Question

A block on a ramp slides down a 6.28 m long ramp. The ramp has an angle of inclination of 38°. If the block starts from rest and the amount of energy lost due to friction along the ramp is 21.6m J, where m is the mass of the block, use energy concepts to determine how fast the block is going at the bottom of the ramp. 

Answer 1

Using energy conservation

KE at bottom = initial pE - frictional loss

$\frac{1}{2} \times m v^2 = mg\times(Hsin 38 - h)$

$\frac{1}{2} \times m v^2 = m \times 9.8 \times 6.28 sin 38 - 21.6$

$v=\sqrt{2 (9.8 \times 6.28sin 38 -21.6)}$

$v = 5.708 m/s$