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# ps09sol - MASSACHUSETTS INSTITUTE OF TECHNOLOGY Department...

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MASSACHUSETTS INSTITUTE OF TECHNOLOGY Department of Physics Physics 8.01T Fall Term 2004 Problem Set 9: Momentum and Collision Theory : Solutions Problem 1: Impulse and Momentum The compressive force per area necessary to break the tibia in the lower leg, is about F A = 1.6 × 10 N m 2 . The smallest cross sectional area of the tibia, about 3.2 cm 2 , is slightly / 8 1 above the ankle. Suppose a person of mass m = 6.0 × 10 kg jumps to the ground from a height h 0 = 2.0 m and absorbs the shock of hitting the ground by bending the knees. Assume that there is constant deceleration during the collision. During the collision, the person lowers his center of mass by an amount = d 1cm . a) What is the collision time t col ? b) Find the average force of the ground on the person during the collision. c) What is the average impulse of the ground on the person? d) Will the person break his ankle? How much would you need to lower your center of mass so you do not break your ankle? 1

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Problem 2: Two Dimensional Elastic Collision An object with mass m 1 is initially moving with a velocity v 1,0 = 3.0 m s and collides elastically with another object of equal mass m 2 = m that is initially at rest. After the collision m 1 moves 1 0 with an unknown speed v 1, f at an angle θ = 30 with respect to its initial direction of motion. 1, f After the collision, m 2 moves with an unknown speed v 2, f , at an unknown angle θ 2, f (see sketch). Find the final velocities of each of the masses and the angle θ 2, f . 2
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Problem 3: Experiment 9: Collisions Part One Inelastic Collision: Analysis: Complete the analysis of your data table by following the two steps below, and answer Question 1 below. You will analyze this collision as seen by two different observers. One observer is at rest with respect to the classroom. This reference frame is called the lab reference frame. The observer is moving at a velocity equal to the center of mass velocity of the two cart system. This frame is called the center of mass reference frame. Step 1: Draw two momentum diagrams for both carts immediately before and immediately after the collision, one describing the collision in the lab reference frame, and one describing the collision in the center of mass reference frame. Answer: Figure 1: Collision in lab reference frame Figure 2: Collision in center of mass reference frame You made three different trial collisions; the first with equal masses, and the second and third with unequal masses. Use your measured values to complete the following table. Entries to the left of the double vertical bar are before the two carts collide; those to the right are after the two carts collide but before the collision with the force sensor. Hand the table in with your homework solutions.

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