# A mass, m = 1 kg initially at rest at height, h = 2 m slides to the bottom of a 45 deg ramp....

## Question:

A mass, m = 1 kg initially at rest at height, h = 2 m slides to the bottom of a 45° ramp. There is no friction between the mass and the ramp. At the bottom of the ramp the speed of the mass is 4 m/s. How much heat was generated by the friction as the mass slides down the ramp?

## The energy lost due to friction:

According to energy conservation, energy neither be created nor be destroyed. Therefore, if there is no loss of energy, then the energy of the system will remain constant. If it is decreasing, that means some of the energy has been lost due to some resistance.

Given Data

Mass of the block (m) = 1 kg

Height of the ramp (h) = 2 m

The angle of the ramp {eq}\theta = 45^\circ {/eq}

The speed at the bottom (v) = 4 m/s

Now, the initial energy of the object

{eq}E_{1} = mgh \\ E_{1} = 1*9.8*2 \\ E_{1} = 19.6 \ J {/eq}

When the object reaches the bottom, then potential energy would be converted into the kinetic energy,

therefore energy at the bottom would be

{eq}E_{2} = \dfrac{1}{2}mv^{2} \\ E_{2} = \dfrac{1}{2}(1)(4)^{2} \\ E_{2} = 8 \ J {/eq}

Now, the energy lost in the friction would be

{eq}E_{l} = E_{1} -E_{2} \\ E_{l} = 19.6 - 8 \\ E_{l} = 11.6 \ J {/eq}