1. A thin rod of mass M and length d hangs vertically from a frictionless pivot

Question

1. A thin rod of mass M and length d hangs vertically from a frictionless pivot attached to one end. A piece of clay of mass m moving horizontally at a speed v hits the rod a distance x from the pivot and sticks to it. Discussion Questions: (In the first 5-10 min a random group will be selected to explain.) • What “type” of collision is happening? What is and is not conserved? • Consider the analogous linear momentum problem: A mass on a horizontal frictionless table sides into a second stationary mass and the two stick together after the collision. – Which mass feels the greater force? (Hint: think of Newtons 3rd Law) – What is the total force in the collision? – What is the change in total momentum of the collision? • Compare the torques in the problem: – What is the direction of the torque on the rod from the mass? – What is the direction of the torque on the mass from the rod? – What is the total torque in the collision? • What sources of angular momentum are in the problem? • What is the change in total angular momentum in the system? Does this agree with your answer about the total torque in the system? Think ~ = dL/dt ~ • If the clay strikes the rod at a lower position: – How does the total angular momentum of the system change? What would this lead you to conclude about the change in final angular velocity? – How does the total moment of inertia of the rod+mass change? What would this lead you to conclude about the change in final angular velocity? 1 Questions: a) Using the quantities given in the problem find a symbolic equation for the angular velocity of the clay+rod just after the collision. b) Given M = 5kg, d = 1m, m = 2kg, v = 5m/s, and x = 0.75m, calculate the angular velocity in rad/s and tangential velocity of the clay in m/s. c) Calculate the change in total angular momentum during the collision. d) Use your answer in part (c) to calculate the net torque in the system. e) If the collision takes 0.01 s, calculate the torque (magnitude and direction) the clay applies on the rod. (Hint: What is the angular acceleration of the rod?) Explain why this answer is different from part (d)? f) If the collision takes 0.01 s, calculate the torque (magnitude and direction) the rod applies on the clay. (Hint: What is the tangential acceleration of the clay?) g) Use (e) and (f) to calculate the total torque in the system. Explain how this answer compares to part (d). h) Calculate the loss of kinetic energy in this collision. Extra Credit: (5pts) Find a symbolic formula for the x distance of the clay from the pivot that gives the largest angular velocity just after the collision.

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1. A thin rod of mass M and length d hangs vertically from a frictionless pivot

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