Learning Goal: Consider the mass and pulley system shown. Mass m₁ = 32 kg and mass m2 = 10 kg. The angle of the inclined plane is given, and the coefficient of kinetic friction between mass m₂ and the inclined plane is μ = 0.12. Assume the pulleys are massless and frictionless. (Figure 1)

(1) A 50 kg block rests on a 20° incline plane, as shown in Figure 1. The coefficient of static friction between the block and the plane is 0.4. Determine the maximum horizontal force P that can be applied to the block without causing it to slide. P 50 kg H, = 0.40 20° Figure 1

A carnival ride has people stand inside a vertical cylinder with their backs to the wall. The cylinder starts spinning and the riders find that they are “stuck” to the wall and don’t slide down, even if the floor is removed.  The ride has a radius of r. The person has a mass of m and is moving with a constant speed of v. The coefficient of static friction between the person and the wall is μs , and kinetic friction μk. The person is only touching the wall, not touching the floor.   What is the magnitude of the acceleration of the person? In what direction does it point?   The speed is constant. Why is the acceleration not zero? Briefly explain. No equations!

Please answer and show how you got it You are on an elevator fixed to a wall that can move up and down freely while you pull with a force of 150 N on a massless rope (the orange line in the diagram below) with length L. This rope is connected to one end of a beam with the same length, L, and mass m=20 kg. The left end of the beam is in contact with the same wall the elevator is on and the coefficient of static friction =0.2 between the beam and the wall. See diagram below for a representation of the situation and note that free fall acceleration points directly downward 0 L Part A) Label all the forces acting on the beam and discuss the direction of any torques exerted on the beam about the contact point between the beam and the wall Part B) What is the maximum angle the beam can subtend with respect to the horizontal _m such that it will just begin to slip? Potentially useful trig identities are sin(2x)=2sin(x)cos, sin(180-x)=sin(x), sin(90+x)=cos(x)