PHY 2048 Final Exam Review DISCLAIMER - I am a student and there could potentially be errors in the solutions.
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1 PHY 2048 Final Exam Review DISCLAIMER - I am a student and there could potentially be errors in the solutions. 1. A large wheel of cheese, initially at rest, accelerates at a rate of 10 rad/s^2. The radius of the cheese wheel is 2 m. a) Find the time it takes to complete 10 revolutions. b) Find the angular velocity at the moment the cheese wheel hits 10 revolutions. c) Find the distance the cheese wheel has traveled across the ground in 10 revolutions.
2 2. Bob is driving his super awesome car. He starts in reverse and ends driving forward. The angular velocity of the tires when he is reversing is 20 rad/s and the angular velocity when he is driving forward is 30 rad/s. He performs this with a constant angular acceleration. It takes Bob 5 s to make this change in velocity. The radius of the wheels are 0.5 m. a) Find the angular acceleration of the wheels. b) Find the initial linear velocity of the car. c) Find the final linear velocity of the car.
3 3. Bob, Tim, and Mike are standing on a merry go round that is rotating at an angular velocity of 15 rad/s. Bob has a mass of 100 kg and stands at the edge of the merry go round. Tim has a mass of 180 kg and stands halfway from the center of the merry go round to the edge. Mike has a mass of 120 kg and stands a distance two thirds the radius from the center. The radius is 2 m. Which kid has the most kinetic energy. (Treat each kid to be a point mass. Use I = mr^2)
4 4. A fan with 6 blades, each of length 1.5 m and mass of 5 kg, has 500 J of rotational kinetic energy. Calculate the angular velocity of fan. Each fan blade is treated as a rod, so the moment of inertia for a blade in this problem is I = 1/3 mr^2
5 5. A mass pulley system is drawn below. m1 is 80 kg, m2 is 100 kg, the mass of the pulley is 50 kg, the radius of the pulley is 0.2 m, and the height of m2 above the ground is 5 m. The moment of a disk is I = 1/2 mr^2. Calculate the linear acceleration of the system and the time it takes for m2 to hit the floor.
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7 6. A mass is on an inclined plane and attached to a pulley. A second mass is suspended over the pulley but is attached to a smaller pulley. These two pulleys rotate together. The coefficient of kinetic friction is 0.3, m1 is 100 kg, the mass of the large pulley is 20 kg, the mass of the smaller pulley is 15 kg, the radius of the larger pulley is 0.5 m, the radius of the smaller puller is half that of the larger pulley, the angle of the incline is 30 degrees, and the linear acceleration of the system is 2 m/s^2 up the incline. Calculate the mass of m2.
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9 7. Bob just bought the most ratchet shoes ever. These shoes use a bolt instead of a shoe string to tighten. Bob wants to take his shoes off. He has a ratchet of length 0.3 m. Bob can exert a max force of 132 N. A minimum torque of 45 Nm is required to loosen the bolt. Will Bob be able to take off his shoes?
10 8. Bob decides to go fishing. He decides to be e-fish-ent, so he rigs his fishing rod such that there is an extra fishing string attached to the rod as shown below. Two fish are on the lines so there are tensions in the strings. An alien comes in a UFO and decides to play the claw game to win a prize for his alien girlfriend. The claw grabs the rod as shown below and exerts a force. Force values, angles, and the length of the rod are given in the image below. Calculate the net torque about the end of the rod due to these forces. Also find the direction of the net torque vector.
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12 9. A wheel is rotated by a single force. The wheel rotates such that the torque vector is pointing into the page based on the drawing below. The force is applied at the top of the wheel. In which direction is the force acting?
13 10. Comets orbit the sun following an elliptical path as shown below. At which point is the comet moving with the fastest speed.
14 11. Bob and Bobina are spinning on ice initially with arms wide open like Creed. Bob has a moment of inertia of 20.7 kgm^2 and is spinning at an angular velocity of 8.1 rad/s. Bobina has a moment of inertia of 22.5 kgm^2 and is spinning at a rate of 7.8 rad/s. Bob hugs himself out of loneliness and starts spinning at a rate of 14.1 rad/s. Bobina notices this change in Bob and follows suit. She speeds up to 14.5 rad/s. Which skater has the smaller moment of inertia after retracting their arms?
15 12. A rod of mass 50 kg and length L is initially at rest and is free to spin about its center. A ball of mass 1 kg moves at a velocity of 20 m/s as shown below and hits the rod halfway between the center and the top of the rod. The ball sticks onto the rod and the rotate at an angular velocity of 5 rad/s. The moment of inertia for the rod is I = 1/12 ML^2 and the moment of inertia for the ball is I = MR^2. Find the length of the rod.
16 13. A can of vienna sausages is rotating at a rate of 10 rad/s on a frictionless surface. Two identical cans of vienna sausages with no spin are dropped on top of the spinning can. They eventually all spin together. What is the final angular velocity of the cans?
17 14. A tortilla is spinning at a rate of 1 rad/s on a frictionless surface. Bob drops his arepa onto the tortilla. The arepa is spinning at a rate of 5 rad/s in the opposite direction of the spin of the tortilla. They eventually start spinning together. The mass of the tortilla is 10 kg, the mass of the arepa is 20 kg, the radius of the tortilla is 2 m, and the radius of the arepa is 1.5 m. The moment of inertia for both disks are I = 1/2 MR^2. What is the angular velocity of the tortilla-arepa combo?
18 15. A pendulum. The mass at the end of the string is 5000 kg. The pendulum is on the surface of earth. The period of this pendulum is 2 s. Calculate the frequency, the angular frequency, and the length of the pendulum.
19 16. A mass is attached to a spring on a horizontal frictionless surface. The mass is pulled a distance and released. At a time of 2 s after being released, the mass is located 3 m from the equilibrium position. The angular frequency of oscillation is pi/6 radians/s. The mass of is 100 kg. Calculate the amplitude of the oscillation, the spring constant, the maximum potential energy of the mass, and the maximum kinetic energy of the mass. Also, if at a random time the kinetic energy is J, what is the potential energy at that instant?
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