# 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 = ½mv^{2} = 0.5 x 10 x 10^{−3} x 4^{2} = 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 10^{3} = 25F

F = 120000N