## Question:

A crate of mass M rests against a stop block s, which prevents the crate from moving down the plane. If the coefficients of static and kinetic friction between the plane and the crate are ${ μ }_{ s }$ and ${ μ }_{ k }$ respectively, determine the time needed for the force F to give the crate a speed v up the plane. The force always acts parallel to the plane and has a magnitude of F = at. Hint: First determine the time needed to overcome static friction and start the crate moving. Given: M = 50 kg , θ = 30 deg , g = ${ 9.81 m/s }^{ 2 }$ , v = 2 m/s , ${ μ }_{ s }$ = 0.3 , ${ μ }_{ k }$ = 0.2 , a = 300 N/s