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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2,001 | physics | mechanics | newton_second_law | 3 | worked_example | Newton's second law: mass 37.35 kg, acceleration 0.3737 m/s² | A net force acting on a mass of 37.35 kg produces an acceleration of 0.3737 m/s². By Newton's second law, F_net = m a = 37.35 × 0.3737 = 13.96 N. Direction of F_net is the same as the direction of the acceleration. This relation defines the inertial mass and is the foundation of classical dynamics. | F_net = m a | kinematics_1d | Compute net force from mass and acceleration using Newton's second law. |
2,002 | physics | mechanics | newton_second_law | 3 | worked_example | Newton's second law: mass 34.37 kg, acceleration 5.395 m/s² | A net force acting on a mass of 34.37 kg produces an acceleration of 5.395 m/s². By Newton's second law, F_net = m a = 34.37 × 5.395 = 185.4 N. Direction of F_net is the same as the direction of the acceleration. This relation defines the inertial mass and is the foundation of classical dynamics. | F_net = m a | kinematics_1d | Compute net force from mass and acceleration using Newton's second law. |
2,003 | physics | mechanics | newton_second_law | 3 | worked_example | Newton's second law: mass 15.47 kg, acceleration 14.94 m/s² | A net force acting on a mass of 15.47 kg produces an acceleration of 14.94 m/s². By Newton's second law, F_net = m a = 15.47 × 14.94 = 231.1 N. Direction of F_net is the same as the direction of the acceleration. This relation defines the inertial mass and is the foundation of classical dynamics. | F_net = m a | kinematics_1d | Compute net force from mass and acceleration using Newton's second law. |
2,004 | physics | mechanics | newton_second_law | 3 | worked_example | Newton's second law: mass 48.94 kg, acceleration 4.211 m/s² | A net force acting on a mass of 48.94 kg produces an acceleration of 4.211 m/s². By Newton's second law, F_net = m a = 48.94 × 4.211 = 206.1 N. Direction of F_net is the same as the direction of the acceleration. This relation defines the inertial mass and is the foundation of classical dynamics. | F_net = m a | kinematics_1d | Compute net force from mass and acceleration using Newton's second law. |
2,005 | physics | mechanics | newton_second_law | 3 | worked_example | Newton's second law: mass 3.569 kg, acceleration 3.939 m/s² | A net force acting on a mass of 3.569 kg produces an acceleration of 3.939 m/s². By Newton's second law, F_net = m a = 3.569 × 3.939 = 14.06 N. Direction of F_net is the same as the direction of the acceleration. This relation defines the inertial mass and is the foundation of classical dynamics. | F_net = m a | kinematics_1d | Compute net force from mass and acceleration using Newton's second law. |
2,006 | physics | mechanics | newton_second_law | 3 | worked_example | Newton's second law: mass 19.66 kg, acceleration 15 m/s² | A net force acting on a mass of 19.66 kg produces an acceleration of 15 m/s². By Newton's second law, F_net = m a = 19.66 × 15 = 295 N. Direction of F_net is the same as the direction of the acceleration. This relation defines the inertial mass and is the foundation of classical dynamics. | F_net = m a | kinematics_1d | Compute net force from mass and acceleration using Newton's second law. |
2,007 | physics | mechanics | newton_second_law | 3 | worked_example | Newton's second law: mass 49.52 kg, acceleration 14.17 m/s² | A net force acting on a mass of 49.52 kg produces an acceleration of 14.17 m/s². By Newton's second law, F_net = m a = 49.52 × 14.17 = 701.6 N. Direction of F_net is the same as the direction of the acceleration. This relation defines the inertial mass and is the foundation of classical dynamics. | F_net = m a | kinematics_1d | Compute net force from mass and acceleration using Newton's second law. |
2,008 | physics | mechanics | newton_second_law | 3 | worked_example | Newton's second law: mass 47.48 kg, acceleration 3.461 m/s² | A net force acting on a mass of 47.48 kg produces an acceleration of 3.461 m/s². By Newton's second law, F_net = m a = 47.48 × 3.461 = 164.3 N. Direction of F_net is the same as the direction of the acceleration. This relation defines the inertial mass and is the foundation of classical dynamics. | F_net = m a | kinematics_1d | Compute net force from mass and acceleration using Newton's second law. |
2,009 | physics | mechanics | newton_second_law | 3 | worked_example | Newton's second law: mass 17.42 kg, acceleration 5.953 m/s² | A net force acting on a mass of 17.42 kg produces an acceleration of 5.953 m/s². By Newton's second law, F_net = m a = 17.42 × 5.953 = 103.7 N. Direction of F_net is the same as the direction of the acceleration. This relation defines the inertial mass and is the foundation of classical dynamics. | F_net = m a | kinematics_1d | Compute net force from mass and acceleration using Newton's second law. |
2,010 | physics | mechanics | newton_second_law | 3 | worked_example | Newton's second law: mass 7.294 kg, acceleration 10.98 m/s² | A net force acting on a mass of 7.294 kg produces an acceleration of 10.98 m/s². By Newton's second law, F_net = m a = 7.294 × 10.98 = 80.06 N. Direction of F_net is the same as the direction of the acceleration. This relation defines the inertial mass and is the foundation of classical dynamics. | F_net = m a | kinematics_1d | Compute net force from mass and acceleration using Newton's second law. |
2,011 | physics | mechanics | newton_second_law | 3 | worked_example | Newton's second law: mass 26.28 kg, acceleration 10.2 m/s² | A net force acting on a mass of 26.28 kg produces an acceleration of 10.2 m/s². By Newton's second law, F_net = m a = 26.28 × 10.2 = 268.1 N. Direction of F_net is the same as the direction of the acceleration. This relation defines the inertial mass and is the foundation of classical dynamics. | F_net = m a | kinematics_1d | Compute net force from mass and acceleration using Newton's second law. |
2,012 | physics | mechanics | newton_second_law | 3 | worked_example | Newton's second law: mass 43.7 kg, acceleration 10.33 m/s² | A net force acting on a mass of 43.7 kg produces an acceleration of 10.33 m/s². By Newton's second law, F_net = m a = 43.7 × 10.33 = 451.4 N. Direction of F_net is the same as the direction of the acceleration. This relation defines the inertial mass and is the foundation of classical dynamics. | F_net = m a | kinematics_1d | Compute net force from mass and acceleration using Newton's second law. |
2,013 | physics | mechanics | newton_second_law | 3 | worked_example | Newton's second law: mass 21.16 kg, acceleration 8.636 m/s² | A net force acting on a mass of 21.16 kg produces an acceleration of 8.636 m/s². By Newton's second law, F_net = m a = 21.16 × 8.636 = 182.7 N. Direction of F_net is the same as the direction of the acceleration. This relation defines the inertial mass and is the foundation of classical dynamics. | F_net = m a | kinematics_1d | Compute net force from mass and acceleration using Newton's second law. |
