physics question

Question

A child decides to sled down a 12 m tall hill. They reach the bottom with a speed of 14 m/s. What percentage of their initial mechanical energy was lost due to friction?

a) 17%

or

b) 9%

Answer 1

potential energy at the top = force * distance. Force = mass * acceleration

In this case, acceleration is from gravity, so it is 9.8 m/sec^2

We are given the distance (12m), so:

PE = m * 9.8 * 12

At the bottom, the potential energy has been converted to kinetic (or lost in friction)

KE = 1/2 * m * v^2

We are given v = 14m/sec

KE = 196 * m/2

To find the energy lost, we would subtract the KE at the end from the PE at the start. However, this requires that we know the mass of of the child + sled.

BUT--we are only asked about the percentage loss...

To get this, we can divide KE by PE:

(196 * m/2 ) / (m * 9.8 * 12)

196 / (2*9.8*12) = 0.83333

83% remaining means 17% was lost