Question

A 3.25-kg block is sent up a ramp inclined at an angle theta = 37.5degree from the horizontal. It is given an initial velocity v_0 = 15.0 m/s up the ramp. Between the block and the ramp, the coefficient of kinetic friction is mu _k = 0.460 and the coefficient of static friction is mu _s = 0.817. How far up the ramp (in the direction along the ramp) does the block go before it comes to a stop?

Answer 1

mg*d* sin theta = 1/2*mv^2 - mu_k*m*g*costheta *d

mu_k*m*g*costheta *d = 1/2*mv^2 - mg*d*sintheta

mu_k*g*costheta *d = 1/2 * v^2 - gd sintheta

0.460 * 9.8 * cos37.5 * d = 1/2 *(15)^2 - 9.8 * sin37.5 * d

3.576 d = 112.5 - 5.966d

d = 11.75 m