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 |
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501 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 35.5 m, speed 17.29 m/s | An object moves in a circle of radius 35.5 m at constant speed 17.29 m/s. The centripetal acceleration has magnitude a_c = v² / r = 8.42 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. |
502 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 5.847 m, speed 1.813 m/s | An object moves in a circle of radius 5.847 m at constant speed 1.813 m/s. The centripetal acceleration has magnitude a_c = v² / r = 0.5624 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. |
503 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 16.31 m, speed 32.25 m/s | An object moves in a circle of radius 16.31 m at constant speed 32.25 m/s. The centripetal acceleration has magnitude a_c = v² / r = 63.79 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. |
504 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 30.94 m, speed 33.45 m/s | An object moves in a circle of radius 30.94 m at constant speed 33.45 m/s. The centripetal acceleration has magnitude a_c = v² / r = 36.16 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. |
505 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 46 m, speed 4.437 m/s | An object moves in a circle of radius 46 m at constant speed 4.437 m/s. The centripetal acceleration has magnitude a_c = v² / r = 0.428 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. |
506 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 42.24 m, speed 10.49 m/s | An object moves in a circle of radius 42.24 m at constant speed 10.49 m/s. The centripetal acceleration has magnitude a_c = v² / r = 2.605 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. |
507 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 29.48 m, speed 21.43 m/s | An object moves in a circle of radius 29.48 m at constant speed 21.43 m/s. The centripetal acceleration has magnitude a_c = v² / r = 15.58 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. |
508 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 19.85 m, speed 13.1 m/s | An object moves in a circle of radius 19.85 m at constant speed 13.1 m/s. The centripetal acceleration has magnitude a_c = v² / r = 8.647 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. |
509 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 17.04 m, speed 13.99 m/s | An object moves in a circle of radius 17.04 m at constant speed 13.99 m/s. The centripetal acceleration has magnitude a_c = v² / r = 11.48 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. |
510 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 8.49 m, speed 20.91 m/s | An object moves in a circle of radius 8.49 m at constant speed 20.91 m/s. The centripetal acceleration has magnitude a_c = v² / r = 51.49 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. |
511 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 5.79 m, speed 20.89 m/s | An object moves in a circle of radius 5.79 m at constant speed 20.89 m/s. The centripetal acceleration has magnitude a_c = v² / r = 75.36 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. |
512 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 45.31 m, speed 14.63 m/s | An object moves in a circle of radius 45.31 m at constant speed 14.63 m/s. The centripetal acceleration has magnitude a_c = v² / r = 4.721 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. |
513 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 36.4 m, speed 32.94 m/s | An object moves in a circle of radius 36.4 m at constant speed 32.94 m/s. The centripetal acceleration has magnitude a_c = v² / r = 29.81 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. |
514 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 40.77 m, speed 10.21 m/s | An object moves in a circle of radius 40.77 m at constant speed 10.21 m/s. The centripetal acceleration has magnitude a_c = v² / r = 2.559 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. |
515 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 7.408 m, speed 8.694 m/s | An object moves in a circle of radius 7.408 m at constant speed 8.694 m/s. The centripetal acceleration has magnitude a_c = v² / r = 10.2 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. |
516 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 30.16 m, speed 30.65 m/s | An object moves in a circle of radius 30.16 m at constant speed 30.65 m/s. The centripetal acceleration has magnitude a_c = v² / r = 31.15 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. |
517 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 32.81 m, speed 7.909 m/s | An object moves in a circle of radius 32.81 m at constant speed 7.909 m/s. The centripetal acceleration has magnitude a_c = v² / r = 1.906 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. |
518 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 38.67 m, speed 20.27 m/s | An object moves in a circle of radius 38.67 m at constant speed 20.27 m/s. The centripetal acceleration has magnitude a_c = v² / r = 10.63 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. |
519 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 37.75 m, speed 30.64 m/s | An object moves in a circle of radius 37.75 m at constant speed 30.64 m/s. The centripetal acceleration has magnitude a_c = v² / r = 24.86 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. |
520 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 22.5 m, speed 37.04 m/s | An object moves in a circle of radius 22.5 m at constant speed 37.04 m/s. The centripetal acceleration has magnitude a_c = v² / r = 60.98 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. |
521 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 28.27 m, speed 25.78 m/s | An object moves in a circle of radius 28.27 m at constant speed 25.78 m/s. The centripetal acceleration has magnitude a_c = v² / r = 23.5 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. |
