PROBLEM No. 2 (20 pts.) Given: Blocks A and B (having masses of 2m and m, respectively) are connected by an inextensible cable, with the cable being pulled over a small pulley of negligible mass. Block A is able to slide along a rough horizontal surface (with coefficient of kinetic friction of µ k ), and B is allowed to slide along a smooth horizontal guide, as shown below. A constant force P acts to the right on block B. The system is at rest when sb = 0. Find: Determine the speed of block B as a function of sb. Leave your answer in terms of, at most, h, g, µ k, m, P and sb. You must provide free body diagram(s) that are appropriate for your analysis in order to receive full credit for the problem. A sa 2m rough, µ k h g B smooth m sb P
PROBLEM No. 3 (20 pts.) YOU ARE NOT ASKED TO PROVIDE JUSTIFICATION FOR YOUR ANSWERS IN ANY PART OF THIS PROBLEM. PART A 3 points Bar AB rotates counterclockwise with a constant angular velocity ω. Pin C is constrained to move within a straight slot in AB as well as within a fixed circular slot of radius R. Rod AB is pinned to fixed ground at point A. The velocity of the point C is to be found using the moving reference frame kinematics equation: v C = v A + ( v C/ A ) + ω r C/ A a) Draw the velocity vector of point C. b) Draw the vector ω r C/A at point C. c) Draw the vector v ( C/A ) at point C.
PROBLEM No. 3 (continued) PART B 3 points Two systems as shown below are initially at rest. In both systems the blocks move in a vertical plane. In system 1) the two blocks, of mass m A and m B, are placed on top of each other and allowed to fall a distance d. Next, they compress a massless spring. The masses touch each other but are otherwise unconnected. In system 2) block m A is pushed by a constant force F B = m B g as it falls through a distance d and during the subsequent compression of a massless spring. The stiffness in the spring is k in both systems. 1) Circle the answer that most accurately describes the velocity of block A in the two systems when they initially touch the spring. a) v A1 < v A2 b) v A1 > v A2 c) v A1 = v A2 d) More information is needed about the problem in order to answer this question.
PROBLEM No. 3 (continued) PART C 3 points Two blocks of mass m 1 and m 2 are arranged as seen in the figure with a known applied force F to the right such that the lower block accelerates to the right. The acceleration is also known. The coefficients of static and kinetic friction are µ s and µ k, respectively, between the blocks and the mass 2 sits on a frictionless surface. Using the six FBDs below, match the FBD that best describes the situation. Indicate you answer in the blanks below. HINT: DRAW THE FBD CORRESPONDING TO EACH SITUATION BEFORE LOOKING AT THE CHOICES a) FBDs if mass 1 sticks to mass 2, and mass 1 is not near impending slip, i.e., not about to slip. b) FBDs if mass 1 is about to slip with respect to mass 2. c) FBDs if mass 1 slips with respect to mass 2.
PROBLEM No. 3 (continued) PART D 3 points Each figure shows a particle moving in a horizontal plane from Position 1 to Position 2 along the path defined by the solid line. The dashed grid lines on each figure are 1m square; the width/length of the square encapsulating the grid is 5m. The particle is subjected to the forces as shown on each figure. As the particle moves from Position 1 to Position 2, calculate the change in its kinetic energy. a) T 2 T 1 = b) T 2 T 1 = c) T 2 T 1 =
PROBLEM No. 3 (continued) PART E 8 points At a given instant, rod AB is rotating about a fixed axis passing through points A and B with a constant angular velocity ω 1. Also, when θ = 90, link OP is rotating downward at a constant rate, θ. The XYZ axes are fixed in space. The acceleration of point P is to be described by the following equation: a P = a O + ( a P/O ) + α r P/O +2 ω ( v P/O ) + ω ω r P/O ( ) 1) For the case of an observer and a set of xyz axis attached to shaft AB, determine the following terms a) ω = b) α = c) v P/O ( ) = d) a P/O ( ) = 2) For the case of an observer and a set of xyz axis attached to shaft OP, determine the following terms a) ω = b) α = c) v P/O ( ) = d) a P/O ( ) =