In scenario 1, the box sliding down a ramp, the energy approach yields -196.2 J, and the forces approach calculates 9.82 J. For scenario 2, the box thrown upward, the energy approach results in -24.5 J, and the forces approach gives 120.07 J. In scenario 3, the box dropped from height, the energy approach indicates -196.2 J, and the forces approach computes 196.2 J. Energy approaches consider changes in potential or kinetic energy, while forces approaches involve the force applied and distance traveled.
Scenario 1: Box sliding down a frictionless ramp
Energy Approach
Initial potential energy: 2 kg * 9.81 m/s^2 * 10 m = 196.2 J
Final potential energy: 0 J
Change in potential energy: -196.2 J
Work done by gravity: -196.2 J
Forces Approach
Force of gravity: 2 kg * 9.81 m/s^2 = 19.62 N
Angle of the ramp: 15 degrees
Component of force parallel to the ramp: 19.62 N * sin(15 degrees) = 4.91 N
Distance traveled: d = vt = (1 s) * (2 m/s) = 2 m
Work done by gravity: 4.91 N * 2 m = 9.82 J
Scenario 2: Box thrown upward
Energy Approach
Initial kinetic energy: 0.5 * 2 kg * (3.5 m/s)^2 = 24.5 J
Final kinetic energy: 0 J
Change in kinetic energy: -24.5 J
Work done by gravity: -24.5 J
Forces Approach
Force of gravity: 2 kg * 9.81 m/s^2 = 19.62 N
Displacement: d = h = (v^2 - u^2) / (2a) = (0^2 - (3.5 m/s)^2) / (2 * -9.81 m/s^2) = 6.08 m
Work done by gravity: 19.62 N * 6.08 m = 120.07 J
Scenario 3: Box dropped from an initial height
Energy Approach
Initial potential energy: 2 kg * 9.81 m/s^2 * 10 m = 196.2 J
Final potential energy: 0 J
Change in potential energy: -196.2 J
Work done by gravity: -196.2 J
Forces Approach
Force of gravity: 2 kg * 9.81 m/s^2 = 19.62 N
Displacement: d = h = 10 m
Work done by gravity: 19.62 N * 10 m = 196.2 J