522 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 31.26 m, speed 34.71 m/s | An object moves in a circle of radius 31.26 m at constant speed 34.71 m/s. The centripetal acceleration has magnitude a_c = v² / r = 38.53 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. |
523 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 31.4 m, speed 6.887 m/s | An object moves in a circle of radius 31.4 m at constant speed 6.887 m/s. The centripetal acceleration has magnitude a_c = v² / r = 1.511 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. |
524 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 3.507 m, speed 18.25 m/s | An object moves in a circle of radius 3.507 m at constant speed 18.25 m/s. The centripetal acceleration has magnitude a_c = v² / r = 94.92 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. |
525 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 15.21 m, speed 11.71 m/s | An object moves in a circle of radius 15.21 m at constant speed 11.71 m/s. The centripetal acceleration has magnitude a_c = v² / r = 9.018 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. |
526 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 2.903 m, speed 20.79 m/s | An object moves in a circle of radius 2.903 m at constant speed 20.79 m/s. The centripetal acceleration has magnitude a_c = v² / r = 148.8 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. |
527 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 15.59 m, speed 18.62 m/s | An object moves in a circle of radius 15.59 m at constant speed 18.62 m/s. The centripetal acceleration has magnitude a_c = v² / r = 22.25 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. |
528 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 2.939 m, speed 33.44 m/s | An object moves in a circle of radius 2.939 m at constant speed 33.44 m/s. The centripetal acceleration has magnitude a_c = v² / r = 380.4 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. |
529 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 3.929 m, speed 34.71 m/s | An object moves in a circle of radius 3.929 m at constant speed 34.71 m/s. The centripetal acceleration has magnitude a_c = v² / r = 306.6 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. |
530 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 42.78 m, speed 24.99 m/s | An object moves in a circle of radius 42.78 m at constant speed 24.99 m/s. The centripetal acceleration has magnitude a_c = v² / r = 14.59 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. |
531 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 25.4 m, speed 19.05 m/s | An object moves in a circle of radius 25.4 m at constant speed 19.05 m/s. The centripetal acceleration has magnitude a_c = v² / r = 14.28 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. |
532 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 27.76 m, speed 31.88 m/s | An object moves in a circle of radius 27.76 m at constant speed 31.88 m/s. The centripetal acceleration has magnitude a_c = v² / r = 36.61 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. |
533 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 44.8 m, speed 18.54 m/s | An object moves in a circle of radius 44.8 m at constant speed 18.54 m/s. The centripetal acceleration has magnitude a_c = v² / r = 7.672 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. |
534 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 40.51 m, speed 26.42 m/s | An object moves in a circle of radius 40.51 m at constant speed 26.42 m/s. The centripetal acceleration has magnitude a_c = v² / r = 17.23 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. |
535 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 16.14 m, speed 19.55 m/s | An object moves in a circle of radius 16.14 m at constant speed 19.55 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. |
536 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 7.628 m, speed 3.413 m/s | An object moves in a circle of radius 7.628 m at constant speed 3.413 m/s. The centripetal acceleration has magnitude a_c = v² / r = 1.527 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. |
537 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 5.265 m, speed 36.07 m/s | An object moves in a circle of radius 5.265 m at constant speed 36.07 m/s. The centripetal acceleration has magnitude a_c = v² / r = 247.1 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. |
538 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 17.24 m, speed 28.86 m/s | An object moves in a circle of radius 17.24 m at constant speed 28.86 m/s. The centripetal acceleration has magnitude a_c = v² / r = 48.31 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. |
539 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 25.28 m, speed 7.73 m/s | An object moves in a circle of radius 25.28 m at constant speed 7.73 m/s. The centripetal acceleration has magnitude a_c = v² / r = 2.364 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. |
540 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 12.46 m, speed 18.07 m/s | An object moves in a circle of radius 12.46 m at constant speed 18.07 m/s. The centripetal acceleration has magnitude a_c = v² / r = 26.21 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. |
541 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 22.03 m, speed 21.39 m/s | An object moves in a circle of radius 22.03 m at constant speed 21.39 m/s. The centripetal acceleration has magnitude a_c = v² / r = 20.77 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. |
542 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 8.021 m, speed 15.54 m/s | An object moves in a circle of radius 8.021 m at constant speed 15.54 m/s. The centripetal acceleration has magnitude a_c = v² / r = 30.11 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. |
543 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 14.22 m, speed 16.94 m/s | An object moves in a circle of radius 14.22 m at constant speed 16.94 m/s. The centripetal acceleration has magnitude a_c = v² / r = 20.19 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. |