2,014 | physics | mechanics | newton_second_law | 3 | worked_example | Newton's second law: mass 21.61 kg, acceleration 4.755 m/s² | A net force acting on a mass of 21.61 kg produces an acceleration of 4.755 m/s². By Newton's second law, F_net = m a = 21.61 × 4.755 = 102.7 N. Direction of F_net is the same as the direction of the acceleration. This relation defines the inertial mass and is the foundation of classical dynamics. | F_net = m a | kinematics_1d | Compute net force from mass and acceleration using Newton's second law. |
2,015 | physics | mechanics | newton_second_law | 3 | worked_example | Newton's second law: mass 30.47 kg, acceleration 6.793 m/s² | A net force acting on a mass of 30.47 kg produces an acceleration of 6.793 m/s². By Newton's second law, F_net = m a = 30.47 × 6.793 = 206.9 N. Direction of F_net is the same as the direction of the acceleration. This relation defines the inertial mass and is the foundation of classical dynamics. | F_net = m a | kinematics_1d | Compute net force from mass and acceleration using Newton's second law. |
2,016 | physics | mechanics | newton_second_law | 3 | worked_example | Newton's second law: mass 7.023 kg, acceleration 9.822 m/s² | A net force acting on a mass of 7.023 kg produces an acceleration of 9.822 m/s². By Newton's second law, F_net = m a = 7.023 × 9.822 = 68.98 N. Direction of F_net is the same as the direction of the acceleration. This relation defines the inertial mass and is the foundation of classical dynamics. | F_net = m a | kinematics_1d | Compute net force from mass and acceleration using Newton's second law. |
2,017 | physics | mechanics | newton_second_law | 3 | worked_example | Newton's second law: mass 29.26 kg, acceleration 10.29 m/s² | A net force acting on a mass of 29.26 kg produces an acceleration of 10.29 m/s². By Newton's second law, F_net = m a = 29.26 × 10.29 = 301.2 N. Direction of F_net is the same as the direction of the acceleration. This relation defines the inertial mass and is the foundation of classical dynamics. | F_net = m a | kinematics_1d | Compute net force from mass and acceleration using Newton's second law. |
2,018 | physics | mechanics | newton_second_law | 3 | worked_example | Newton's second law: mass 10.51 kg, acceleration 2.158 m/s² | A net force acting on a mass of 10.51 kg produces an acceleration of 2.158 m/s². By Newton's second law, F_net = m a = 10.51 × 2.158 = 22.69 N. Direction of F_net is the same as the direction of the acceleration. This relation defines the inertial mass and is the foundation of classical dynamics. | F_net = m a | kinematics_1d | Compute net force from mass and acceleration using Newton's second law. |
2,019 | physics | mechanics | newton_second_law | 3 | worked_example | Newton's second law: mass 34.58 kg, acceleration 13.49 m/s² | A net force acting on a mass of 34.58 kg produces an acceleration of 13.49 m/s². By Newton's second law, F_net = m a = 34.58 × 13.49 = 466.5 N. Direction of F_net is the same as the direction of the acceleration. This relation defines the inertial mass and is the foundation of classical dynamics. | F_net = m a | kinematics_1d | Compute net force from mass and acceleration using Newton's second law. |
2,020 | physics | mechanics | newton_second_law | 3 | worked_example | Newton's second law: mass 45.52 kg, acceleration 6.508 m/s² | A net force acting on a mass of 45.52 kg produces an acceleration of 6.508 m/s². By Newton's second law, F_net = m a = 45.52 × 6.508 = 296.3 N. Direction of F_net is the same as the direction of the acceleration. This relation defines the inertial mass and is the foundation of classical dynamics. | F_net = m a | kinematics_1d | Compute net force from mass and acceleration using Newton's second law. |
2,021 | physics | mechanics | newton_second_law | 3 | worked_example | Newton's second law: mass 45.5 kg, acceleration 11.57 m/s² | A net force acting on a mass of 45.5 kg produces an acceleration of 11.57 m/s². By Newton's second law, F_net = m a = 45.5 × 11.57 = 526.6 N. Direction of F_net is the same as the direction of the acceleration. This relation defines the inertial mass and is the foundation of classical dynamics. | F_net = m a | kinematics_1d | Compute net force from mass and acceleration using Newton's second law. |
2,022 | physics | mechanics | newton_second_law | 3 | worked_example | Newton's second law: mass 32.98 kg, acceleration 8.516 m/s² | A net force acting on a mass of 32.98 kg produces an acceleration of 8.516 m/s². By Newton's second law, F_net = m a = 32.98 × 8.516 = 280.9 N. Direction of F_net is the same as the direction of the acceleration. This relation defines the inertial mass and is the foundation of classical dynamics. | F_net = m a | kinematics_1d | Compute net force from mass and acceleration using Newton's second law. |
2,023 | physics | mechanics | newton_second_law | 3 | worked_example | Newton's second law: mass 8.323 kg, acceleration 1.11 m/s² | A net force acting on a mass of 8.323 kg produces an acceleration of 1.11 m/s². By Newton's second law, F_net = m a = 8.323 × 1.11 = 9.243 N. Direction of F_net is the same as the direction of the acceleration. This relation defines the inertial mass and is the foundation of classical dynamics. | F_net = m a | kinematics_1d | Compute net force from mass and acceleration using Newton's second law. |
2,024 | physics | mechanics | newton_second_law | 3 | worked_example | Newton's second law: mass 26.88 kg, acceleration 10.82 m/s² | A net force acting on a mass of 26.88 kg produces an acceleration of 10.82 m/s². By Newton's second law, F_net = m a = 26.88 × 10.82 = 290.8 N. Direction of F_net is the same as the direction of the acceleration. This relation defines the inertial mass and is the foundation of classical dynamics. | F_net = m a | kinematics_1d | Compute net force from mass and acceleration using Newton's second law. |
2,025 | physics | mechanics | newton_second_law | 3 | worked_example | Newton's second law: mass 9.615 kg, acceleration 12.61 m/s² | A net force acting on a mass of 9.615 kg produces an acceleration of 12.61 m/s². By Newton's second law, F_net = m a = 9.615 × 12.61 = 121.2 N. Direction of F_net is the same as the direction of the acceleration. This relation defines the inertial mass and is the foundation of classical dynamics. | F_net = m a | kinematics_1d | Compute net force from mass and acceleration using Newton's second law. |
