Practice Exam #3 1. A barbell is mounted on a nearly frictionless axle through its center. The low-mass rod has a length d = 0.9 m, and each ball has a mass m = 0.5 kg. At this instant, there are two forces of equal magnitude F applied to the system as shown in the figure, with the directions indicated, and at this instant the angular velocity is 96 radians/s, counterclockwise, and the angle θ = 8. n the next 0.008 s, the angular momentum relative to the center increases by an amount 4.7 10 4 kg m /s. What is the magnitude of each force? A. 0.863 N B. 1. N C. 0.53 N D. 0.5 N E. 0 N. As shown in the figure, an object is made of two masses attached to a massless rod. Mass M is placed at the origin, and mass m is placed at x = 10 cm. f M=4m, what is the coordinate of the center of mass of this object is: A. x = 0 cm B. x = cm y C. x = 4 cm D. x = 5cm E. x = 10 cm M m x
3. What is the moment of inertia of the 4-body object in the figure below if the system rotates about the y axis. Assume that you can treat all 4 masses as point-like objects. A. Ma B. Ma C. mb D. mb E. Ma +mb 4. Wheel 1 of mass M rolls down a slope. Wheel of the same mass M slides down the same slope (ignore friction). Which of the following statements is CORRECT? A. (sliding) will get down first. B. 1 (rolling) will get down first. C. Both will get down at the same time. D. Total kinetic energy of wheel will be larger than.that of wheel 1 E. The translational kinetic energy of wheel 1 is the same as that of wheel 5. A truck collides with a mosquito. Which one experiences a larger change in the momentum (i.e. magnitude of the momentum change vector)? A. the truck B. the mosquito C. the same D. not enough information
6. Two masses are connected to each other with a spring. The initial and final configurations of the masses are shown in the figure. nitially, the spring is at its equilibrium length. The rightmost mass is pulled with a force of 40 N to the right. What is the kinetic energy of the point-particle-system? A. 0.84 J B. 5.6 J C. 0.07 J D. 0.4 J E..8 J 7. Assume one pulls a block with a constant force F such that the block moves with a constant speed. According to Newton s second law the magnitude of the friction force f is equal to F. Apparently no work is done on the object and yet we know it gets hotter. Pick the correct answer: A. This paradox cannot be resolved. B. There is no paradox, because the block does not actually get hotter. C. t s not actually possible to have the frictional force exactly equal the force pulling the block. D. Friction must somehow not be doing the same amount of work as the force pulling the block. E. None of the above.
8. Particle 1 of mass m moving with speed v in the +x direction has an elastic collision with particle of mass 3m which was originally at rest. After the collision, particle is moving in the +x direction. What is its speed? A. 5 v B. 1 3 v C. 3 v D. 1 v E. 7 v 9. Which of the following is a property of both elastic and inelastic collisions? A. The internal energy of the system after the collision is different from what it was before the collision. B. The total momentum of the system doesn t change. C. The total kinetic energy of the system doesn t change. D. There is energy dissipated often in form of heat. E. The momentum of the surroundings changes. 10. A bullet of mass m traveling horizontally at a very high speed v embeds itself in a block of mass M that is sitting at rest on a frictionless horizontal surface. After the collision both objects move with a velocity w. Which of the following equations is the proper energy balance for this collision, for the system of bullet + block? m M A. v = w m M + m B. v = w m M + m C. v = w + energy dissipated as heat m M D. v = w + energy dissipated as heat m M + m E. v + mc = w + ( M + m) c
11. n Rutherford s experiment, alpha particles were aimed at a thin gold foil. t was a surprise to see some alpha particles scattered backwards. What explains this? A. The existence of a repulsive electric force. B. The existence of a strong nuclear force. C. The existence of a small massive nucleus. D. The effects of rest mass energy. E. none of the above. 1. A ball of mass m=1.5 kg is falling straight down. At the instant shown, it is a height h=4.0 m above the floor and has a speed of 5 m/s. Consider point A and B at positions r 3.0 ˆ A = + x m r 3.0 ˆ B = x m, respectively. What is the angular momentum of the ball about point B? y A. 0 B..5 ẑ kg m / s C. -.5 ẑ D. 15 ŷ E. -15 ˆx kg m / s kg m / s kg m / s B 0 A x z 13. For the previous problem what is the torque due to gravitational force (weight) on the object with respect to point A? Use g=10 m / s A. 45 ẑ N m B. 60 ˆx N m C. 45 ˆx N m D. 60 ẑ N m E. 45 ŷ N m
14. A playground merry-go-around of with moment of inertia and radius R is spinning with an initial angular velocity ω about its frictionless axis. A child of mass M that is much smaller than the mass of the merry-go-round runs along a path tangential to the rim with a speed v and jumps onto the merry-go-around. The angular velocity of the merrygo-around after the child jumps onto it will be MRv A. ω + v MR v B. ω + MR ω M C. v + MRω D. v + MR v E. ω + ω
Hand-Graded part of exam 3 Two small objects each of mass m are connected by a lightweight rod of length L. At a particular instant they have velocities as shown and are subjected to external forces as shown. The system is moving in outer space. n the following questions involving vectors, give components along the axes shown. (a) What is the total (linear) momentum p total of this system? (b) What is the velocity v CM of the center of mass?
(c) What is the total angular momentum L total, C of the system relative to point C? (d) What is the translational angular momentum L trans, C of the system relative to point C? (e) What is the rotational angular momentum L rot of the system?
After a short time interval t, (f) What is the total (linear) momentum p total of the system? (g) What is the total angular momentum L total, C of the system?