E1 - Review for Exam 1 Exam 1 • Next Monday during class...

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Unformatted text preview: Review for Exam 1 Exam 1 • Next Monday during class • Covers up to C9 • 3 problems, 33 points each • No calculator or notes • Formula sheet will be provided • Be on time! Formula Sheet Velocity: dr dt = vAB + vCD v= vAC Momentum and center of mass: 1 (m1 r1 + m2 r2 + · · ·) , M p = M vcm dp Fnet = dt M = m1 + m2 + · · · rcm = Energy: E =K +V K = 1 mv 2 2 dV dx GM m =− mgh + const r = 1 k (r − r0 )2 2 Fx = − Vgrav Vspring dE = Fnet · dr Rotation: v = ω r, Krot = 1 I ω 2 , 2 2 m i ri = I= 2 2 Krot cm = 1 M vcm + 1 I ωcm 2 2 i dm r 2 What the *&$#! does this mean? Problem 1: Two balls with equal mass m are suspended from a light string of length L. One of the balls is pulled to the left by an initial angle θ and then released from rest. When it collides with the other ball, the two balls stick together and move to the right. (a) (10 points) During what part of this process is momentum conserved? During what part of this process is energy conserved? Explain. (b) (23 points) Find the maximum height of the two balls after the collision. M θ F Problem 2: A wheel of mass M and radius R on a horizontal surface is initially at rest. A constant force F then begins to pull on the axle of the wheel at an angle θ below the horizontal. The wheel rolls without sliding until it travels a horizontal distance d. The moment of inertia of the wheel is (a) (15 points) How much does the energy of the wheel change during this process? (b) (18 points) What is the speed of the wheel at the end of this process? shown below. Compute the moment of inertia of the rod for this kind of rotation. Does your answer makes sense as θ33 points) A rod of mass M and length L rotates about an axis that Problem 3: ( → 0? makes an angle θ with the rod, as shown. Find the moment of inertia of the rod for this kind of rotation. ...
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E1 - Review for Exam 1 Exam 1 • Next Monday during class...

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