2,026 | physics | mechanics | newton_second_law | 3 | worked_example | Newton's second law: mass 7.703 kg, acceleration 0.5393 m/s² | A net force acting on a mass of 7.703 kg produces an acceleration of 0.5393 m/s². By Newton's second law, F_net = m a = 7.703 × 0.5393 = 4.154 N. Direction of F_net is the same as the direction of the acceleration. This relation defines the inertial mass and is the foundation of classical dynamics. | F_net = m a | kinematics_1d | Compute net force from mass and acceleration using Newton's second law. |
2,027 | physics | mechanics | newton_second_law | 3 | worked_example | Newton's second law: mass 16.28 kg, acceleration 14.6 m/s² | A net force acting on a mass of 16.28 kg produces an acceleration of 14.6 m/s². By Newton's second law, F_net = m a = 16.28 × 14.6 = 237.6 N. Direction of F_net is the same as the direction of the acceleration. This relation defines the inertial mass and is the foundation of classical dynamics. | F_net = m a | kinematics_1d | Compute net force from mass and acceleration using Newton's second law. |
2,028 | physics | mechanics | newton_second_law | 3 | worked_example | Newton's second law: mass 48.08 kg, acceleration 4.62 m/s² | A net force acting on a mass of 48.08 kg produces an acceleration of 4.62 m/s². By Newton's second law, F_net = m a = 48.08 × 4.62 = 222.1 N. Direction of F_net is the same as the direction of the acceleration. This relation defines the inertial mass and is the foundation of classical dynamics. | F_net = m a | kinematics_1d | Compute net force from mass and acceleration using Newton's second law. |
2,029 | physics | mechanics | newton_second_law | 3 | worked_example | Newton's second law: mass 37.41 kg, acceleration 12.34 m/s² | A net force acting on a mass of 37.41 kg produces an acceleration of 12.34 m/s². By Newton's second law, F_net = m a = 37.41 × 12.34 = 461.7 N. Direction of F_net is the same as the direction of the acceleration. This relation defines the inertial mass and is the foundation of classical dynamics. | F_net = m a | kinematics_1d | Compute net force from mass and acceleration using Newton's second law. |
2,030 | physics | mechanics | newton_second_law | 3 | worked_example | Newton's second law: mass 32.02 kg, acceleration 11.1 m/s² | A net force acting on a mass of 32.02 kg produces an acceleration of 11.1 m/s². By Newton's second law, F_net = m a = 32.02 × 11.1 = 355.5 N. Direction of F_net is the same as the direction of the acceleration. This relation defines the inertial mass and is the foundation of classical dynamics. | F_net = m a | kinematics_1d | Compute net force from mass and acceleration using Newton's second law. |
2,031 | physics | mechanics | newton_second_law | 3 | worked_example | Newton's second law: mass 8.022 kg, acceleration 2.9 m/s² | A net force acting on a mass of 8.022 kg produces an acceleration of 2.9 m/s². By Newton's second law, F_net = m a = 8.022 × 2.9 = 23.27 N. Direction of F_net is the same as the direction of the acceleration. This relation defines the inertial mass and is the foundation of classical dynamics. | F_net = m a | kinematics_1d | Compute net force from mass and acceleration using Newton's second law. |
2,032 | physics | mechanics | newton_second_law | 3 | worked_example | Newton's second law: mass 7.012 kg, acceleration 0.4904 m/s² | A net force acting on a mass of 7.012 kg produces an acceleration of 0.4904 m/s². By Newton's second law, F_net = m a = 7.012 × 0.4904 = 3.438 N. Direction of F_net is the same as the direction of the acceleration. This relation defines the inertial mass and is the foundation of classical dynamics. | F_net = m a | kinematics_1d | Compute net force from mass and acceleration using Newton's second law. |
2,033 | physics | mechanics | newton_second_law | 3 | worked_example | Newton's second law: mass 49.3 kg, acceleration 9.293 m/s² | A net force acting on a mass of 49.3 kg produces an acceleration of 9.293 m/s². By Newton's second law, F_net = m a = 49.3 × 9.293 = 458.2 N. Direction of F_net is the same as the direction of the acceleration. This relation defines the inertial mass and is the foundation of classical dynamics. | F_net = m a | kinematics_1d | Compute net force from mass and acceleration using Newton's second law. |
2,034 | physics | mechanics | newton_second_law | 3 | worked_example | Newton's second law: mass 30.48 kg, acceleration 9.224 m/s² | A net force acting on a mass of 30.48 kg produces an acceleration of 9.224 m/s². By Newton's second law, F_net = m a = 30.48 × 9.224 = 281.1 N. Direction of F_net is the same as the direction of the acceleration. This relation defines the inertial mass and is the foundation of classical dynamics. | F_net = m a | kinematics_1d | Compute net force from mass and acceleration using Newton's second law. |
2,035 | physics | mechanics | newton_second_law | 3 | worked_example | Newton's second law: mass 30.02 kg, acceleration 3.541 m/s² | A net force acting on a mass of 30.02 kg produces an acceleration of 3.541 m/s². By Newton's second law, F_net = m a = 30.02 × 3.541 = 106.3 N. Direction of F_net is the same as the direction of the acceleration. This relation defines the inertial mass and is the foundation of classical dynamics. | F_net = m a | kinematics_1d | Compute net force from mass and acceleration using Newton's second law. |
2,036 | physics | mechanics | newton_second_law | 3 | worked_example | Newton's second law: mass 1.791 kg, acceleration 1.284 m/s² | A net force acting on a mass of 1.791 kg produces an acceleration of 1.284 m/s². By Newton's second law, F_net = m a = 1.791 × 1.284 = 2.3 N. Direction of F_net is the same as the direction of the acceleration. This relation defines the inertial mass and is the foundation of classical dynamics. | F_net = m a | kinematics_1d | Compute net force from mass and acceleration using Newton's second law. |
2,037 | physics | mechanics | newton_second_law | 3 | worked_example | Newton's second law: mass 39.1 kg, acceleration 2.098 m/s² | A net force acting on a mass of 39.1 kg produces an acceleration of 2.098 m/s². By Newton's second law, F_net = m a = 39.1 × 2.098 = 82.03 N. Direction of F_net is the same as the direction of the acceleration. This relation defines the inertial mass and is the foundation of classical dynamics. | F_net = m a | kinematics_1d | Compute net force from mass and acceleration using Newton's second law. |
2,038 | physics | mechanics | newton_second_law | 3 | worked_example | Newton's second law: mass 42.38 kg, acceleration 7.085 m/s² | A net force acting on a mass of 42.38 kg produces an acceleration of 7.085 m/s². By Newton's second law, F_net = m a = 42.38 × 7.085 = 300.3 N. Direction of F_net is the same as the direction of the acceleration. This relation defines the inertial mass and is the foundation of classical dynamics. | F_net = m a | kinematics_1d | Compute net force from mass and acceleration using Newton's second law. |
