A-level Physics (Advancing Physics)/Forces and Power/Worked Solutions

1. I hit a ball of mass 5g with a cue on a billiards table with a force of 20N. If friction opposes me with a force of 14.2N, what is the resultant acceleration of the ball away from the cue?

Resultant force = 20 - 14.2 = 5.8N

F = ma

5.8 = (5 x 10⁻³)a = 1160ms⁻²

2. A 10g ball rolls down a 1.2m slope, and leaves it with a velocity of 4ms⁻¹. How much work is done by friction?

g.p.e. at top of slope = mgh = 10 x 10⁻³ x 9.81 x 1.2 = 0.117J

k.e. at bottom of slope = ½mv² = 0.5 x 10 x 10⁻³ x 4² = 0.08J

Assuming the remainder of the g.p.e. becomes heat / sound due to friction:

work done by friction = 0.117 - 0.08 = 0.037J.

3. An electric train is powered on a 30kV power supply, where the current is 100A. The train is travelling at 90 kmh⁻¹. What is the net force exerted on it in a forwards direction?

P = IV = Fv

90 kmh⁻¹ = 0.025 km⁻¹ = 25 ms⁻¹

100 x 30 x 10³ = 25F

F = 120000N