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The final exam for the general physics i course at st. Vincent college, held on december 14, 2004. The exam consists of 8 questions worth a total of 200 points, with varying point values for each problem. Topics covered include moment of inertia, rotational equilibrium, simple harmonic oscillators, vectors, energy transfers, and ladder problems.
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St. Vincent College PH 111: General Physics I
The exam consists of 8 questions. There will be two hours to complete the exam. The questions may not be worth the same number of points, read the entire exam before beginning work. Put your name on all pages.
Problem 1 20
Problem 2 35 Problem 3 20
Problem 4 25 Problem 5 25 Problem 6 25
Problem 7 30 Problem 8 20
Total 200
a) (5 pts) What does the moment of inertia I tell you (physically) about an object?
b) (5 pts) If the torque on an object due to an applied force depends not only on the magnitude and direction of the force but also the distance at which the force is applied from the axis of rotation, why does the choice of axis of rotation not matter for rotational equilibrium problems such as the “ladder leaning against a building?”
c) (5 pts) “I’d rather be a hammer than a nail.” Is there any physical basis for this belief? Ie. Is a greater force exerted on one or the other of these objects when the nail is hit by the hammer?
d) (5 pts) A table cloth is pulled out from under a table setting. The same frictional force is exerted on the setting whether the cloth is pulled out quickly or slowly. However, when pulled quickly, the setting barely moves. Why is this? ( Hint: it has nothing to do with the inertia of the setting, which is also the same in both cases.)
a) (5 pts) A person sitting on a frictionless stool holds a horizontally spinning bicycle wheel. As the person flips the wheel over (while it is still spinning) the person begins to rotate on the stool. Explain why, making appropriate use of vectors in your discussion.
b) (5 pts) The equation of motion for a simple harmonic oscillator is x(t) = A cos(ωt + φ). What should be the units of the quantity ωt + φ?
c) (5 pts) Is it possible for the energy of a system of objects to be greater after a “collision” type event than before? If so, cite a real example.
d) (5 pts) What force gives rise to the physical sensation of “weight?” Your answer should be able to explain why someone in an elevator accelerating upward “feels” heavier and why an astronaut in orbit “feels” weight-less even though there is almost as much gravitational force there as at the surface of the earth.
a) (10 pts) What is the velocity of the third piece? (You may leave your answer in terms of components if that is easier.)
b) (10 pts) What are the kinetic energies of the shell before and after the explosion?
c) (5 pts) Explain any difference between the before and after kinetic energies in part (b).
a) (10 pts) How fast is Jill moving when she reaches the bottom of the hill, assuming she tumbles (ie. rolls) all the way down.
b) (10 pts) Jack, on the other hand, slides without friction down the (now) wet grassy slope. How fast is Jack moving when he reaches the bottom of the hill?
c) (5 pts) Does the actual shape of the hill-side make any difference in the results of this problem?
a) (10 pts) The 0.2 kg ball is moving at 40 m/s after being in contact with the foot for 0.1 s. What average force is exerted on the player’s foot during the kick?
b) (10 pts) The 1.5 m tall goalie (with arms outstretched) jumps to try to catch the ball. At the instant before impact, the ball is moving perpendicularly to the goalie’s body and directly into his hands. What is the angular momentum of the ball with respect to the mid-point of the goalie’s body?
c) (10 pts) Treating the goalie as a long, thin, uniform rod rotating about the center (his mid-point) with moment of inertia (1/12)M L^2 and mass 50 kg, calculate the rotation rate of the goalie after successfully catching the ball. (Since he is in the air when the catch is made, there is no net torque on the goalie.)
