A block of mass 5 kg starting from rest pulled up on a smooth incline plane making an angle of 30° with horizontal with an affective acceleration of 1 ms⁻². The power delivered by the pulling force at t=10 s from the start is ___________ W.
[use g=10 ms⁻² ]
(calculate the nearest integer value)

Solution

Physics sir · 3 steps

Find the pulling force from Newton's second law along the incline, then multiply by the speed at 10 s.

1. Force along incline. Along the smooth incline, only the pull F acts up the slope and only mg sin 30° acts down it. Their difference gives the acceleration.

   F - mg sin 30° = ma ⇒ F = 5 × 1 + 5 × 10 × 1/2 = 30 N

2. Speed at 10 s. The block starts from rest with constant acceleration, so v = at = 1 × 10 = 10 m s⁻¹, directed up the incline along F.
3. So. Instantaneous power is P = Fv = 30 × 10 = 300 W. The answer is 300.

The common slip: 50. Taking the pulling force as the net force ma = 5 N and leaving out mg sin 30° gives 50 W, not 300 W.

The idea to keep. Instantaneous power is P = Fv, where F is the force you are asked about, not the net force. On an incline, the pull must cover ma plus mg sin θ.

Answer from the NTA final answer key. Solution by PrepWiser.