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