / r; F_c = m v^2 / r | newton_second_law | Calculate centripetal acceleration and identify the force providing it. |
5,735 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 25.54 m, speed 34.59 m/s | An object moves in a circle of radius 25.54 m at constant speed 34.59 m/s. The centripetal acceleration has magnitude a_c = v² / r = 46.83 m/s² and is directed toward the center of the circle. The corresponding centripetal force is supplied by whatever agent constrains the motion (tension, gravity, friction, etc.). | a_c = v^2 / r; F_c = m v^2 / r | newton_second_law | Calculate centripetal acceleration and identify the force providing it. |
5,736 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 3.493 m, speed 21.02 m/s | An object moves in a circle of radius 3.493 m at constant speed 21.02 m/s. The centripetal acceleration has magnitude a_c = v² / r = 126.5 m/s² and is directed toward the center of the circle. The corresponding centripetal force is supplied by whatever agent constrains the motion (tension, gravity, friction, etc.). | a_c = v^2 / r; F_c = m v^2 / r | newton_second_law | Calculate centripetal acceleration and identify the force providing it. |
5,737 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 49.37 m, speed 23.08 m/s | An object moves in a circle of radius 49.37 m at constant speed 23.08 m/s. The centripetal acceleration has magnitude a_c = v² / r = 10.79 m/s² and is directed toward the center of the circle. The corresponding centripetal force is supplied by whatever agent constrains the motion (tension, gravity, friction, etc.). | a_c = v^2 / r; F_c = m v^2 / r | newton_second_law | Calculate centripetal acceleration and identify the force providing it. |
5,738 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 12.43 m, speed 30.38 m/s | An object moves in a circle of radius 12.43 m at constant speed 30.38 m/s. The centripetal acceleration has magnitude a_c = v² / r = 74.27 m/s² and is directed toward the center of the circle. The corresponding centripetal force is supplied by whatever agent constrains the motion (tension, gravity, friction, etc.). | a_c = v^2 / r; F_c = m v^2 / r | newton_second_law | Calculate centripetal acceleration and identify the force providing it. |
5,739 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 42 m, speed 15.11 m/s | An object moves in a circle of radius 42 m at constant speed 15.11 m/s. The centripetal acceleration has magnitude a_c = v² / r = 5.433 m/s² and is directed toward the center of the circle. The corresponding centripetal force is supplied by whatever agent constrains the motion (tension, gravity, friction, etc.). | a_c = v^2 / r; F_c = m v^2 / r | newton_second_law | Calculate centripetal acceleration and identify the force providing it. |
5,740 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 11.34 m, speed 11.24 m/s | An object moves in a circle of radius 11.34 m at constant speed 11.24 m/s. The centripetal acceleration has magnitude a_c = v² / r = 11.13 m/s² and is directed toward the center of the circle. The corresponding centripetal force is supplied by whatever agent constrains the motion (tension, gravity, friction, etc.). | a_c = v^2 / r; F_c = m v^2 / r | newton_second_law | Calculate centripetal acceleration and identify the force providing it. |
5,741 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 3.078 m, speed 17.84 m/s | An object moves in a circle of radius 3.078 m at constant speed 17.84 m/s. The centripetal acceleration has magnitude a_c = v² / r = 103.4 m/s² and is directed toward the center of the circle. The corresponding centripetal force is supplied by whatever agent constrains the motion (tension, gravity, friction, etc.). | a_c = v^2 / r; F_c = m v^2 / r | newton_second_law | Calculate centripetal acceleration and identify the force providing it. |
5,742 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 43.55 m, speed 31.44 m/s | An object moves in a circle of radius 43.55 m at constant speed 31.44 m/s. The centripetal acceleration has magnitude a_c = v² / r = 22.71 m/s² and is directed toward the center of the circle. The corresponding centripetal force is supplied by whatever agent constrains the motion (tension, gravity, friction, etc.). | a_c = v^2 / r; F_c = m v^2 / r | newton_second_law | Calculate centripetal acceleration and identify the force providing it. |