2,039 | physics | mechanics | newton_second_law | 3 | worked_example | Newton's second law: mass 32.65 kg, acceleration 2.841 m/s² | A net force acting on a mass of 32.65 kg produces an acceleration of 2.841 m/s². By Newton's second law, F_net = m a = 32.65 × 2.841 = 92.78 N. Direction of F_net is the same as the direction of the acceleration. This relation defines the inertial mass and is the foundation of classical dynamics. | F_net = m a | kinematics_1d | Compute net force from mass and acceleration using Newton's second law. |
2,040 | physics | mechanics | newton_second_law | 3 | worked_example | Newton's second law: mass 19.68 kg, acceleration 7.16 m/s² | A net force acting on a mass of 19.68 kg produces an acceleration of 7.16 m/s². By Newton's second law, F_net = m a = 19.68 × 7.16 = 140.9 N. Direction of F_net is the same as the direction of the acceleration. This relation defines the inertial mass and is the foundation of classical dynamics. | F_net = m a | kinematics_1d | Compute net force from mass and acceleration using Newton's second law. |
2,041 | physics | mechanics | newton_second_law | 3 | worked_example | Newton's second law: mass 8.607 kg, acceleration 3.471 m/s² | A net force acting on a mass of 8.607 kg produces an acceleration of 3.471 m/s². By Newton's second law, F_net = m a = 8.607 × 3.471 = 29.88 N. Direction of F_net is the same as the direction of the acceleration. This relation defines the inertial mass and is the foundation of classical dynamics. | F_net = m a | kinematics_1d | Compute net force from mass and acceleration using Newton's second law. |
2,042 | physics | mechanics | newton_second_law | 3 | worked_example | Newton's second law: mass 20.73 kg, acceleration 14.54 m/s² | A net force acting on a mass of 20.73 kg produces an acceleration of 14.54 m/s². By Newton's second law, F_net = m a = 20.73 × 14.54 = 301.2 N. Direction of F_net is the same as the direction of the acceleration. This relation defines the inertial mass and is the foundation of classical dynamics. | F_net = m a | kinematics_1d | Compute net force from mass and acceleration using Newton's second law. |
2,043 | physics | mechanics | newton_second_law | 3 | worked_example | Newton's second law: mass 46.31 kg, acceleration 14.26 m/s² | A net force acting on a mass of 46.31 kg produces an acceleration of 14.26 m/s². By Newton's second law, F_net = m a = 46.31 × 14.26 = 660.3 N. Direction of F_net is the same as the direction of the acceleration. This relation defines the inertial mass and is the foundation of classical dynamics. | F_net = m a | kinematics_1d | Compute net force from mass and acceleration using Newton's second law. |
2,044 | physics | mechanics | newton_second_law | 3 | worked_example | Newton's second law: mass 11.52 kg, acceleration 10.1 m/s² | A net force acting on a mass of 11.52 kg produces an acceleration of 10.1 m/s². By Newton's second law, F_net = m a = 11.52 × 10.1 = 116.3 N. Direction of F_net is the same as the direction of the acceleration. This relation defines the inertial mass and is the foundation of classical dynamics. | F_net = m a | kinematics_1d | Compute net force from mass and acceleration using Newton's second law. |
2,045 | physics | mechanics | newton_second_law | 3 | worked_example | Newton's second law: mass 10.54 kg, acceleration 3.148 m/s² | A net force acting on a mass of 10.54 kg produces an acceleration of 3.148 m/s². By Newton's second law, F_net = m a = 10.54 × 3.148 = 33.18 N. Direction of F_net is the same as the direction of the acceleration. This relation defines the inertial mass and is the foundation of classical dynamics. | F_net = m a | kinematics_1d | Compute net force from mass and acceleration using Newton's second law. |
2,046 | physics | mechanics | newton_second_law | 3 | worked_example | Newton's second law: mass 9.265 kg, acceleration 14.33 m/s² | A net force acting on a mass of 9.265 kg produces an acceleration of 14.33 m/s². By Newton's second law, F_net = m a = 9.265 × 14.33 = 132.7 N. Direction of F_net is the same as the direction of the acceleration. This relation defines the inertial mass and is the foundation of classical dynamics. | F_net = m a | kinematics_1d | Compute net force from mass and acceleration using Newton's second law. |
2,047 | physics | mechanics | newton_second_law | 3 | worked_example | Newton's second law: mass 22.24 kg, acceleration 9.294 m/s² | A net force acting on a mass of 22.24 kg produces an acceleration of 9.294 m/s². By Newton's second law, F_net = m a = 22.24 × 9.294 = 206.7 N. Direction of F_net is the same as the direction of the acceleration. This relation defines the inertial mass and is the foundation of classical dynamics. | F_net = m a | kinematics_1d | Compute net force from mass and acceleration using Newton's second law. |
2,048 | physics | mechanics | newton_second_law | 3 | worked_example | Newton's second law: mass 34.55 kg, acceleration 13.01 m/s² | A net force acting on a mass of 34.55 kg produces an acceleration of 13.01 m/s². By Newton's second law, F_net = m a = 34.55 × 13.01 = 449.7 N. Direction of F_net is the same as the direction of the acceleration. This relation defines the inertial mass and is the foundation of classical dynamics. | F_net = m a | kinematics_1d | Compute net force from mass and acceleration using Newton's second law. |
2,049 | physics | mechanics | newton_second_law | 3 | worked_example | Newton's second law: mass 44.44 kg, acceleration 6.471 m/s² | A net force acting on a mass of 44.44 kg produces an acceleration of 6.471 m/s². By Newton's second law, F_net = m a = 44.44 × 6.471 = 287.5 N. Direction of F_net is the same as the direction of the acceleration. This relation defines the inertial mass and is the foundation of classical dynamics. | F_net = m a | kinematics_1d | Compute net force from mass and acceleration using Newton's second law. |
2,050 | physics | mechanics | newton_second_law | 3 | worked_example | Newton's second law: mass 38.92 kg, acceleration 9.158 m/s² | A net force acting on a mass of 38.92 kg produces an acceleration of 9.158 m/s². By Newton's second law, F_net = m a = 38.92 × 9.158 = 356.5 N. Direction of F_net is the same as the direction of the acceleration. This relation defines the inertial mass and is the foundation of classical dynamics. | F_net = m a | kinematics_1d | Compute net force from mass and acceleration using Newton's second law. |
2,051 | physics | mechanics | newton_second_law | 3 | worked_example | Newton's second law: mass 41.3 kg, acceleration 10.83 m/s² | A net force acting on a mass of 41.3 kg produces an acceleration of 10.83 m/s². By Newton's second law, F_net = m a = 41.3 × 10.83 = 447.4 N. Direction of F_net is the same as the direction of the acceleration. This relation defines the inertial mass and is the foundation of classical dynamics. | F_net = m a | kinematics_1d | Compute net force from mass and acceleration using Newton's second law. |
