Question

A metal ball with a mass of 0.028 kg is dropped from rest at a height of 1.0 meters above the ground. Assuming the energy in the ball is conserved, how much kinetic energy will the ball have when it is 0.5 meters above the ground?

Answer 1

0.137 J

Step-by-step explanation:

The conservation of energy states that the mechanical energy of the system is conserved:

`E=U+K=const.`

where

`U=mgh` is the potential energy, where m is the mass, g is the gravitational acceleration and h the height above the ground

`K=(1)/(2)mv^2` is the kinetic energy, where m is the mass and v is the speed

- When the ball is dropped, the kinetic energy is zero (because it starts from rest). So, the mechanical energy is just potential energy:

`E=U=mgh=(0.028 kg)(9.8 m/s^2)(1.0 m)=0.274 J`

- When it is h=0.5 m above the ground, part of the energy is now kinetic energy. The potential energy now is

`U=mgh=(0.028 kg)(9.8 m/s^2)(0.5 m)=0.137 J`

And since the mechanical energy is conserved, we can write

`E=U+K\\K=E-U=0.274 J-0.137 J=0.137 J`

So, the kinetic energy is 0.137 J.