Question

A. A mass of 5kg is on too of a building of height 10m. Calculate its potential energy.
B. The mass then falls at a speed of 8m/s in 4 secs, find its KE and momentum p. What is the force and impulse the mass transfers to the ground?
C. What is the work done by gravity if the mass falls a distance 2 meters. If the mass falls for 11 seconds, what is the energy expended by this force?

Answer 1

A. The potential energy:

$$E_P=mgh=5\cdot9.8\cdot10=490 \text{ J}.$$

B. The kinetic energy (when the velocity was 8 m/s):

$$E_K=\frac{1}{2}mv^2=160\text{ J}.$$

The momentum:

$$p=mv=40\text{ kg-m/s}.$$

The force:

$$F=\frac{\Delta p}{\Delta t}=\frac{40}{4}=10\text{ N}.$$

The impulse;

$$J=\Delta p=p-0=40\text{ kg-m/s}.$$

C. The work done by gravity:

$$W=mgh=98\text{ J}.$$

The height required to fall within 11 s:

$$h=gt^2/2.$$

The energy expended by the force of gravity:

$$E=Fh=mgh=mg^2t^2/2=29052.1\text{ J}.$$