Question

An object of mass 0.5 kg at rest started to fall from a height of 180 cm from the surface of earth calculate it's momentum when it reaches the earth's surface

Answer 1

Solution:

Given:

$$m=0.5 kg$$

$$h = 180 cm =1.8 m$$

Initial potential energy of the object is:

$$E_p=m*g*h$$

Kinetic energy at the surface:

$$E_k=\frac{mv^2}{2}$$

According to the law of conservation of energy (assuming no air resistance):

$$E_p = E_k$$

So,

$$mgh=\frac{mv^2}{2}$$

Solving for v:

$$v=\sqrt{2gh}$$

Definition of momentum:

$$p=mv$$

So,

$$p= m*v = m\sqrt{2gh}$$

Calculating:

$$p= 0.5\sqrt{2*9.8*1.8}\approx 2.97 \frac{kg*m}{s}$$

Answer:

$$p \approx 2.97 \frac{kg*m}{s}$$