5,743 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 1.48 m, speed 27.19 m/s | An object moves in a circle of radius 1.48 m at constant speed 27.19 m/s. The centripetal acceleration has magnitude a_c = v² / r = 499.5 m/s² and is directed toward the center of the circle. The corresponding centripetal force is supplied by whatever agent constrains the motion (tension, gravity, friction, etc.). | a_c = v^2 / r; F_c = m v^2 / r | newton_second_law | Calculate centripetal acceleration and identify the force providing it. |
5,744 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 46.55 m, speed 16.24 m/s | An object moves in a circle of radius 46.55 m at constant speed 16.24 m/s. The centripetal acceleration has magnitude a_c = v² / r = 5.666 m/s² and is directed toward the center of the circle. The corresponding centripetal force is supplied by whatever agent constrains the motion (tension, gravity, friction, etc.). | a_c = v^2 / r; F_c = m v^2 / r | newton_second_law | Calculate centripetal acceleration and identify the force providing it. |
5,745 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 30.36 m, speed 34.81 m/s | An object moves in a circle of radius 30.36 m at constant speed 34.81 m/s. The centripetal acceleration has magnitude a_c = v² / r = 39.91 m/s² and is directed toward the center of the circle. The corresponding centripetal force is supplied by whatever agent constrains the motion (tension, gravity, friction, etc.). | a_c = v^2 / r; F_c = m v^2 / r | newton_second_law | Calculate centripetal acceleration and identify the force providing it. |
5,746 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 37.46 m, speed 5.966 m/s | An object moves in a circle of radius 37.46 m at constant speed 5.966 m/s. The centripetal acceleration has magnitude a_c = v² / r = 0.9502 m/s² and is directed toward the center of the circle. The corresponding centripetal force is supplied by whatever agent constrains the motion (tension, gravity, friction, etc.). | a_c = v^2 / r; F_c = m v^2 / r | newton_second_law | Calculate centripetal acceleration and identify the force providing it. |
5,747 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 30.78 m, speed 31.83 m/s | An object moves in a circle of radius 30.78 m at constant speed 31.83 m/s. The centripetal acceleration has magnitude a_c = v² / r = 32.91 m/s² and is directed toward the center of the circle. The corresponding centripetal force is supplied by whatever agent constrains the motion (tension, gravity, friction, etc.). | a_c = v^2 / r; F_c = m v^2 / r | newton_second_law | Calculate centripetal acceleration and identify the force providing it. |
5,748 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 44.45 m, speed 26.2 m/s | An object moves in a circle of radius 44.45 m at constant speed 26.2 m/s. The centripetal acceleration has magnitude a_c = v² / r = 15.44 m/s² and is directed toward the center of the circle. The corresponding centripetal force is supplied by whatever agent constrains the motion (tension, gravity, friction, etc.). | a_c = v^2 / r; F_c = m v^2 / r | newton_second_law | Calculate centripetal acceleration and identify the force providing it. |
5,749 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 37.8 m, speed 7.134 m/s | An object moves in a circle of radius 37.8 m at constant speed 7.134 m/s. The centripetal acceleration has magnitude a_c = v² / r = 1.347 m/s² and is directed toward the center of the circle. The corresponding centripetal force is supplied by whatever agent constrains the motion (tension, gravity, friction, etc.). | a_c = v^2 / r; F_c = m v^2 / r | newton_second_law | Calculate centripetal acceleration and identify the force providing it. |
5,750 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 29.99 m, speed 12.22 m/s | An object moves in a circle of radius 29.99 m at constant speed 12.22 m/s. The centripetal acceleration has magnitude a_c = v² / r = 4.977 m/s² and is directed toward the center of the circle. The corresponding centripetal force is supplied by whatever agent constrains the motion (tension, gravity, friction, etc.). | a_c = v^2 / r; F_c = m v^2 / r | newton_second_law | Calculate centripetal acceleration and identify the force providing it. |