2,052 | physics | mechanics | newton_second_law | 3 | worked_example | Newton's second law: mass 20.01 kg, acceleration 14.09 m/s² | A net force acting on a mass of 20.01 kg produces an acceleration of 14.09 m/s². By Newton's second law, F_net = m a = 20.01 × 14.09 = 282 N. Direction of F_net is the same as the direction of the acceleration. This relation defines the inertial mass and is the foundation of classical dynamics. | F_net = m a | kinematics_1d | Compute net force from mass and acceleration using Newton's second law. |
2,053 | physics | mechanics | newton_second_law | 3 | worked_example | Newton's second law: mass 28.81 kg, acceleration 8.089 m/s² | A net force acting on a mass of 28.81 kg produces an acceleration of 8.089 m/s². By Newton's second law, F_net = m a = 28.81 × 8.089 = 233 N. Direction of F_net is the same as the direction of the acceleration. This relation defines the inertial mass and is the foundation of classical dynamics. | F_net = m a | kinematics_1d | Compute net force from mass and acceleration using Newton's second law. |
2,054 | physics | mechanics | newton_second_law | 3 | worked_example | Newton's second law: mass 32.25 kg, acceleration 10.59 m/s² | A net force acting on a mass of 32.25 kg produces an acceleration of 10.59 m/s². By Newton's second law, F_net = m a = 32.25 × 10.59 = 341.6 N. Direction of F_net is the same as the direction of the acceleration. This relation defines the inertial mass and is the foundation of classical dynamics. | F_net = m a | kinematics_1d | Compute net force from mass and acceleration using Newton's second law. |
2,055 | physics | mechanics | newton_second_law | 3 | worked_example | Newton's second law: mass 2.406 kg, acceleration 1.729 m/s² | A net force acting on a mass of 2.406 kg produces an acceleration of 1.729 m/s². By Newton's second law, F_net = m a = 2.406 × 1.729 = 4.16 N. Direction of F_net is the same as the direction of the acceleration. This relation defines the inertial mass and is the foundation of classical dynamics. | F_net = m a | kinematics_1d | Compute net force from mass and acceleration using Newton's second law. |
2,056 | physics | mechanics | newton_second_law | 3 | worked_example | Newton's second law: mass 23.12 kg, acceleration 13.18 m/s² | A net force acting on a mass of 23.12 kg produces an acceleration of 13.18 m/s². By Newton's second law, F_net = m a = 23.12 × 13.18 = 304.6 N. Direction of F_net is the same as the direction of the acceleration. This relation defines the inertial mass and is the foundation of classical dynamics. | F_net = m a | kinematics_1d | Compute net force from mass and acceleration using Newton's second law. |
2,057 | physics | mechanics | newton_second_law | 3 | worked_example | Newton's second law: mass 43.95 kg, acceleration 3.761 m/s² | A net force acting on a mass of 43.95 kg produces an acceleration of 3.761 m/s². By Newton's second law, F_net = m a = 43.95 × 3.761 = 165.3 N. Direction of F_net is the same as the direction of the acceleration. This relation defines the inertial mass and is the foundation of classical dynamics. | F_net = m a | kinematics_1d | Compute net force from mass and acceleration using Newton's second law. |
2,058 | physics | mechanics | newton_second_law | 3 | worked_example | Newton's second law: mass 27.12 kg, acceleration 14.76 m/s² | A net force acting on a mass of 27.12 kg produces an acceleration of 14.76 m/s². By Newton's second law, F_net = m a = 27.12 × 14.76 = 400.3 N. Direction of F_net is the same as the direction of the acceleration. This relation defines the inertial mass and is the foundation of classical dynamics. | F_net = m a | kinematics_1d | Compute net force from mass and acceleration using Newton's second law. |
2,059 | physics | mechanics | newton_second_law | 3 | worked_example | Newton's second law: mass 2.443 kg, acceleration 5.872 m/s² | A net force acting on a mass of 2.443 kg produces an acceleration of 5.872 m/s². By Newton's second law, F_net = m a = 2.443 × 5.872 = 14.35 N. Direction of F_net is the same as the direction of the acceleration. This relation defines the inertial mass and is the foundation of classical dynamics. | F_net = m a | kinematics_1d | Compute net force from mass and acceleration using Newton's second law. |
2,060 | physics | mechanics | newton_second_law | 3 | worked_example | Newton's second law: mass 38.38 kg, acceleration 14.44 m/s² | A net force acting on a mass of 38.38 kg produces an acceleration of 14.44 m/s². By Newton's second law, F_net = m a = 38.38 × 14.44 = 554.2 N. Direction of F_net is the same as the direction of the acceleration. This relation defines the inertial mass and is the foundation of classical dynamics. | F_net = m a | kinematics_1d | Compute net force from mass and acceleration using Newton's second law. |
2,061 | physics | mechanics | newton_second_law | 3 | worked_example | Newton's second law: mass 9.898 kg, acceleration 6.649 m/s² | A net force acting on a mass of 9.898 kg produces an acceleration of 6.649 m/s². By Newton's second law, F_net = m a = 9.898 × 6.649 = 65.81 N. Direction of F_net is the same as the direction of the acceleration. This relation defines the inertial mass and is the foundation of classical dynamics. | F_net = m a | kinematics_1d | Compute net force from mass and acceleration using Newton's second law. |
2,062 | physics | mechanics | newton_second_law | 3 | worked_example | Newton's second law: mass 44.28 kg, acceleration 11.63 m/s² | A net force acting on a mass of 44.28 kg produces an acceleration of 11.63 m/s². By Newton's second law, F_net = m a = 44.28 × 11.63 = 514.9 N. Direction of F_net is the same as the direction of the acceleration. This relation defines the inertial mass and is the foundation of classical dynamics. | F_net = m a | kinematics_1d | Compute net force from mass and acceleration using Newton's second law. |
2,063 | physics | mechanics | newton_second_law | 3 | worked_example | Newton's second law: mass 14.65 kg, acceleration 2.581 m/s² | A net force acting on a mass of 14.65 kg produces an acceleration of 2.581 m/s². By Newton's second law, F_net = m a = 14.65 × 2.581 = 37.81 N. Direction of F_net is the same as the direction of the acceleration. This relation defines the inertial mass and is the foundation of classical dynamics. | F_net = m a | kinematics_1d | Compute net force from mass and acceleration using Newton's second law. |
