How to use MATLAB to solve this problem? Fig. P12.C1 Block B of mass 10 kg is in

Question

How to use MATLAB to solve this problem? Fig. P12.C1 Block B of mass 10 kg is initially at rest as shown on the upper surface of a 20-kg wedge A which is supported by a horizontal surface. A 2-kg block C is connected to block B by a cord which passes over a pulley of negligible mass. Using computational software and denoting by mu the coefficient of friction at all surfaces, use this program to determine the accelerations for values of mu 0. Use 0.01 increments for mu until the wedge does not move and then use 0.1 increments until no motion occurs.

Explanation / Answer

Solving Rotational Dynamics Problems MINDS¥ON PHYSICS Purpose and Expected Outcome In this activity, you will learn more about rotational dynamics, which involves the forces exerted on rotating systems and the response of those systems (i.e., angular acceleration). You will learn how to apply the concepts of torque and moment of inertia to problem situations involving rotating systems. Prior Experience / Knowledge Needed You should know dynamics. You should know NewtonÕs laws and how to apply them to physical situations. You should have some experience analyzing and solving problems in dynamics, and you should know how to apply empirical force laws. In addition, you should have some experience with rotational kinematics, and you should be able to recognize when a system is accelerating. You should know the definitions of torque, net torque, and moment of inertia relative to a fixed axis. NEWTONÕS 2ND LAW IN ROTATIONAL FORM NewtonÕs 2nd law (Fnet = m a) is valid and applicable for all objects and systems. However, when a rigid body is spinning about a fixed axis, it is more convenient to use angular quantities, such as angular velocity and angular acceleration, to describe its motion. (At any particular instant, every part of the rigid body has a different velocity but the same angular velocity.) In terms of angular acceleration, NewtonÕs 2nd law is written: tnet,p = Ip ap NewtonÕs 2nd law for rotations about a fixed axis where tnet,p is the net torque on the rigid body about a fixed axis through point p, Ip is the objectÕs moment of inertia for rotations about the same axis, and ap is its angular acceleration. Note that tnet,p and ap are vectors. Reflection R1. What do you find most difficult about solving problems in rotational dynamics? R2. For any of the situations or problems, did you think about what the linear motion situation or problem might look like? Why or why not? R M, Ic m R3. (a) What is the general relationship between the angular displacement Æq of a spinning wheel and the displacement Æy of a mass hanging from a string wound around the wheel? Explain. In your relationship, what are the units of the angular displacement? Why? (b) What is the general relationship between the angular velocity w of the wheel and the velocity vy of the hanging mass? Explain. (c) What is the general relationship between the angular acceleration a of the wheel and the acceleration ay of the hanging mass? Explain. R4. Reconsider situation A2, in which a hanging mass is attached to a string wound around a solid wheel. (a) When the arrangement is free to spin, which is larger, the tension in the string or the weight of the hanging mass? Explain your reasoning. (b) Did you ignore this difference when you solved problem A2? Did you know that you had ignored this difference? (c) How does this affect your answers? (If you do not ignore this difference, which answers become slightly larger, which ones stay the same, and which ones become slightly smaller?) R5. Reconsider situation A3, in which a bicycle is held off the ground with a clamp. (a) What features did you ignore to answer the questions? (b) How would your answers change if you did not ignore these features? (If you did not ignore these features, which answers would be larger, which would stay the same, and which would be smaller?) R6. Is it possible to exert a force at the edge of an object without exerting a torque about its center? Give an example of a situation involving a bicycle wheel in which a force is exerted to the rim of the wheel, but no torque is exerted about the center of the wheel.

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