5,751 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 38.68 m, speed 17.88 m/s | An object moves in a circle of radius 38.68 m at constant speed 17.88 m/s. The centripetal acceleration has magnitude a_c = v² / r = 8.263 m/s² and is directed toward the center of the circle. The corresponding centripetal force is supplied by whatever agent constrains the motion (tension, gravity, friction, etc.). | a_c = v^2 / r; F_c = m v^2 / r | newton_second_law | Calculate centripetal acceleration and identify the force providing it. |
5,752 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 1.643 m, speed 3.587 m/s | An object moves in a circle of radius 1.643 m at constant speed 3.587 m/s. The centripetal acceleration has magnitude a_c = v² / r = 7.833 m/s² and is directed toward the center of the circle. The corresponding centripetal force is supplied by whatever agent constrains the motion (tension, gravity, friction, etc.). | a_c = v^2 / r; F_c = m v^2 / r | newton_second_law | Calculate centripetal acceleration and identify the force providing it. |
5,753 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 4.334 m, speed 35.77 m/s | An object moves in a circle of radius 4.334 m at constant speed 35.77 m/s. The centripetal acceleration has magnitude a_c = v² / r = 295.3 m/s² and is directed toward the center of the circle. The corresponding centripetal force is supplied by whatever agent constrains the motion (tension, gravity, friction, etc.). | a_c = v^2 / r; F_c = m v^2 / r | newton_second_law | Calculate centripetal acceleration and identify the force providing it. |
5,754 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 7.364 m, speed 26.01 m/s | An object moves in a circle of radius 7.364 m at constant speed 26.01 m/s. The centripetal acceleration has magnitude a_c = v² / r = 91.91 m/s² and is directed toward the center of the circle. The corresponding centripetal force is supplied by whatever agent constrains the motion (tension, gravity, friction, etc.). | a_c = v^2 / r; F_c = m v^2 / r | newton_second_law | Calculate centripetal acceleration and identify the force providing it. |
5,755 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 18.54 m, speed 16.34 m/s | An object moves in a circle of radius 18.54 m at constant speed 16.34 m/s. The centripetal acceleration has magnitude a_c = v² / r = 14.4 m/s² and is directed toward the center of the circle. The corresponding centripetal force is supplied by whatever agent constrains the motion (tension, gravity, friction, etc.). | a_c = v^2 / r; F_c = m v^2 / r | newton_second_law | Calculate centripetal acceleration and identify the force providing it. |
5,756 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 23.28 m, speed 32.47 m/s | An object moves in a circle of radius 23.28 m at constant speed 32.47 m/s. The centripetal acceleration has magnitude a_c = v² / r = 45.28 m/s² and is directed toward the center of the circle. The corresponding centripetal force is supplied by whatever agent constrains the motion (tension, gravity, friction, etc.). | a_c = v^2 / r; F_c = m v^2 / r | newton_second_law | Calculate centripetal acceleration and identify the force providing it. |
5,757 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 45.86 m, speed 12.84 m/s | An object moves in a circle of radius 45.86 m at constant speed 12.84 m/s. The centripetal acceleration has magnitude a_c = v² / r = 3.593 m/s² and is directed toward the center of the circle. The corresponding centripetal force is supplied by whatever agent constrains the motion (tension, gravity, friction, etc.). | a_c = v^2 / r; F_c = m v^2 / r | newton_second_law | Calculate centripetal acceleration and identify the force providing it. |
5,758 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 26.81 m, speed 13.76 m/s | An object moves in a circle of radius 26.81 m at constant speed 13.76 m/s. The centripetal acceleration has magnitude a_c = v² / r = 7.058 m/s² and is directed toward the center of the circle. The corresponding centripetal force is supplied by whatever agent constrains the motion (tension, gravity, friction, etc.). | a_c = v^2 / r; F_c = m v^2 / r | newton_second_law | Calculate centripetal acceleration and identify the force providing it. |