2,064 | physics | mechanics | newton_second_law | 3 | worked_example | Newton's second law: mass 15.07 kg, acceleration 13.79 m/s² | A net force acting on a mass of 15.07 kg produces an acceleration of 13.79 m/s². By Newton's second law, F_net = m a = 15.07 × 13.79 = 207.9 N. Direction of F_net is the same as the direction of the acceleration. This relation defines the inertial mass and is the foundation of classical dynamics. | F_net = m a | kinematics_1d | Compute net force from mass and acceleration using Newton's second law. |
2,065 | physics | mechanics | newton_second_law | 3 | worked_example | Newton's second law: mass 34.65 kg, acceleration 13.56 m/s² | A net force acting on a mass of 34.65 kg produces an acceleration of 13.56 m/s². By Newton's second law, F_net = m a = 34.65 × 13.56 = 470.1 N. Direction of F_net is the same as the direction of the acceleration. This relation defines the inertial mass and is the foundation of classical dynamics. | F_net = m a | kinematics_1d | Compute net force from mass and acceleration using Newton's second law. |
2,066 | physics | mechanics | newton_second_law | 3 | worked_example | Newton's second law: mass 23.45 kg, acceleration 9.727 m/s² | A net force acting on a mass of 23.45 kg produces an acceleration of 9.727 m/s². By Newton's second law, F_net = m a = 23.45 × 9.727 = 228.1 N. Direction of F_net is the same as the direction of the acceleration. This relation defines the inertial mass and is the foundation of classical dynamics. | F_net = m a | kinematics_1d | Compute net force from mass and acceleration using Newton's second law. |
2,067 | physics | mechanics | newton_second_law | 3 | worked_example | Newton's second law: mass 4.977 kg, acceleration 7.56 m/s² | A net force acting on a mass of 4.977 kg produces an acceleration of 7.56 m/s². By Newton's second law, F_net = m a = 4.977 × 7.56 = 37.62 N. Direction of F_net is the same as the direction of the acceleration. This relation defines the inertial mass and is the foundation of classical dynamics. | F_net = m a | kinematics_1d | Compute net force from mass and acceleration using Newton's second law. |
2,068 | physics | mechanics | newton_second_law | 3 | worked_example | Newton's second law: mass 9.399 kg, acceleration 8.823 m/s² | A net force acting on a mass of 9.399 kg produces an acceleration of 8.823 m/s². By Newton's second law, F_net = m a = 9.399 × 8.823 = 82.93 N. Direction of F_net is the same as the direction of the acceleration. This relation defines the inertial mass and is the foundation of classical dynamics. | F_net = m a | kinematics_1d | Compute net force from mass and acceleration using Newton's second law. |
2,069 | physics | mechanics | newton_second_law | 3 | worked_example | Newton's second law: mass 44.77 kg, acceleration 8.241 m/s² | A net force acting on a mass of 44.77 kg produces an acceleration of 8.241 m/s². By Newton's second law, F_net = m a = 44.77 × 8.241 = 369 N. Direction of F_net is the same as the direction of the acceleration. This relation defines the inertial mass and is the foundation of classical dynamics. | F_net = m a | kinematics_1d | Compute net force from mass and acceleration using Newton's second law. |
2,070 | physics | mechanics | newton_second_law | 3 | worked_example | Newton's second law: mass 19.96 kg, acceleration 4.92 m/s² | A net force acting on a mass of 19.96 kg produces an acceleration of 4.92 m/s². By Newton's second law, F_net = m a = 19.96 × 4.92 = 98.18 N. Direction of F_net is the same as the direction of the acceleration. This relation defines the inertial mass and is the foundation of classical dynamics. | F_net = m a | kinematics_1d | Compute net force from mass and acceleration using Newton's second law. |
2,071 | physics | mechanics | newton_second_law | 3 | worked_example | Newton's second law: mass 1.733 kg, acceleration 6.86 m/s² | A net force acting on a mass of 1.733 kg produces an acceleration of 6.86 m/s². By Newton's second law, F_net = m a = 1.733 × 6.86 = 11.89 N. Direction of F_net is the same as the direction of the acceleration. This relation defines the inertial mass and is the foundation of classical dynamics. | F_net = m a | kinematics_1d | Compute net force from mass and acceleration using Newton's second law. |
2,072 | physics | mechanics | newton_second_law | 3 | worked_example | Newton's second law: mass 44.88 kg, acceleration 13.45 m/s² | A net force acting on a mass of 44.88 kg produces an acceleration of 13.45 m/s². By Newton's second law, F_net = m a = 44.88 × 13.45 = 603.6 N. Direction of F_net is the same as the direction of the acceleration. This relation defines the inertial mass and is the foundation of classical dynamics. | F_net = m a | kinematics_1d | Compute net force from mass and acceleration using Newton's second law. |
2,073 | physics | mechanics | newton_second_law | 3 | worked_example | Newton's second law: mass 44.19 kg, acceleration 1.444 m/s² | A net force acting on a mass of 44.19 kg produces an acceleration of 1.444 m/s². By Newton's second law, F_net = m a = 44.19 × 1.444 = 63.79 N. Direction of F_net is the same as the direction of the acceleration. This relation defines the inertial mass and is the foundation of classical dynamics. | F_net = m a | kinematics_1d | Compute net force from mass and acceleration using Newton's second law. |
2,074 | physics | mechanics | newton_second_law | 3 | worked_example | Newton's second law: mass 16.54 kg, acceleration 9.764 m/s² | A net force acting on a mass of 16.54 kg produces an acceleration of 9.764 m/s². By Newton's second law, F_net = m a = 16.54 × 9.764 = 161.5 N. Direction of F_net is the same as the direction of the acceleration. This relation defines the inertial mass and is the foundation of classical dynamics. | F_net = m a | kinematics_1d | Compute net force from mass and acceleration using Newton's second law. |
2,075 | physics | mechanics | newton_second_law | 3 | worked_example | Newton's second law: mass 35.72 kg, acceleration 2.544 m/s² | A net force acting on a mass of 35.72 kg produces an acceleration of 2.544 m/s². By Newton's second law, F_net = m a = 35.72 × 2.544 = 90.85 N. Direction of F_net is the same as the direction of the acceleration. This relation defines the inertial mass and is the foundation of classical dynamics. | F_net = m a | kinematics_1d | Compute net force from mass and acceleration using Newton's second law. |
2,076 | physics | mechanics | newton_second_law | 3 | worked_example | Newton's second law: mass 36.8 kg, acceleration 1.459 m/s² | A net force acting on a mass of 36.8 kg produces an acceleration of 1.459 m/s². By Newton's second law, F_net = m a = 36.8 × 1.459 = 53.68 N. Direction of F_net is the same as the direction of the acceleration. This relation defines the inertial mass and is the foundation of classical dynamics. | F_net = m a | kinematics_1d | Compute net force from mass and acceleration using Newton's second law. |
