An 8.74-kg block slides with an initial speed of 1.52 m/s down a ramp inclined at an angle of 27.0° with the horizontal. The coefficient of kinetic friction between the block and the ramp is 0.64. Use energy conservation to find the distance the block slides before coming to rest.

Answer 1

The friction force opposing motion is
Ff = M*g*cos27*Uk = 49.4 Newtons

Let X be the distance it travels down the ramp before it stops. When it stops,

(Work done against friction) = (Potential energy loss)+ (Kinetic energy loss)

49.4*X = (1/2)M*(1.52)^2 + M*g*sin27*X

Solve for X