5,759 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 15.48 m, speed 37.99 m/s | An object moves in a circle of radius 15.48 m at constant speed 37.99 m/s. The centripetal acceleration has magnitude a_c = v² / r = 93.26 m/s² and is directed toward the center of the circle. The corresponding centripetal force is supplied by whatever agent constrains the motion (tension, gravity, friction, etc.). | a_c = v^2 / r; F_c = m v^2 / r | newton_second_law | Calculate centripetal acceleration and identify the force providing it. |
5,760 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 25.62 m, speed 16.06 m/s | An object moves in a circle of radius 25.62 m at constant speed 16.06 m/s. The centripetal acceleration has magnitude a_c = v² / r = 10.06 m/s² and is directed toward the center of the circle. The corresponding centripetal force is supplied by whatever agent constrains the motion (tension, gravity, friction, etc.). | a_c = v^2 / r; F_c = m v^2 / r | newton_second_law | Calculate centripetal acceleration and identify the force providing it. |
5,761 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 43.57 m, speed 27.85 m/s | An object moves in a circle of radius 43.57 m at constant speed 27.85 m/s. The centripetal acceleration has magnitude a_c = v² / r = 17.8 m/s² and is directed toward the center of the circle. The corresponding centripetal force is supplied by whatever agent constrains the motion (tension, gravity, friction, etc.). | a_c = v^2 / r; F_c = m v^2 / r | newton_second_law | Calculate centripetal acceleration and identify the force providing it. |
5,762 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 34.79 m, speed 37.01 m/s | An object moves in a circle of radius 34.79 m at constant speed 37.01 m/s. The centripetal acceleration has magnitude a_c = v² / r = 39.38 m/s² and is directed toward the center of the circle. The corresponding centripetal force is supplied by whatever agent constrains the motion (tension, gravity, friction, etc.). | a_c = v^2 / r; F_c = m v^2 / r | newton_second_law | Calculate centripetal acceleration and identify the force providing it. |
5,763 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 30.3 m, speed 26.78 m/s | An object moves in a circle of radius 30.3 m at constant speed 26.78 m/s. The centripetal acceleration has magnitude a_c = v² / r = 23.67 m/s² and is directed toward the center of the circle. The corresponding centripetal force is supplied by whatever agent constrains the motion (tension, gravity, friction, etc.). | a_c = v^2 / r; F_c = m v^2 / r | newton_second_law | Calculate centripetal acceleration and identify the force providing it. |
5,764 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 28.74 m, speed 19.3 m/s | An object moves in a circle of radius 28.74 m at constant speed 19.3 m/s. The centripetal acceleration has magnitude a_c = v² / r = 12.96 m/s² and is directed toward the center of the circle. The corresponding centripetal force is supplied by whatever agent constrains the motion (tension, gravity, friction, etc.). | a_c = v^2 / r; F_c = m v^2 / r | newton_second_law | Calculate centripetal acceleration and identify the force providing it. |
5,765 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 4.64 m, speed 20.1 m/s | An object moves in a circle of radius 4.64 m at constant speed 20.1 m/s. The centripetal acceleration has magnitude a_c = v² / r = 87.04 m/s² and is directed toward the center of the circle. The corresponding centripetal force is supplied by whatever agent constrains the motion (tension, gravity, friction, etc.). | a_c = v^2 / r; F_c = m v^2 / r | newton_second_law | Calculate centripetal acceleration and identify the force providing it. |
5,766 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 17.19 m, speed 21.16 m/s | An object moves in a circle of radius 17.19 m at constant speed 21.16 m/s. The centripetal acceleration has magnitude a_c = v² / r = 26.06 m/s² and is directed toward the center of the circle. The corresponding centripetal force is supplied by whatever agent constrains the motion (tension, gravity, friction, etc.). | a_c = v^2 / r; F_c = m v^2 / r | newton_second_law | Calculate centripetal acceleration and identify the force providing it. |
5,767 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges -2.5234e-04 C and 9.3423e-04 C separated by 1.751 m | Two point charges q1 = -2.5234e-04 C and q2 = 9.3423e-04 C are separated by distance r = 1.751 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 691.2 N, where k = 8.9875517923 × 10⁹ N·m²/C². The force is repulsive if the charges have the same sign and attractive if opposite. | F = k |q1 q2| / r^2; k = 1/(4 π ε_0) | newton_second_law | Compute the Coulomb force between two point charges. |
5,768 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges -3.1374e-04 C and 9.0731e-04 C separated by 1.136 m | Two point charges q1 = -3.1374e-04 C and q2 = 9.0731e-04 C are separated by distance r = 1.136 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 1981 N, where k = 8.9875517923 × 10⁹ N·m²/C². The force is repulsive if the charges have the same sign and attractive if opposite. | F = k |q1 q2| / r^2; k = 1/(4 π ε_0) | newton_second_law | Compute the Coulomb force between two point charges. |
5,769 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges 9.7237e-04 C and -8.2591e-04 C separated by 1.04 m | Two point charges q1 = 9.7237e-04 C and q2 = -8.2591e-04 C are separated by distance r = 1.04 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 6671 N, where k = 8.9875517923 × 10⁹ N·m²/C². The force is repulsive if the charges have the same sign and attractive if opposite. | F = k |q1 q2| / r^2; k = 1/(4 π ε_0) | newton_second_law | Compute the Coulomb force between two point charges. |
5,770 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges 2.7924e-04 C and 6.7001e-04 C separated by 0.3848 m | Two point charges q1 = 2.7924e-04 C and q2 = 6.7001e-04 C are separated by distance r = 0.3848 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 1.1355e+04 N, where k = 8.9875517923 × 10⁹ N·m²/C². The force is repulsive if the charges have the same sign and attractive if opposite. | F = k |q1 q2| / r^2; k = 1/(4 π ε_0) | newton_second_law | Compute the Coulomb force between two point charges. |
5,771 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges -8.0244e-04 C and 1.9078e-04 C separated by 1.375 m | Two point charges q1 = -8.0244e-04 C and q2 = 1.9078e-04 C are separated by distance r = 1.375 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 727.6 N, where k = 8.9875517923 × 10⁹ N·m²/C². The force is repulsive if the charges have the same sign and attractive if opposite. | F = k |q1 q2| / r^2; k = 1/(4 π ε_0) | newton_second_law | Compute the Coulomb force between two point charges. |
5,772 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges 2.0526e-04 C and 5.8217e-04 C separated by 0.3551 m | Two point charges q1 = 2.0526e-04 C and q2 = 5.8217e-04 C are separated by distance r = 0.3551 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 8517 N, where k = 8.9875517923 × 10⁹ N·m²/C². The force is repulsive if the charges have the same sign and attractive if opposite. | F = k |q1 q2| / r^2; k = 1/(4 π ε_0) | newton_second_law | Compute the Coulomb force between two point charges. |
5,773 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges 6.3896e-04 C and -5.9853e-04 C separated by 1.271 m | Two point charges q1 = 6.3896e-04 C and q2 = -5.9853e-04 C are separated by distance r = 1.271 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 2129 N, where k = 8.9875517923 × 10⁹ N·m²/C². The force is repulsive if the charges have the same sign and attractive if opposite. | F = k |q1 q2| / r^2; k = 1/(4 π ε_0) | newton_second_law | Compute the Coulomb force between two point charges. |
5,774 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges 1.8389e-04 C and 3.7562e-04 C separated by 0.7893 m | Two point charges q1 = 1.8389e-04 C and q2 = 3.7562e-04 C are separated by distance r = 0.7893 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 996.4 N, where k = 8.9875517923 × 10⁹ N·m²/C². The force is repulsive if the charges have the same sign and attractive if opposite. | F = k |q1 q2| / r^2; k = 1/(4 π ε_0) | newton_second_law | Compute the Coulomb force between two point charges. |
5,775 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges 9.3255e-04 C and 5.3787e-04 C separated by 0.3012 m | Two point charges q1 = 9.3255e-04 C and q2 = 5.3787e-04 C are separated by distance r = 0.3012 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 4.9686e+04 N, where k = 8.9875517923 × 10⁹ N·m²/C². The force is repulsive if the charges have the same sign and attractive if opposite. | F = k |q1 q2| / r^2; k = 1/(4 π ε_0) | newton_second_law | Compute the Coulomb force between two point charges. |