2,077 | physics | mechanics | newton_second_law | 3 | worked_example | Newton's second law: mass 35.46 kg, acceleration 9.548 m/s² | A net force acting on a mass of 35.46 kg produces an acceleration of 9.548 m/s². By Newton's second law, F_net = m a = 35.46 × 9.548 = 338.5 N. Direction of F_net is the same as the direction of the acceleration. This relation defines the inertial mass and is the foundation of classical dynamics. | F_net = m a | kinematics_1d | Compute net force from mass and acceleration using Newton's second law. |
2,078 | physics | mechanics | newton_second_law | 3 | worked_example | Newton's second law: mass 4.723 kg, acceleration 10.64 m/s² | A net force acting on a mass of 4.723 kg produces an acceleration of 10.64 m/s². By Newton's second law, F_net = m a = 4.723 × 10.64 = 50.24 N. Direction of F_net is the same as the direction of the acceleration. This relation defines the inertial mass and is the foundation of classical dynamics. | F_net = m a | kinematics_1d | Compute net force from mass and acceleration using Newton's second law. |
2,079 | physics | mechanics | newton_second_law | 3 | worked_example | Newton's second law: mass 36.48 kg, acceleration 14.63 m/s² | A net force acting on a mass of 36.48 kg produces an acceleration of 14.63 m/s². By Newton's second law, F_net = m a = 36.48 × 14.63 = 533.7 N. Direction of F_net is the same as the direction of the acceleration. This relation defines the inertial mass and is the foundation of classical dynamics. | F_net = m a | kinematics_1d | Compute net force from mass and acceleration using Newton's second law. |
2,080 | physics | mechanics | newton_second_law | 3 | worked_example | Newton's second law: mass 30.8 kg, acceleration 2.483 m/s² | A net force acting on a mass of 30.8 kg produces an acceleration of 2.483 m/s². By Newton's second law, F_net = m a = 30.8 × 2.483 = 76.46 N. Direction of F_net is the same as the direction of the acceleration. This relation defines the inertial mass and is the foundation of classical dynamics. | F_net = m a | kinematics_1d | Compute net force from mass and acceleration using Newton's second law. |
2,081 | physics | mechanics | newton_second_law | 3 | worked_example | Newton's second law: mass 27.74 kg, acceleration 0.7542 m/s² | A net force acting on a mass of 27.74 kg produces an acceleration of 0.7542 m/s². By Newton's second law, F_net = m a = 27.74 × 0.7542 = 20.92 N. Direction of F_net is the same as the direction of the acceleration. This relation defines the inertial mass and is the foundation of classical dynamics. | F_net = m a | kinematics_1d | Compute net force from mass and acceleration using Newton's second law. |
2,082 | physics | mechanics | newton_second_law | 3 | worked_example | Newton's second law: mass 8.959 kg, acceleration 5.094 m/s² | A net force acting on a mass of 8.959 kg produces an acceleration of 5.094 m/s². By Newton's second law, F_net = m a = 8.959 × 5.094 = 45.64 N. Direction of F_net is the same as the direction of the acceleration. This relation defines the inertial mass and is the foundation of classical dynamics. | F_net = m a | kinematics_1d | Compute net force from mass and acceleration using Newton's second law. |
2,083 | physics | mechanics | newton_second_law | 3 | worked_example | Newton's second law: mass 43.63 kg, acceleration 12.95 m/s² | A net force acting on a mass of 43.63 kg produces an acceleration of 12.95 m/s². By Newton's second law, F_net = m a = 43.63 × 12.95 = 565.2 N. Direction of F_net is the same as the direction of the acceleration. This relation defines the inertial mass and is the foundation of classical dynamics. | F_net = m a | kinematics_1d | Compute net force from mass and acceleration using Newton's second law. |
2,084 | physics | mechanics | newton_second_law | 3 | worked_example | Newton's second law: mass 8.525 kg, acceleration 2.255 m/s² | A net force acting on a mass of 8.525 kg produces an acceleration of 2.255 m/s². By Newton's second law, F_net = m a = 8.525 × 2.255 = 19.22 N. Direction of F_net is the same as the direction of the acceleration. This relation defines the inertial mass and is the foundation of classical dynamics. | F_net = m a | kinematics_1d | Compute net force from mass and acceleration using Newton's second law. |
2,085 | physics | mechanics | newton_second_law | 3 | worked_example | Newton's second law: mass 38.57 kg, acceleration 0.8645 m/s² | A net force acting on a mass of 38.57 kg produces an acceleration of 0.8645 m/s². By Newton's second law, F_net = m a = 38.57 × 0.8645 = 33.35 N. Direction of F_net is the same as the direction of the acceleration. This relation defines the inertial mass and is the foundation of classical dynamics. | F_net = m a | kinematics_1d | Compute net force from mass and acceleration using Newton's second law. |
2,086 | physics | mechanics | newton_second_law | 3 | worked_example | Newton's second law: mass 15.75 kg, acceleration 10.98 m/s² | A net force acting on a mass of 15.75 kg produces an acceleration of 10.98 m/s². By Newton's second law, F_net = m a = 15.75 × 10.98 = 172.9 N. Direction of F_net is the same as the direction of the acceleration. This relation defines the inertial mass and is the foundation of classical dynamics. | F_net = m a | kinematics_1d | Compute net force from mass and acceleration using Newton's second law. |
2,087 | physics | mechanics | newton_second_law | 3 | worked_example | Newton's second law: mass 48.07 kg, acceleration 4.403 m/s² | A net force acting on a mass of 48.07 kg produces an acceleration of 4.403 m/s². By Newton's second law, F_net = m a = 48.07 × 4.403 = 211.6 N. Direction of F_net is the same as the direction of the acceleration. This relation defines the inertial mass and is the foundation of classical dynamics. | F_net = m a | kinematics_1d | Compute net force from mass and acceleration using Newton's second law. |
2,088 | physics | mechanics | newton_second_law | 3 | worked_example | Newton's second law: mass 9.444 kg, acceleration 13.49 m/s² | A net force acting on a mass of 9.444 kg produces an acceleration of 13.49 m/s². By Newton's second law, F_net = m a = 9.444 × 13.49 = 127.4 N. Direction of F_net is the same as the direction of the acceleration. This relation defines the inertial mass and is the foundation of classical dynamics. | F_net = m a | kinematics_1d | Compute net force from mass and acceleration using Newton's second law. |
2,089 | physics | mechanics | newton_second_law | 3 | worked_example | Newton's second law: mass 48.04 kg, acceleration 0.1526 m/s² | A net force acting on a mass of 48.04 kg produces an acceleration of 0.1526 m/s². By Newton's second law, F_net = m a = 48.04 × 0.1526 = 7.333 N. Direction of F_net is the same as the direction of the acceleration. This relation defines the inertial mass and is the foundation of classical dynamics. | F_net = m a | kinematics_1d | Compute net force from mass and acceleration using Newton's second law. |
