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 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)

3. Two blocks, masses m₁ and m2, on a horizontal, frictionless surface are being pulled by a massless, unstretchable rope that goes over a frictionless pulley and is connected to a block of mass m3. Assumer two blocks move together. The coefficient of friction between block 1 and block 2 is . Find the force that block 2 exerts on block 1. 2 [ Free Body Diagrams and Law or Definitio. 3

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4) This Atwood's machine includes two blocks connected by a cable, going over a pulley without slipping. Block 1 (30.0 kg) is connected to a spring (70.0 N/m), and slides on a horizontal surface with a coefficient of kinetic friction of 0.0100. Block 2 is 50.0 kg, and hangs vertically from the cable. The pulley is a disk with a radius of 0.500 m, and its moment of inertia about the center of mass is 10. 0 kg-m“. a) Draw the three free body diagrams, and write out Newton's 2nd Law for each. b) Derive the equation of motion (inhomogeneous 2nd order ODE) for this system. c) Use u-substitution to rewrite this as a homogeneous 2nd order ODE. d) Assume the position x as a function of time t is of the form x(t) = A cos (wt + p) I disk for undamped natural frequency w, phase angle P, and amplitude A. The initial conditions are: x(0) v(0) = -3. 00 m/s. Solve for the position of the mass as a function of time (you need to solve for w, 4, and A). = 2. 00 m and Mz

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A block of mass M = 109.0 kg on an inclined plane is attached to another block of mass m via a string, as in the figure below. The coefficients of static and kinetic friction for the block and the incline are u, = 0.40 and uy = 0.20 and the plane is inclined 16.9° with horizontal. (a) Determine the range of values for m, the mass of the hanging block, for which the block will not move unless disturbed, but if nudged, will slide down the incline. 73.4 kg s m s.03 kg (b) Determine a range of values for m for which the block will not move unless nudged, but if nudged will slide up the incline. 52.94 kg s m s 10.82 kg eBook