Question

How do you think the energy at the top of the ramp will compare with the energy at the bottom of the ramp? Why do you think this?

Answer 1

We are asked to compare the energy of a mass at the top of a ramp with the energy at the bottom:

The energy at the top is the gravitational potential energy and is given by:

`U=mgh`

Where:

`\begin{gathered} m=\text{ mass} \\ g=\text{ acceleration of gravity} \\ h=\text{ height} \end{gathered}`

The energy at the bottom is kinetic energy and is given by:

`K=(1)/(2)mv^2`

Where:

`v=\text{ velocity}`

Due to the principle of conservation of energy, the energy at the top is equal to the energy at the bottom is no energy is lost. Therefore, we have:

`U=K`

Or:

`mgh=(1)/(2)mv^2`