5,776 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges -2.5328e-04 C and 8.1330e-04 C separated by 1.968 m | Two point charges q1 = -2.5328e-04 C and q2 = 8.1330e-04 C are separated by distance r = 1.968 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 478.1 N, where k = 8.9875517923 × 10⁹ N·m²/C². The force is repulsive if the charges have the same sign and attractive if opposite. | F = k |q1 q2| / r^2; k = 1/(4 π ε_0) | newton_second_law | Compute the Coulomb force between two point charges. |
5,777 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges -6.7480e-05 C and 9.2788e-04 C separated by 0.915 m | Two point charges q1 = -6.7480e-05 C and q2 = 9.2788e-04 C are separated by distance r = 0.915 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 672.2 N, where k = 8.9875517923 × 10⁹ N·m²/C². The force is repulsive if the charges have the same sign and attractive if opposite. | F = k |q1 q2| / r^2; k = 1/(4 π ε_0) | newton_second_law | Compute the Coulomb force between two point charges. |
5,778 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges 5.1161e-04 C and 1.9999e-04 C separated by 0.1115 m | Two point charges q1 = 5.1161e-04 C and q2 = 1.9999e-04 C are separated by distance r = 0.1115 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 7.3999e+04 N, where k = 8.9875517923 × 10⁹ N·m²/C². The force is repulsive if the charges have the same sign and attractive if opposite. | F = k |q1 q2| / r^2; k = 1/(4 π ε_0) | newton_second_law | Compute the Coulomb force between two point charges. |
5,779 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges 6.2848e-04 C and 5.9568e-04 C separated by 0.958 m | Two point charges q1 = 6.2848e-04 C and q2 = 5.9568e-04 C are separated by distance r = 0.958 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 3666 N, where k = 8.9875517923 × 10⁹ N·m²/C². The force is repulsive if the charges have the same sign and attractive if opposite. | F = k |q1 q2| / r^2; k = 1/(4 π ε_0) | newton_second_law | Compute the Coulomb force between two point charges. |
5,780 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges 3.1383e-04 C and -1.8192e-04 C separated by 0.7291 m | Two point charges q1 = 3.1383e-04 C and q2 = -1.8192e-04 C are separated by distance r = 0.7291 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 965.4 N, where k = 8.9875517923 × 10⁹ N·m²/C². The force is repulsive if the charges have the same sign and attractive if opposite. | F = k |q1 q2| / r^2; k = 1/(4 π ε_0) | newton_second_law | Compute the Coulomb force between two point charges. |
5,781 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges -4.1994e-05 C and -2.7808e-04 C separated by 1.101 m | Two point charges q1 = -4.1994e-05 C and q2 = -2.7808e-04 C are separated by distance r = 1.101 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 86.5 N, where k = 8.9875517923 × 10⁹ N·m²/C². The force is repulsive if the charges have the same sign and attractive if opposite. | F = k |q1 q2| / r^2; k = 1/(4 π ε_0) | newton_second_law | Compute the Coulomb force between two point charges. |
5,782 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges 1.2829e-04 C and -9.2582e-04 C separated by 1.377 m | Two point charges q1 = 1.2829e-04 C and q2 = -9.2582e-04 C are separated by distance r = 1.377 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 563.3 N, where k = 8.9875517923 × 10⁹ N·m²/C². The force is repulsive if the charges have the same sign and attractive if opposite. | F = k |q1 q2| / r^2; k = 1/(4 π ε_0) | newton_second_law | Compute the Coulomb force between two point charges. |
5,783 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges -4.0897e-05 C and -1.0846e-05 C separated by 0.6818 m | Two point charges q1 = -4.0897e-05 C and q2 = -1.0846e-05 C are separated by distance r = 0.6818 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 8.575 N, where k = 8.9875517923 × 10⁹ N·m²/C². The force is repulsive if the charges have the same sign and attractive if opposite. | F = k |q1 q2| / r^2; k = 1/(4 π ε_0) | newton_second_law | Compute the Coulomb force between two point charges. |