544 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 16.98 m, speed 24.32 m/s | An object moves in a circle of radius 16.98 m at constant speed 24.32 m/s. The centripetal acceleration has magnitude a_c = v² / r = 34.82 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. |
545 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 39.48 m, speed 26.24 m/s | An object moves in a circle of radius 39.48 m at constant speed 26.24 m/s. The centripetal acceleration has magnitude a_c = v² / r = 17.45 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. |
546 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 3.389 m, speed 4.686 m/s | An object moves in a circle of radius 3.389 m at constant speed 4.686 m/s. The centripetal acceleration has magnitude a_c = v² / r = 6.479 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. |
547 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 33.95 m, speed 12.08 m/s | An object moves in a circle of radius 33.95 m at constant speed 12.08 m/s. The centripetal acceleration has magnitude a_c = v² / r = 4.299 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. |
548 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 36.21 m, speed 26.61 m/s | An object moves in a circle of radius 36.21 m at constant speed 26.61 m/s. The centripetal acceleration has magnitude a_c = v² / r = 19.55 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. |
549 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 45.33 m, speed 35.06 m/s | An object moves in a circle of radius 45.33 m at constant speed 35.06 m/s. The centripetal acceleration has magnitude a_c = v² / r = 27.12 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. |
550 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 16.73 m, speed 23.73 m/s | An object moves in a circle of radius 16.73 m at constant speed 23.73 m/s. The centripetal acceleration has magnitude a_c = v² / r = 33.64 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. |
551 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 7.157 m, speed 14.64 m/s | An object moves in a circle of radius 7.157 m at constant speed 14.64 m/s. The centripetal acceleration has magnitude a_c = v² / r = 29.96 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. |
552 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 48.39 m, speed 28.24 m/s | An object moves in a circle of radius 48.39 m at constant speed 28.24 m/s. The centripetal acceleration has magnitude a_c = v² / r = 16.48 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. |
553 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 19.66 m, speed 24.21 m/s | An object moves in a circle of radius 19.66 m at constant speed 24.21 m/s. The centripetal acceleration has magnitude a_c = v² / r = 29.81 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. |
554 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 46.91 m, speed 13.07 m/s | An object moves in a circle of radius 46.91 m at constant speed 13.07 m/s. The centripetal acceleration has magnitude a_c = v² / r = 3.644 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. |
555 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 18.9 m, speed 31.87 m/s | An object moves in a circle of radius 18.9 m at constant speed 31.87 m/s. The centripetal acceleration has magnitude a_c = v² / r = 53.77 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. |
556 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges -6.7045e-04 C and -6.4638e-04 C separated by 0.8526 m | Two point charges q1 = -6.7045e-04 C and q2 = -6.4638e-04 C are separated by distance r = 0.8526 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 5358 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. |
557 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges 1.9212e-05 C and 1.8108e-04 C separated by 0.4362 m | Two point charges q1 = 1.9212e-05 C and q2 = 1.8108e-04 C are separated by distance r = 0.4362 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 164.3 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. |
558 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges 1.9281e-04 C and -1.5579e-04 C separated by 0.5986 m | Two point charges q1 = 1.9281e-04 C and q2 = -1.5579e-04 C are separated by distance r = 0.5986 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 753.4 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. |
559 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges -5.0818e-04 C and -6.6227e-04 C separated by 1.754 m | Two point charges q1 = -5.0818e-04 C and q2 = -6.6227e-04 C are separated by distance r = 1.754 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 983.2 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. |
560 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges -5.9765e-04 C and -1.6308e-04 C separated by 1.664 m | Two point charges q1 = -5.9765e-04 C and q2 = -1.6308e-04 C are separated by distance r = 1.664 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 316.2 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. |
561 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges -7.2146e-04 C and -4.1145e-04 C separated by 1.356 m | Two point charges q1 = -7.2146e-04 C and q2 = -4.1145e-04 C are separated by distance r = 1.356 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 1451 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. |
562 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges -9.6962e-04 C and 7.5264e-04 C separated by 1.57 m | Two point charges q1 = -9.6962e-04 C and q2 = 7.5264e-04 C are separated by distance r = 1.57 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 2662 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. |
563 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges -5.3448e-04 C and 9.6563e-04 C separated by 1.571 m | Two point charges q1 = -5.3448e-04 C and q2 = 9.6563e-04 C are separated by distance r = 1.571 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 1880 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. |
