hour 4 - University of Minnesota Name: School of Physics...

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Unformatted text preview: University of Minnesota Name: School of Physics and Astronomy Student ID No: Physics 1301, Section 200, Fall 2008 TA Name: Hour Exam 4: Problem 1 (Friday, November 21, 2008) [Please do the problem on the front and back of this sheet of paper.] The Earth travels around the Sun in a nearly circular orbit with a radius of 1.50 x 1011 m. The period of the Earth’s orbit is one year or 365.24 solar days. The Earth also rotates on its axis in one solar day. The Earth can be simply modeled as a solid, homogenous sphere with a radius of 6378 km and a mass of the Earth is 5.97 x 1024 kg. (a) What is the orbital angular momentum of the Earth as it travels around the Sun. (10 points) (b) What is the angular momentum of the Earth as it rotates on its axis? (10 points) (c) The Earth’s orbital angular momentum and rotational angular momentum can be represented by vectors. The two vectors point generally in the same direction, that is, both the orbital motion and the rotational motion are counter‐clockwise, when viewed from the direction of the Earth’s or Sun’s North Pole. The angle between the two vectors is 23.44°. What is the Earth’s total angular momentum. University of Minnesota Name: School of Physics and Astronomy Student ID No: Physics 1301, Section 200, Fall 2008 TA Name: Hour Exam 4: Problem 2 (Friday, November 21, 2008) [This problem is similar to the “Optional Homework Problem”, Chapter 9, Problem 46. Please do the problem on the front and back of this sheet of paper.] A massless rope is wrapped around a hollow cylinder of radius 0.100 m. The central axis of the cylinder is held in a horizontal position by frictionless bearings. A mass of 2.00 kg hangs from the rope. (a) Starting from rest, the mass accelerates and falls 1.50 m in 2.00 s. What is the velocity of the falling mass after it falls 1.50 m? (5 points) (b) What is the kinetic energy of the mass at this point? (5 points) (c) What is the kinetic energy of the cylinder at this point? (5 points) (d) What is the moment of inertia of the cylinder? (5 points) (e) What is the mass of the cylinder? (5 points) University of Minnesota School of Physics and Astronomy Physics 1301, Section 200, Fall 2008 Hour Exam 4: Multiple Choice (Friday, November 21, 2008) [Please mark the answers to the problems below on the bubble sheet. Each question is 5 points.] 1. You decide to exercise on a stationary bicycle. As you pedal, the chain applies a force of 18 N to the rear sprocket wheel at a point 7.00 cm from the rotation axis. Consider the wheel to be a hoop of mass 2.4 kg and radius 35.0 cm. If the wheel starts at rest, what is its angular velocity after 5.00 s? (a) 5 rad/s (b) 10 rad/s (c) 16 rad/s (d) 21 rad/s (e) 26 rad/s 2. The maximum torque produced by the 5.4 liter V8 engine of a 2005 Ford GT is 678 N‐m of torque at 4500 revolutions per minute. What is the power output of this engine? (a) 315 kW (b) 375 kW (c) 410 kW (d) 470 kW (e) 510 kW 3. A child with a mass of 25 kg runs with an initial speed of 2.5 m/s along a path tangent to the rim of a merry‐go‐round, whose radius is 2.00 m. The merry‐go‐round has a moment of inertia of 500.0 kg‐m2 and is initially at rest. The child then jumps on the merry‐go‐round and lands on the very edge. What is the angular velocity of the child and merry‐goround together? (a) 0 (b) 0.11 rad/s (c) 0.21 rad/s (d) 0.26 rad/s (e) 0.31 rad/s 4. A student sits at rest on a stool that is free to rotate. She is then handed a bicycle wheel that is rotating counterclockwise in the horizontal plane on a vertical shaft, when viewed from above. The student then turns the shaft by 180°, so the wheel is rotating clockwise in the horizontal plane, when viewed from above. Which of the following statements is true? I. Turning the wheel over violates conservation of angular momentum. II. The student will begin spinning counterclockwise when viewed from above. III. To turn the wheel over, the student must exert a torque in the horizontal plane. (a) Statement I only. (b) Statement II only. (c) Statement III only. (d) Statements I and II only. (e) Statements II and III only. 5. An old‐fashioned well has a bucket attached to a rope wrapped around a drum. The drum is turned with a crank to raise and lower the bucket. Water is fetched by lowering the bucket to the bottom of the well and submerging it into the water at the bottom of the well. The bucket is raised by turning the crank and the water is then retrieved from the raised bucket. If the bucket is at the top of the well and full of water and the crank is free to rotate, the bucket will lower itself to the bottom of the well. Which of the following statements is true? I. The speed of the freely descending bucket depends on the radius of the drum to which the rope is attached. II. The speed of the freely descending bucket depends on the mass of the drum to which the rope is attached. III. If the mass of the drum is doubled and the radius is halved, the speed of the freely descending bucket will be the same in both cases. (a) Statement I only. (b) Statement II only. (c) Statement III only. (d) Statements I and II only. (e) Statements II and III only. ...
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