A block of mass rests on a plane that makes an angle above the horizontal
PHYSICS · Multi-part · A Level · Physics · Mechanics and materials · Mechanics and materials
Problem
A block of mass m1 rests on a plane that makes an angle θ above the horizontal. The coefficient of kinetic friction between the block and the plane is μk. The block is connected by a light, inextensible string that passes over a small, frictionless pulley at the top of the incline to a hanging mass m2 suspended vertically on the other side. Immediately after the system is released from rest, both masses accelerate.
Assume the string remains taut and the blocks move without leaving their respective surfaces.
(a) Draw clearly labeled free-body diagrams for each mass, identifying all forces acting on each mass immediately after release.
(b) Taking the direction of motion of the block on the incline to be positive along the plane, write an expression for the net force on each mass in terms of m1, m2, θ, μk, and g.
(c) Derive an algebraic expression for the magnitude of the common acceleration of the two masses in terms of the given quantities. Show all steps in your derivation.
(d) For m1=3.0kg, m2=2.0kg, θ=25∘, and μk=0.15, calculate the numerical value of the acceleration of the system. Include correct units.
(e) Using your result from part (d), determine the magnitude of the tension in the string while the system is accelerating.