2,090 | physics | mechanics | newton_second_law | 3 | worked_example | Newton's second law: mass 38.39 kg, acceleration 0.2819 m/s² | A net force acting on a mass of 38.39 kg produces an acceleration of 0.2819 m/s². By Newton's second law, F_net = m a = 38.39 × 0.2819 = 10.82 N. Direction of F_net is the same as the direction of the acceleration. This relation defines the inertial mass and is the foundation of classical dynamics. | F_net = m a | kinematics_1d | Compute net force from mass and acceleration using Newton's second law. |
2,091 | physics | mechanics | newton_second_law | 3 | worked_example | Newton's second law: mass 25.13 kg, acceleration 7.53 m/s² | A net force acting on a mass of 25.13 kg produces an acceleration of 7.53 m/s². By Newton's second law, F_net = m a = 25.13 × 7.53 = 189.2 N. Direction of F_net is the same as the direction of the acceleration. This relation defines the inertial mass and is the foundation of classical dynamics. | F_net = m a | kinematics_1d | Compute net force from mass and acceleration using Newton's second law. |
2,092 | physics | mechanics | newton_second_law | 3 | worked_example | Newton's second law: mass 40.47 kg, acceleration 9.159 m/s² | A net force acting on a mass of 40.47 kg produces an acceleration of 9.159 m/s². By Newton's second law, F_net = m a = 40.47 × 9.159 = 370.7 N. Direction of F_net is the same as the direction of the acceleration. This relation defines the inertial mass and is the foundation of classical dynamics. | F_net = m a | kinematics_1d | Compute net force from mass and acceleration using Newton's second law. |
2,093 | physics | mechanics | mechanical_energy | 4 | worked_example | Conservation of mechanical energy: drop from height 9.067 m | An object of mass 9.971 kg is released from rest at height 9.067 m above a reference level. Taking gravitational potential energy as m g h and kinetic energy as (1/2) m v², conservation of mechanical energy (neglecting non-conservative work) yields (1/2) m v² = m g h, so v = sqrt(2 g h) = 13.34 m/s at the reference lev... | K + U = constant (conservative systems); U_g = m g h; K = (1/2) m v^2 | newton_second_law; work-energy theorem | Apply conservation of mechanical energy to free-fall motion. |
2,094 | physics | mechanics | mechanical_energy | 4 | worked_example | Conservation of mechanical energy: drop from height 18.42 m | An object of mass 13.26 kg is released from rest at height 18.42 m above a reference level. Taking gravitational potential energy as m g h and kinetic energy as (1/2) m v², conservation of mechanical energy (neglecting non-conservative work) yields (1/2) m v² = m g h, so v = sqrt(2 g h) = 19.01 m/s at the reference lev... | K + U = constant (conservative systems); U_g = m g h; K = (1/2) m v^2 | newton_second_law; work-energy theorem | Apply conservation of mechanical energy to free-fall motion. |
2,095 | physics | mechanics | mechanical_energy | 4 | worked_example | Conservation of mechanical energy: drop from height 24.25 m | An object of mass 8.949 kg is released from rest at height 24.25 m above a reference level. Taking gravitational potential energy as m g h and kinetic energy as (1/2) m v², conservation of mechanical energy (neglecting non-conservative work) yields (1/2) m v² = m g h, so v = sqrt(2 g h) = 21.81 m/s at the reference lev... | K + U = constant (conservative systems); U_g = m g h; K = (1/2) m v^2 | newton_second_law; work-energy theorem | Apply conservation of mechanical energy to free-fall motion. |
2,096 | physics | mechanics | mechanical_energy | 4 | worked_example | Conservation of mechanical energy: drop from height 35.35 m | An object of mass 0.3301 kg is released from rest at height 35.35 m above a reference level. Taking gravitational potential energy as m g h and kinetic energy as (1/2) m v², conservation of mechanical energy (neglecting non-conservative work) yields (1/2) m v² = m g h, so v = sqrt(2 g h) = 26.33 m/s at the reference le... | K + U = constant (conservative systems); U_g = m g h; K = (1/2) m v^2 | newton_second_law; work-energy theorem | Apply conservation of mechanical energy to free-fall motion. |
2,097 | physics | mechanics | mechanical_energy | 4 | worked_example | Conservation of mechanical energy: drop from height 25.33 m | An object of mass 5.707 kg is released from rest at height 25.33 m above a reference level. Taking gravitational potential energy as m g h and kinetic energy as (1/2) m v², conservation of mechanical energy (neglecting non-conservative work) yields (1/2) m v² = m g h, so v = sqrt(2 g h) = 22.29 m/s at the reference lev... | K + U = constant (conservative systems); U_g = m g h; K = (1/2) m v^2 | newton_second_law; work-energy theorem | Apply conservation of mechanical energy to free-fall motion. |
2,098 | physics | mechanics | mechanical_energy | 4 | worked_example | Conservation of mechanical energy: drop from height 8.702 m | An object of mass 16.44 kg is released from rest at height 8.702 m above a reference level. Taking gravitational potential energy as m g h and kinetic energy as (1/2) m v², conservation of mechanical energy (neglecting non-conservative work) yields (1/2) m v² = m g h, so v = sqrt(2 g h) = 13.06 m/s at the reference lev... | K + U = constant (conservative systems); U_g = m g h; K = (1/2) m v^2 | newton_second_law; work-energy theorem | Apply conservation of mechanical energy to free-fall motion. |
2,099 | physics | mechanics | mechanical_energy | 4 | worked_example | Conservation of mechanical energy: drop from height 2.675 m | An object of mass 3.86 kg is released from rest at height 2.675 m above a reference level. Taking gravitational potential energy as m g h and kinetic energy as (1/2) m v², conservation of mechanical energy (neglecting non-conservative work) yields (1/2) m v² = m g h, so v = sqrt(2 g h) = 7.243 m/s at the reference leve... | K + U = constant (conservative systems); U_g = m g h; K = (1/2) m v^2 | newton_second_law; work-energy theorem | Apply conservation of mechanical energy to free-fall motion. |
2,100 | physics | mechanics | mechanical_energy | 4 | worked_example | Conservation of mechanical energy: drop from height 6.242 m | An object of mass 7.111 kg is released from rest at height 6.242 m above a reference level. Taking gravitational potential energy as m g h and kinetic energy as (1/2) m v², conservation of mechanical energy (neglecting non-conservative work) yields (1/2) m v² = m g h, so v = sqrt(2 g h) = 11.06 m/s at the reference lev... | K + U = constant (conservative systems); U_g = m g h; K = (1/2) m v^2 | newton_second_law; work-energy theorem | Apply conservation of mechanical energy to free-fall motion. |
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