Problem 1. Find the horizontal force magnitude P needed to start the motion of the block with mass mo in two scenarios: (a) when P is applied to the right and (b) when P is applied to the left. Develop a general solution for each scenario, and subsequently, substitute the values 0= 25°, m = mo = 2.5 kg, µs = 0.40, and µk = 0.35 into your expressions for evaluation. Mgr Hk P (a) A mo e m P (b) B

Consider the system shown below. The incline plane is fixed and the coefficient kinetic friction between M and 2M is ?1, and coefficient kinetic friction between the plane and 2M is ?2. Let M=2.0kg, ?=22o, ?1=0.14, and ?2=0.25. (a) What is the magnitude of the frictional force on mass M? (b) What is the magnitude of the total frictional force on mass 2M? (c) What is the acceleration of mass M? (d) What is the acceleration of mass 2M?

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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