Question

A 4 kg mass compresses a spring by 60 cm at the bottom of a ramp. The mass then glides through a horizontal plane for 10 m before going up a ramp and stopping there. The planar road has a coefficient of friction of 0.2, but the ramp is frictionless. How high up the ramp does the mass reach?

Answer 1

Assume that $k=15N/cm=1500N/m$. So,

$\frac{k\cdot(\Delta x)^2}{2}=A_{fr}+mgh;$

$\frac{k\cdot(\Delta x)^2}{2}=\mu mgl+mgh;$

$h=\frac{k\cdot(\Delta x)^2}{2mg}-\mu l=\frac{1500\cdot(0.6)^2}{2\cdot 4\cdot 9.81}-0.2\cdot10=4.88m$