0.3 Gravity and mechanical energy  (Page 6/9)

Consider the $1\mathrm{kg}$ suitcase on the cupboard that was discussed earlier. When the suitcase falls, it will gain velocity (fall faster), until it reaches the ground with a maximum velocity. The suitcase will not have any kinetic energy when it is on top of the cupboard because it is not moving. Once it starts to fall it will gain kinetic energy, because it gains velocity. Its kinetic energy will increase until it is a maximum when the suitcase reaches the ground.

Checking units

According to the equation for kinetic energy, the unit should be $\mathrm{kg}·m{}^2·s{}^{-2}$ . We can prove that this unit is equal to the joule, the unit for energy.

We can do the same to prove that the unit for potential energy is equal to the joule:

Kinetic energy

1. Describe the relationship between an object's kinetic energy and its:
   1. mass and
   2. velocity
2. A stone with a mass of $100g$ is thrown up into the air. It has an initial velocity of $3m·s{}^{-1}$ . Calculate its kinetic energy
   1. as it leaves the thrower's hand.
   2. when it reaches its turning point.
3. A car with a mass of $700\mathrm{kg}$ is travelling at a constant velocity of $100\mathrm{km}·\mathrm{hr}{}^{-1}$ . Calculate the kinetic energy of the car.
   

Mechanical energy

Mechanical energy, $U$ , is simply the sum of gravitational potential energy ( $PE$ ) and the kinetic energy ( $KE$ ). Mechanical energy is defined as: