Question

A steel ball (78 kg) is dropped from the top of a 370m tall building. It lands in a
snowbank, creating a crater 1.1m deep. The speed of the ball is 35m/s just before
it hits the snowbank.

(a) Calculate the work done by the snow in bringing the ball to rest.

(b) Calculate the magnitude of the force exerted on the ball by the snow (assuming
the force is constant).

(c) Calculate the work done by air drag before the collision.

Answer 1

Work done by the snow in bringing the ball to rest = Change in kinetic energy of ball in the snow

So, Work done by the snow in bringing the ball to rest = 0.5*78*(35^2-0^2) = 47775J

Also, magnitude of the force exerted on the ball by the snow*deepness of crater it creates = Work done by the snow in bringing the ball to rest

So, magnitude of the force exerted on the ball by the snow = 47775/1.1 = 43431.8N

work done by air drag before the collision = Change in energy of ball in the air

So, work done by air drag before the collision = 78*9.81*370 - 0.5*78*35^2 = 235341.6 J