Physics 201, Practice Midterm Exam 3, Fall 2006

Transcription

1 Physics 201, Practice Midterm Exam 3, Fall A figure skater is spinning with arms stretched out. A moment later she rapidly brings her arms close to her body, but maintains her dynamic equilibrium. Which of the following statements about physical quantities that describe her motion is false? a. Skater's total energy increases b. Skater's kinetic energy increases c. Skater's angular momentum remains constant d. Skater's moment of inertia decreases e. Skater's angular velocity increases 2. For the situation depicted in the figure below the tension in the string T can be expressed as: (mass of the horizontal rod is M and mass of the bulb is M b ) a. T = g( M + 2M b ) ( ) ( ) ( ) b. T = g M + M b c. T = g 2M + M b d. T = 2g M + M b e. There is not enough information given to solve the problem

2 3. A satellite is in a circular orbit above the Earth with a radius 2.5 x 10 7 m. Given the mass of Earth to be approximately, M E = 6.0 x kg, and G = 6.67x10-11 N- m 2 /kg 2, what is approximately its period of revolution around the Earth? a. 11 seconds b. 11 minutes c. 11 hours d. 11 days e. Not possible to determine without knowledge of satellite's mass 4. A yoyo is being spun in a circle as shown in the figure. What is the magnitude of centripetal acceleration of the yoyo? a. g tanθ b. g sinθ c. g cosθ d. g secθ e. g cscθ 5. Gravitational potential energy is defined to be zero at infinity. What is the minimum speed needed for a rocket ship to escape to infinity from a planet of mass M and radius R? a. Rocket ship can never escape to infinity because it requires infinite speed, whereas speed of any object cannot exceed the speed of light. GM b. c. d. e. R 2 2GM R 2 GM R 2GM R

3 6. What is the moment of inertia of the system of four balls, with mass M and negligible radius, attached as shown in the figure below with two rods of negligible mass and length L, if it is spinning about the axis running through the center, perpendicular to the plane in which balls are located. a ML 2 b. 0.5 ML 2 c. ML 2 d. 2 ML 2 e. 4 ML 2 7. At an altitude 4 times the radius of the earth above the sea-level, the acceleration due to gravity is: a. g, as always b. g/2 c. g/4 d. g/16 e. None of the above 8. A child of mass 60 kg stands at the outer rim of a circular merry-go-round (radius 2.5m), which is moving at 10 rad/s. At the same time that another child of mass 45 kg jumps on the outer edge, the first child moves to a position half way to the center (R/2). The merry-go-round a. stays the same speed b. goes faster c. goes slower d. stops e. velocity cannot be determined with the information given

4 9. A physics professor makes a demo for his class on rotational motion. He ties a knot at the end of a 1-m long string, strings a 50-g nut (A) to that end. He ties another knot 0.1 m from nut A, and strings a second 50-g nut (B). He then sets an electric motor to spin the string with nuts at 10 revolutions per second. Unfortunately, during the class demo, the central knot tightens due to tension in the string, and the nut B slides to the nut A. What will happen to the angular velocity and angular momentum if the power output of the electric motor is unchanged during this process? a. Angular velocity and angular momentum will increase b. Angular velocity and angular momentum will decrease c. Both angular velocity and angular momentum remain unchanged d. Angular velocity increases and angular momentum remains constant e. Angular velocity decreases and angular momentum remains constant B A 10. For the situation described in problem 6, ignore the size of the nuts and the mass of the string, and estimate the angular velocity of the string + nuts system in the steady state after the nut B slides to nut A: a. 9.0 revolutions per second b. 9.5 revolutions per second c. 10 revolutions per second d revolutions per second e. 11 revolutions per second 11. Consider the situation shown in the figure below. Use the coordinate system in which the origin is at the support of the wooden plank, the bear is walking in +X direction to the goodies, and vertically up is +Y direction. In which direction does the force at the support of the wooden plank point? a. 90 o, i.e., along +Y b. Above 0 o but below 90 o c. 0 o, i.e., along +X d. Below 0 o but above -90 o e. -90 o, i.e., along -Y

5 12. Of the nine known planets in our solar system, the innermost is Mercury. When compared to the other planets in the system, Mercury has the: a. greatest centripetal acceleration. b. greatest period of revolution. c. smallest angular velocity. d. smallest tangential velocity. e. highest density 13. If a non-zero net torque and zero net force are applied to an object, that object will experience: a. a constant angular speed, but does not experience any translation b. an angular acceleration, but no linear acceleration c. an increasing angular acceleration, but no linear acceleration d. an increasing angular and linear acceleration e. none of the above 14. A turntable has a moment of inertia of kg m 2 and spins freely on a frictionless bearing at 25.0 rev/min. A kg ball of putty is dropped vertically onto the turntable and sticks at a point m from the center. What is the new rate of rotation of the system? a rev/min b rev/min c rev/min d rev/min e. none of the above 15. When you compare a car A, which is going around a round-about, to another car B, which is going along a straight road, which of the following statements is true, if the two cars have same constant speed v? a. There are more forces acting on the car A than on car B. b. The net force acting on both cars is zero. c. The net force acting on car A is non-zero but that acting on car B is zero. d. Neither car is accelerating, because car B has constant speed, and centripetal force cancels the frictional force acting on car A. e. The frictional force acting on both cars is the same in magnitude and direction.

6 16. The acceleration due to gravity, g X, on planet X which has the same density (=mass/volume) as the Earth but twice its radius will be a. one fourth as large as g Earth =9.8 m/s 2 b. the same as on earth, i.e., g X =g Earth =9.8 m/s 2 c. twice as large as g Earth =9.8 m/s 2 d. four times as large as g Earth =9.8 m/s 2 e. eight times as large as g Earth =9.8 m/s 17. A satellite is orbiting the earth in a circular orbit of radius R o. That satellite's speed is a. dependent on the satellite's mass. b. dependent on the radius of earth but not on mass of earth. c. independent of the mass of earth. d. e. 2GM E R E GM E R o 18. A skier starts at rest at the top of a large hemispherical hill as shown. Neglecting friction, the speed of the skier, v, after dropping a height h is: a. v = gh /2 b. v = gh /2 c. v = gh d. v = 2gh e. v = 2 gh

7 19. The magnitude of normal force experienced by the skier of problem 14 is: (Hint: Use the figure shown here.) a. mg 1! 5h % # 4R& b. mg 1! 3h % # 2R& c. mg 1! 2h % # R & d. mg 1! 3h % # $ R & ' e. mg 1! 5h % # R & 20. The skier leaves the hill and becomes airborne when he drops by a height a. h = R /5 b. h = R /4 c. h = R / 3 d. h = R /2 e. h = R