5,784 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges 2.8490e-04 C and -2.3126e-04 C separated by 1.24 m | Two point charges q1 = 2.8490e-04 C and q2 = -2.3126e-04 C are separated by distance r = 1.24 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 384.8 N, where k = 8.9875517923 × 10⁹ N·m²/C². The force is repulsive if the charges have the same sign and attractive if opposite. | F = k |q1 q2| / r^2; k = 1/(4 π ε_0) | newton_second_law | Compute the Coulomb force between two point charges. |
5,785 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges 9.2792e-04 C and 8.4093e-04 C separated by 0.3119 m | Two point charges q1 = 9.2792e-04 C and q2 = 8.4093e-04 C are separated by distance r = 0.3119 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 7.2096e+04 N, where k = 8.9875517923 × 10⁹ N·m²/C². The force is repulsive if the charges have the same sign and attractive if opposite. | F = k |q1 q2| / r^2; k = 1/(4 π ε_0) | newton_second_law | Compute the Coulomb force between two point charges. |
5,786 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges 7.6259e-04 C and -8.0590e-04 C separated by 1.652 m | Two point charges q1 = 7.6259e-04 C and q2 = -8.0590e-04 C are separated by distance r = 1.652 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 2024 N, where k = 8.9875517923 × 10⁹ N·m²/C². The force is repulsive if the charges have the same sign and attractive if opposite. | F = k |q1 q2| / r^2; k = 1/(4 π ε_0) | newton_second_law | Compute the Coulomb force between two point charges. |
5,787 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges -5.4217e-04 C and -9.5452e-04 C separated by 0.1914 m | Two point charges q1 = -5.4217e-04 C and q2 = -9.5452e-04 C are separated by distance r = 0.1914 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 1.2691e+05 N, where k = 8.9875517923 × 10⁹ N·m²/C². The force is repulsive if the charges have the same sign and attractive if opposite. | F = k |q1 q2| / r^2; k = 1/(4 π ε_0) | newton_second_law | Compute the Coulomb force between two point charges. |
5,788 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges 8.0974e-04 C and -9.6588e-05 C separated by 1.692 m | Two point charges q1 = 8.0974e-04 C and q2 = -9.6588e-05 C are separated by distance r = 1.692 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 245.4 N, where k = 8.9875517923 × 10⁹ N·m²/C². The force is repulsive if the charges have the same sign and attractive if opposite. | F = k |q1 q2| / r^2; k = 1/(4 π ε_0) | newton_second_law | Compute the Coulomb force between two point charges. |
5,789 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges -2.4278e-04 C and -8.9199e-04 C separated by 1.836 m | Two point charges q1 = -2.4278e-04 C and q2 = -8.9199e-04 C are separated by distance r = 1.836 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 577.4 N, where k = 8.9875517923 × 10⁹ N·m²/C². The force is repulsive if the charges have the same sign and attractive if opposite. | F = k |q1 q2| / r^2; k = 1/(4 π ε_0) | newton_second_law | Compute the Coulomb force between two point charges. |
5,790 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges 1.0828e-04 C and -6.7149e-04 C separated by 0.876 m | Two point charges q1 = 1.0828e-04 C and q2 = -6.7149e-04 C are separated by distance r = 0.876 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 851.5 N, where k = 8.9875517923 × 10⁹ N·m²/C². The force is repulsive if the charges have the same sign and attractive if opposite. | F = k |q1 q2| / r^2; k = 1/(4 π ε_0) | newton_second_law | Compute the Coulomb force between two point charges. |
5,791 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges 4.4672e-04 C and -1.0127e-04 C separated by 0.1732 m | Two point charges q1 = 4.4672e-04 C and q2 = -1.0127e-04 C are separated by distance r = 0.1732 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 1.3557e+04 N, where k = 8.9875517923 × 10⁹ N·m²/C². The force is repulsive if the charges have the same sign and attractive if opposite. | F = k |q1 q2| / r^2; k = 1/(4 π ε_0) | newton_second_law | Compute the Coulomb force between two point charges. |
5,792 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges 4.4309e-04 C and 8.5074e-04 C separated by 1.504 m | Two point charges q1 = 4.4309e-04 C and q2 = 8.5074e-04 C are separated by distance r = 1.504 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 1498 N, where k = 8.9875517923 × 10⁹ N·m²/C². The force is repulsive if the charges have the same sign and attractive if opposite. | F = k |q1 q2| / r^2; k = 1/(4 π ε_0) | newton_second_law | Compute the Coulomb force between two point charges. |