564 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges -3.6847e-04 C and 4.6222e-04 C separated by 0.5707 m | Two point charges q1 = -3.6847e-04 C and q2 = 4.6222e-04 C are separated by distance r = 0.5707 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 4699 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. |
565 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges 5.0340e-04 C and 9.6630e-04 C separated by 1.636 m | Two point charges q1 = 5.0340e-04 C and q2 = 9.6630e-04 C are separated by distance r = 1.636 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 1634 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. |
566 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges -8.7313e-04 C and -6.4154e-04 C separated by 1.749 m | Two point charges q1 = -8.7313e-04 C and q2 = -6.4154e-04 C are separated by distance r = 1.749 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 1645 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. |
567 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges -7.1169e-04 C and -2.8578e-04 C separated by 1.529 m | Two point charges q1 = -7.1169e-04 C and q2 = -2.8578e-04 C are separated by distance r = 1.529 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 782.3 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. |
568 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges 4.4987e-04 C and -8.3122e-04 C separated by 0.1925 m | Two point charges q1 = 4.4987e-04 C and q2 = -8.3122e-04 C are separated by distance r = 0.1925 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 9.0685e+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. |
569 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges -8.1689e-04 C and 9.3054e-04 C separated by 0.8356 m | Two point charges q1 = -8.1689e-04 C and q2 = 9.3054e-04 C are separated by distance r = 0.8356 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 9784 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. |
570 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges 5.0251e-04 C and -3.8678e-04 C separated by 0.1724 m | Two point charges q1 = 5.0251e-04 C and q2 = -3.8678e-04 C are separated by distance r = 0.1724 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 5.8776e+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. |
571 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges -2.9159e-05 C and -8.3934e-04 C separated by 1.303 m | Two point charges q1 = -2.9159e-05 C and q2 = -8.3934e-04 C are separated by distance r = 1.303 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 129.5 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. |
572 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges -1.3846e-04 C and 9.1748e-04 C separated by 0.9502 m | Two point charges q1 = -1.3846e-04 C and q2 = 9.1748e-04 C are separated by distance r = 0.9502 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 1265 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. |
573 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges -7.5908e-04 C and 4.4915e-04 C separated by 0.02045 m | Two point charges q1 = -7.5908e-04 C and q2 = 4.4915e-04 C are separated by distance r = 0.02045 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 7.3273e+06 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. |
574 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges -1.9985e-05 C and -8.3513e-04 C separated by 1.102 m | Two point charges q1 = -1.9985e-05 C and q2 = -8.3513e-04 C are separated by distance r = 1.102 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 123.5 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. |
575 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges 1.1208e-04 C and 2.3840e-04 C separated by 0.2525 m | Two point charges q1 = 1.1208e-04 C and q2 = 2.3840e-04 C are separated by distance r = 0.2525 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 3767 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. |
576 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges -4.2041e-04 C and 6.3744e-05 C separated by 1.675 m | Two point charges q1 = -4.2041e-04 C and q2 = 6.3744e-05 C are separated by distance r = 1.675 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 85.85 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. |
577 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges 5.9714e-04 C and -6.3232e-04 C separated by 1.154 m | Two point charges q1 = 5.9714e-04 C and q2 = -6.3232e-04 C are separated by distance r = 1.154 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 2547 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. |
578 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges -2.9198e-04 C and -6.1519e-04 C separated by 0.4887 m | Two point charges q1 = -2.9198e-04 C and q2 = -6.1519e-04 C are separated by distance r = 0.4887 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 6759 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. |
579 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges 1.8813e-04 C and -5.2396e-04 C separated by 0.7276 m | Two point charges q1 = 1.8813e-04 C and q2 = -5.2396e-04 C are separated by distance r = 0.7276 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 1673 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. |
580 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges -3.9106e-04 C and 4.4491e-05 C separated by 0.7799 m | Two point charges q1 = -3.9106e-04 C and q2 = 4.4491e-05 C are separated by distance r = 0.7799 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 257.1 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. |
581 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges 2.5440e-04 C and -3.5774e-04 C separated by 0.1444 m | Two point charges q1 = 2.5440e-04 C and q2 = -3.5774e-04 C are separated by distance r = 0.1444 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 3.9203e+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. |
582 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges -7.3321e-04 C and -7.7173e-04 C separated by 1.473 m | Two point charges q1 = -7.3321e-04 C and q2 = -7.7173e-04 C are separated by distance r = 1.473 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 2344 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. |
