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1 of 8 Don't forget to review the old stuff. RIII-1. A mass m is moving east at with constant velocity, coasting under its own inertia. Then a constant force of magnitude F is applied in the northern direction. What happens to the speed of the mass? F A) speed increases B) decreases C) remains constant v m Answer: speed increases. This is different than circular motion with constant speed. With circular motion, the force changes direction to always be perpendicular to the velocity. That is not the case here. RIII-2. A mass m is dropped from rest from a height hi above a table top on which sits a spring with spring constant k. The mass compresses the spring by a maximum amount x and stops for an instant at a height hf . There is no friction in this problem. Which of the following equations correctly expresses conservation of energy and allows one to solve for the compression x of the spring? A) mgh i 12 mv 2 12 kx 2 B) mgh i 12 kx 2 mgh f C) mgh i 12 kx 2 mgh f D) mg h f h i 12 kx 2 12 mv 2 E) None of these equations is correct. Answer: mgh i 12 kx 2 mgh f m hi k x hf 2 of 8 RIII-3. Ball 1 of mass m moving right with speed v bounces off ball 2 with mass M (M > m), and then moves left with speed 2v. What is the magnitude of the impulse I = p of ball 1? M m M m v 2v A) mv B) 2mv E) None of these C) 3mv D) (1/2)mv Answer: 3mv By how much did the momentum of ball 2 decrease? A) Mv B) 2Mv C) 3mv D) (1/2)mv E) zero Answer: 3mv (by Conservation of Momentum) RIII-4. A bullet of mass m traveling horizontally with initial speed v strikes a wooden block of mass M resting on a frictionless table. The bullet buries itself in the block, and the block+bullet have a final speed vf. Fill in the blank: The total kinetic energy of the bullet+block after the collision is ___________ the total KE before the collision. m M+m v M vf Before A) greater than B) less than After C) equal to Answer: less than There is friction between the bullet and the block, which generates thermal energy. 3 of 8 RIII-5. Two balls, labeled 1 and 2, collide. Their initial momenta and the final momentum of ball 1 is shown in the figure. +x to right, +y up in diagram. p1f What is the x-component of the final momentum of ball 2? A) –2 B) –1 C) 0 D) +1 E) +2 What is the y-component of the final momentum of ball 2? A) –4 B) –3 C) –1 D) 0 E) +4 p2i p1i Answer: p2f_x = +2, p2f_y = 0. RIII-6. What is the magnitude of the torque about the origin? A) r F sin B) r F cos F r Answer: r F cos axis Try again. What is the torque about the origin? A) r F sin Answer: r F sin B) r F cos F r axis 4 of 8 RIII-7. An irregularly-shaped object of total mass M is free to rotate about a frictionless axis. The moment-of-inertia about the axis is I. The object, initially at rest, is acted on by a torque of constant magnitude for some time t and it reaches a final angular velocity of . There are no other torques acting. What is the time t required to achieve the final angular velocity of the bar? A) I B) I C) M axis M, I M, I D) 0 E) None of these. Answer: I RIII-8. A disk of mass M and area A and radius R is reshaped into a uniform square of the same area A (and the same mass M). The edge length L of the square is related to the radius R of the disk by L2 = R2 (same areas). The moment of inertia I of the square is .. A) larger B) smaller C) the same as that of disk. Answer: larger than RIII-9.Which has larger moment of inertia, axis through C.M. or axis to one side of C.M.? A) Axis through C.M. B) Axis to one side of C.M. C) Depends on shape of object Answer: Axis to one side of C.M. See Parallel Axis Theorem. A B 5 of 8 RIII-10. A very light rod of length L has a mass M at the top end. The bottom end is placed on the ground and the rod is released from rest at an angle . It falls over, rotating about the fixed bottom end. Instantaneously after the rod is released (t=0+, in the limit that t approaches 0 from the + side), the upper end…. (Hint: net = I has initial angular velocity zero. A) zero B) not has initial angular acceleration A) zero B) not zero. has initial tangential acceleration atan A) zero B) not zero. has initial radial acceleration ar A)zero B) not zero. M L Answers: Initially, is zero, is not zero, atan is not zero, ar is zero. As the rod falls over (as decreases to zero), the angular acceleration A) increases B) decreases C) remains constant. Answer: increases (since the torque increases) RIII-11. A frictionless sliding hockey puck and a rolling hoop each have the same mass m and the same initial speed v. Each has enough initial KE to travels up an inclined plane a height h as shown. m h v m v Which object has more total KE at the top of the hill? A) Hoop Answer: Hoop B) puck C) Same KE at the top. 6 of 8 RIII-12. Two forces are applied to a bar as shown in the diagram. Force F is applied at a 45o angle at the center of the bar; force 4F is applied at a 90o angle at the right end of the bar. Is it possible to maintain the bar in static equilibrium by applying an appropriate third force at the left end of the bar? 4F ? F A) No B) Yes Answer: No. You can't have both Fnet and net be zero. The net torque about the left end of the rod is non-zero, no matter what force you apply there. RIII-13. Two people pull on a door which is in static equilibrium. Seen from above the people pulls are .... hinge force? 2F 30o 2F The force on the door from the hinge can be completely determined by using only the equation(s)… A) Fx = 0 , Fy = 0 B) = 0 with origin about right end C) = 0 with origin about center of door Answer: Fx = 0 , Fy = 0 7 of 8 RIII-14. A cylinder with moment of interia IB = 10 kg m2 is rotating on a frictionless platform with initial angular velocity of magnitude i = 4 rad/s. A second non-rotating cylinder with IT = 5 kg m2 is dropped onto the first as shown, and the two cylinders then rotate together. We seek the final angular velocity of the cylinders f . IT f i IB Before After Does Conservation of Angular Momentum apply in this problem? A) Yes B) No C) Depends on how much friction there is between the cylinders Is the following equation true? A) Yes B) No IB i IT f Answers: Conservation of Angular Momentum does apply. The correct equation is IB i (IT IB ) f 8 of 8 RIII-15. A mass on a spring is oscillating and the position x(t) is shown as the solid curve. x t The dotted curve could be … A) the velocity v B) the acceleration a C) both of these D) neither of these Answer: acceleration a RIII-16. A mass on a spring is oscillating with amplitude A. If the amplitude A of the position is doubled, the maximum magnitude of the acceleration .. A) remains unchanged B) doubles C) quadruples (4X) D) decreases by a factor of 2 E) decreases by a factor of 4 Answer: doubles (max magnitude of acceleration = 2 A )