Physics 2210 Fall 2011 David Ailion EXAM 4

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1 Dd Physics 2210 Fall 2011 David Ailion EXAM 4 PLEASE FILL IN THE INFORMATION BELOW: Name (printed): Name (signed): Student ID Number (unid): u Discussion Instructor: Marc Lindley Jon Paul Lundquist Peter Peroncik Rhett Zollinger Useful Information: 1 ft = 12 in (exact) 1 m = 3.28 ft 1 mile = 5280 ft (exact) 1 hour = 3600 sec = 60 min (exact) 1 day = 24 hr (exact) g earth = 9.80 m/s 2 = 32.2 ft/s 2 g moon = 1.67 m/s 2 = 5.48 ft/s2 1 year = days 1 kg = slug 1 N = pound 1 horsepower = 550 ft pounds/s (exact) M earth = kg R earth = km M sun = kg R sun = m M moon = kg R moon = km G = N m 2 /kg 2 k = N m 2 /C 2 ε o = F/m e electron charge = C m electron = kg Mean earth-moon distance = km

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3 Dd Physics 2210 Fall 2011 David Ailion Name: Unid: Discussion TA: Exam 4 1 SHOW ALL WORK!! Place a circle or box around each answer. Specify units for each answer. Report all numbers to two significant figures. Circle all that apply! A. [5 pts.] Which of the following are always true? Circle all that are correct. 1. Angular momentum of a system is conserved if the forces on the system are constant in time. 2. Angular momentum of a system is conserved if the net torque on the system is zero. 3. Angular momentum of a system is conserved even if the net torque on the system is non-zero, provided that the integral of the torque over time is zero. 4. Angular momentum of a system is conserved if the axis of rotation is a symmetry axis that passes through the center of mass. 5. Angular momentum of a system is conserved if the moment of inertia of the system is a constant. B. [5 pts.] When the sum of the external forces and the sum of the external torques on a body are both zero, we can conclude which of the following: 1. The body is moving at constant velocity but is not rotating. 2. The body is rotating at constant angular velocity but has no linear velocity. 3. The body has zero linear and zero angular velocity. 4. The body may have a constant linear or angular velocity but not both simultaneously. 5. The body may have constant linear or angular velocity or both simultaneously. C. [5 pts.] The pilot of a spaceship traveling in deep space decides to increase his speed by burning all his remaining fuel. The initial mass of the fuel is kg, and is thrust at an escape velocity of 2.2 km/s relative to the spaceship. Its burning result is an increase by 5.2 km/s in the speed of the spaceship. Calculate the final mass of the spaceship and contents. D. [5 pts.] Calculate the moment of inertia of a thin spherical shell of mass M and radius R about an axis that is tangent to the shell.

4 ate the angle between vector B and C in part C. Dd Physics 2210 Fall 2011 David Ailion Name: Unid: Discussion TA: Exam 4 2 SHOW ALL WORK!! Place a circle or box around each answer. Specify units for each answer. Report all numbers to two significant figures. Two blocks, m 1 and m 2, are connected by a light string, as shown, with m 2 > m 1. The radius of the pulley is R and its moment of inertia is I. (a) (b) [13 pts.] Calculate the magnitude of the acceleration of m 2. Express your answer in terms of given quantities and g. [7 pts.] Determine the angular momentum vector (magnitude and direction) of the entire system relative to the pulley axis when the velocity of m 2 is v in the downward direction. Answer should be expressed in terms of given quantities, g and v.

5 Physics 2210 Fall 2011 David Ailion Name: Unid: Discussion TA: Exam 4 3 SHOW ALL WORK!! Place a circle or box around each answer. Specify units for each answer. Report all numbers to two significant figures. [20 pts.] If the moon suddenly stopped revolving around the earth, it would crash into the earth. Calculate the speed with which the moon collides with the earth, expressed in m/s. (The relevant parameters for the earth and moon are given under Useful Information on the cover sheet of the exam.) You may neglect the motion of the earth in this problem.

6 Physics 2210 Fall 2011 David Ailion Name: Unid: Discussion TA: Exam 4 4 SHOW ALL WORK!! Place a circle or box around each answer. Specify units for each answer. Report all numbers to two significant figures. A satellite of radius R S, and mass m circles a planet of mass M and radius R in an orbit of height 2R above the surface of the planet. The satellite makes a transition to a circular orbit of height 3R above the surface of the planet. For the questions below, express your answers in terms of given quantities and G. (a) (b) (c) [6 pts.] What is the minimum energy required for the change in orbit? [6 pts.] Calculate the satellite s final speed. [8 pts.] Consider a rocket on the surface of the satellite. If the rocket is fired straight out from the line joining the satellite and planet, calculate its escape speed. In this part you should obtain a numerical answer. Assume that m = kg; M = kg; R S = m, and R = m. Neglect the motion of the satellite in this problem.

7 Physics 2210 Fall 2011 David Ailion Name: Unid: Discussion TA: Exam 4 5 SHOW ALL WORK!! Place a circle or box around each answer. Specify units for each answer. Report all numbers to two significant figures. A solid cylindrical disc of mass M and radius R rotates about a frictionless vertical axle with angular speed ω i. A second solid cylindrical disc of the same material and thickness but of radius R/2 and initially not rotating, drops onto the first disc, as shown in the figure. Because of friction between the surfaces, the two eventually reach the same angular speed, ω f. (a) [10 pts.] Calculate ω f. (b) [10 pts.] Calculate the ratio of the final to the initial rotational energy.

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