583 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges 1.3428e-04 C and 5.4647e-04 C separated by 1.629 m | Two point charges q1 = 1.3428e-04 C and q2 = 5.4647e-04 C are separated by distance r = 1.629 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 248.6 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. |
584 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges -8.3055e-04 C and 9.8084e-04 C separated by 0.9623 m | Two point charges q1 = -8.3055e-04 C and q2 = 9.8084e-04 C are separated by distance r = 0.9623 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 7907 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. |
585 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges -8.1169e-04 C and -7.1633e-04 C separated by 1.888 m | Two point charges q1 = -8.1169e-04 C and q2 = -7.1633e-04 C are separated by distance r = 1.888 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 1466 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. |
586 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges -2.9415e-04 C and -7.9132e-04 C separated by 1.773 m | Two point charges q1 = -2.9415e-04 C and q2 = -7.9132e-04 C are separated by distance r = 1.773 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 665.7 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. |
587 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges 9.3344e-04 C and 9.8913e-04 C separated by 1.091 m | Two point charges q1 = 9.3344e-04 C and q2 = 9.8913e-04 C are separated by distance r = 1.091 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 6976 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. |
588 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges 3.7584e-05 C and -2.8682e-04 C separated by 1.726 m | Two point charges q1 = 3.7584e-05 C and q2 = -2.8682e-04 C are separated by distance r = 1.726 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 32.54 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. |
589 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges -8.6593e-04 C and 2.7394e-04 C separated by 1.601 m | Two point charges q1 = -8.6593e-04 C and q2 = 2.7394e-04 C are separated by distance r = 1.601 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 832.1 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. |
590 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges 8.8960e-04 C and 8.9474e-04 C separated by 0.7794 m | Two point charges q1 = 8.8960e-04 C and q2 = 8.9474e-04 C are separated by distance r = 0.7794 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 1.1776e+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. |
591 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges -4.9671e-04 C and 3.6798e-04 C separated by 1.597 m | Two point charges q1 = -4.9671e-04 C and q2 = 3.6798e-04 C are separated by distance r = 1.597 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 644.4 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. |
592 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges 8.0135e-04 C and 7.9848e-05 C separated by 1.209 m | Two point charges q1 = 8.0135e-04 C and q2 = 7.9848e-05 C are separated by distance r = 1.209 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 393.5 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. |
593 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges -5.4593e-04 C and 1.0350e-04 C separated by 0.6626 m | Two point charges q1 = -5.4593e-04 C and q2 = 1.0350e-04 C are separated by distance r = 0.6626 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 1157 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. |
594 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges 3.0719e-04 C and 1.6748e-04 C separated by 0.8934 m | Two point charges q1 = 3.0719e-04 C and q2 = 1.6748e-04 C are separated by distance r = 0.8934 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 579.3 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. |
595 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges 4.3313e-05 C and 6.1524e-04 C separated by 0.8755 m | Two point charges q1 = 4.3313e-05 C and q2 = 6.1524e-04 C are separated by distance r = 0.8755 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 312.4 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. |
596 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges -7.5966e-05 C and 3.6395e-04 C separated by 1.604 m | Two point charges q1 = -7.5966e-05 C and q2 = 3.6395e-04 C are separated by distance r = 1.604 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 96.56 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. |
597 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges -9.5284e-04 C and -8.4882e-04 C separated by 1.359 m | Two point charges q1 = -9.5284e-04 C and q2 = -8.4882e-04 C are separated by distance r = 1.359 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 3934 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. |
598 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges 3.5764e-05 C and -2.3676e-04 C separated by 1.294 m | Two point charges q1 = 3.5764e-05 C and q2 = -2.3676e-04 C are separated by distance r = 1.294 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 45.46 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. |
599 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges 3.8347e-04 C and -6.0549e-04 C separated by 1.361 m | Two point charges q1 = 3.8347e-04 C and q2 = -6.0549e-04 C are separated by distance r = 1.361 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 1126 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. |
600 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges 3.7264e-04 C and -5.7435e-04 C separated by 1.064 m | Two point charges q1 = 3.7264e-04 C and q2 = -5.7435e-04 C are separated by distance r = 1.064 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 1700 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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