5,793 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges -5.4172e-04 C and 2.0592e-04 C separated by 1.35 m | Two point charges q1 = -5.4172e-04 C and q2 = 2.0592e-04 C are separated by distance r = 1.35 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 550.2 N, where k = 8.9875517923 × 10⁹ N·m²/C². The force is repulsive if the charges have the same sign and attractive if opposite. | F = k |q1 q2| / r^2; k = 1/(4 π ε_0) | newton_second_law | Compute the Coulomb force between two point charges. |
5,794 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges 7.8980e-04 C and 3.2276e-04 C separated by 1.003 m | Two point charges q1 = 7.8980e-04 C and q2 = 3.2276e-04 C are separated by distance r = 1.003 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 2277 N, where k = 8.9875517923 × 10⁹ N·m²/C². The force is repulsive if the charges have the same sign and attractive if opposite. | F = k |q1 q2| / r^2; k = 1/(4 π ε_0) | newton_second_law | Compute the Coulomb force between two point charges. |
5,795 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges 8.3838e-04 C and -3.7359e-04 C separated by 1.41 m | Two point charges q1 = 8.3838e-04 C and q2 = -3.7359e-04 C are separated by distance r = 1.41 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 1416 N, where k = 8.9875517923 × 10⁹ N·m²/C². The force is repulsive if the charges have the same sign and attractive if opposite. | F = k |q1 q2| / r^2; k = 1/(4 π ε_0) | newton_second_law | Compute the Coulomb force between two point charges. |
5,796 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges 1.6921e-04 C and 2.0792e-04 C separated by 0.6353 m | Two point charges q1 = 1.6921e-04 C and q2 = 2.0792e-04 C are separated by distance r = 0.6353 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 783.5 N, where k = 8.9875517923 × 10⁹ N·m²/C². The force is repulsive if the charges have the same sign and attractive if opposite. | F = k |q1 q2| / r^2; k = 1/(4 π ε_0) | newton_second_law | Compute the Coulomb force between two point charges. |
5,797 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges 2.7487e-04 C and 8.9855e-04 C separated by 0.7651 m | Two point charges q1 = 2.7487e-04 C and q2 = 8.9855e-04 C are separated by distance r = 0.7651 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 3792 N, where k = 8.9875517923 × 10⁹ N·m²/C². The force is repulsive if the charges have the same sign and attractive if opposite. | F = k |q1 q2| / r^2; k = 1/(4 π ε_0) | newton_second_law | Compute the Coulomb force between two point charges. |
5,798 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges 9.6069e-04 C and -6.4583e-04 C separated by 0.1387 m | Two point charges q1 = 9.6069e-04 C and q2 = -6.4583e-04 C are separated by distance r = 0.1387 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 2.8968e+05 N, where k = 8.9875517923 × 10⁹ N·m²/C². The force is repulsive if the charges have the same sign and attractive if opposite. | F = k |q1 q2| / r^2; k = 1/(4 π ε_0) | newton_second_law | Compute the Coulomb force between two point charges. |
5,799 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges -3.8948e-04 C and 3.6016e-04 C separated by 0.05078 m | Two point charges q1 = -3.8948e-04 C and q2 = 3.6016e-04 C are separated by distance r = 0.05078 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 4.8886e+05 N, where k = 8.9875517923 × 10⁹ N·m²/C². The force is repulsive if the charges have the same sign and attractive if opposite. | F = k |q1 q2| / r^2; k = 1/(4 π ε_0) | newton_second_law | Compute the Coulomb force between two point charges. |
5,800 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges 7.2445e-04 C and 9.0371e-05 C separated by 0.5173 m | Two point charges q1 = 7.2445e-04 C and q2 = 9.0371e-05 C are separated by distance r = 0.5173 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 2199 N, where k = 8.9875517923 × 10⁹ N·m²/C². The force is repulsive if the charges have the same sign and attractive if opposite. | F = k |q1 q2| / r^2; k = 1/(4 π ε_0) | newton_second_law | Compute the Coulomb force between two point charges. |
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