F.4 PHYSICS--M3

1. Pontetial energy of shell when it hits the target
= 25g x 30 J = 7500 J
where g is the acceleration due to gravity, taken to be 10 m/s2

By conservation of energy,
kinetic energy of shell after firing = kinetic energy when hitting target + potential energy when hitting target
i.e. (1/2).(25)u^2 = 8000 + 7500
where u is the initial speed of the shell
solve for u gives u = 35.2 m/s

2. The use of a counterweight could in an elevator could reduce the force required to lift the elevator-car. The gain in potential energy of the elevator car when it goes up is partly provided by the loss in potential energy of the counterweight when it goes down. Thus minimizing the energy needed to drive the elevator-car up.