Answer to Question #80504 in Mechanics | Relativity for Ankit

Question

A crate of mass 30.0 kg is pulled by a force of 1800 N up an inclined plane which
makes an angle of 30º with the horizon. The coefficient of kinetic friction between the
plane and the crate is μk = 0.225. If the crates starts from rest, calculate its speed after it
has been pulled 15.0 m. Draw the free body diagram

Answer 1

Newton Second Low is:
mg + N + F + fk = ma
fk = µk*N = µk*mg*cos α (N = mg)
ma = F-mg*sin α - µk*mg*cos α
a = (F-mg*sin α - µk*mg*cos α)/m
a = (1800 – 30*9.8*0.5-0.225*30*9.8*0,87)/30 = (1800-147-57.5505)/30 = 53.18165
This mean that crate will not stay at rest. Force is a very big and it compensates weigh projection on x-axis mg*sin α ≈ 147 N
v^2 = 2*a*s
v = (2*53.18165*15)^2 = 39.94 m/s