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Milo McCoy
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1 1 of 7 4/5/ :25 PM Name Date UNIT 3 TEST 1. In the formula F = Gm m /r, the quantity G: depends on the local value of g is used only when Earth is one of the two masses is greatest at the surface of Earth is a universal constant of nature is related to the Sun in the same way that g is related to Earth 2. To measure the mass of a planet with the same radius as Earth, an astronaut drops an object from rest (relative to the planet) from an altitude of one radius above the surface. When the object hits its speed is 4 times what it would be if the same experiment were carried out for Earth. In units of Earth masses, the mass of the planet is: An astronaut on the Moon simultaneously drops a feather and a hammer. The fact that they land together shows that: no gravity forces act on a body in a vacuum the acceleration due to gravity on the Moon is less than on Earth in the absence of air resistance all bodies at a given location fall with the same acceleratio the feather has a greater weight on the Moon than on Earth G = 0 on the Moon 4. A projectile is fired straight upward from Earth s surface with a speed that is half the escape speed. If R is the radius of Earth, the highest altitude reached, measured from the surface, is: R/4 R/3 R/2 R 2R 5. The elliptical orbit of a planet around the Sun is shown on the diagram. Which of the following statements is true?

2 2 of 7 4/5/ :25 PM the eccentricity of the orbit is less than zero the eccentricity of the orbit is greater than 1 the sun might be at point C the sun mught be at point D the sun might be at point B 6. Which one of the following statements is true? the center of mass of an object must lie within the object all the mass of an object is actually concentrated at its center of mass the center of mass of an object cannot move if there is zero net force on the object the center of mass of a cylinder must lie on its axis none of the above 7. The x and y coordinates of the center of mass of the three-particle system shown below are: 0,0 1.3m, 1.7m 1.4 m, 1.9 m 1.9 m, 2.5 m 1.4 m, 2.5 m 8. The center of mass of a system of particles obeys an equation similar to Newton s second law F = ma, where F is the net internal force and m is the total mass of the system F is the net internal force and m is the mass acting on the system F is the net external force and m is the total mass of the system F is the force of gravity and m is the mass of Earth F is the force of gravity and m is the total mass of the system 9. Two bodies, A and B, have equal kinetic energies. The mass of A is nine times that of B. The ratio of the momentum of A to that of B is: 1:9 1:3 1:1 3:1 9:1

3 3 of 7 4/5/ :25 PM 10. A projectile in flight explodes into several fragments. The total momentum of the fragments immediately after this explosion: is the same as the momentum of the projectile immediately before the explosion has been changed into kinetic energy of the fragments is less than the momentum of the projectile immediately before the explosion is more than the momentum of the projectile immediately before the explosion has been changed into radiant energy 11. A rifle of mass M is initially at rest but free to recoil. It fires a bullet of mass m and velocity v (relative to the ground). After firing, the velocity of the rifle (relative to the ground) is: -mv -Mv/m -mv/m -v mv/m 12. A 1000-kg space probe is motionless in space. To start moving, its main engine is fired for 5 s during which time it ejects exhaust gases at 5000m/s. At the end of this process it is moving at 20m/s. The approximate mass of the ejected gas is: 0.8 kg 4 kg 5 kg 20 kg 25 kg 13. The physical quantity impulse has the same dimensions as that of: force power energy momentum work 14. A golf ball of mass m is hit by a golf club so that the ball leaves the tee with speed v. The club is in contact with the ball for time T. The magnitude of the average force on the club on the ball during the time T is: mvt mv/t (1/2)mv 2 T mv 2 /(2T) mt 2 /(2v)

4 4 of 7 4/5/ :25 PM 15. An inelastic collision is one in which: momentum is not conserved but kinetic energy is conserved total mass is not conserved but momentum is conserved neither kinetic energy nor momentum is conserved momentum is conserved but kinetic energy is not conserved the total impulse is equal to the change in kinetic energy 16. If a wheel turns with constant angular speed then: each point on its rim moves with constant velocity each point on its rim moves with constant acceleration the wheel turns through equal angles in equal times the angle through which the wheel turns in each second increases as time goes on the angle through which the wheel turns in each second decreases as time goes on 17. If wheel turning at a constant rate completes 100 revolutions in 10 s its angular speed is: 0.31 rad/s 0.63 rad/s 10 rad/s 31 rad/s 63 rad/s 18. The angular speed of the second hand of a watch is: (π = pi) (π /1800) rad/s (π /60) m/s (π/30) m/s (2 π) m/s (60) m/s 19. A phonograph turntable, initially rotating at 0.75 rev/s, slows down and stops in 30 s. The magnitude of its average angular acceleration in rad/s 2 for this process is: π π / 40 π / The figure shows a cylinder of radius 0.7m rotating about its axis at 10 rad/s. The speed of the point P is:

5 5 of 7 4/5/ :25 PM 7.0 m/s 14 π rad/s 7.0 π rad/s 0.70 m/s none of these 21. A disk starts from rest and rotates around a fixed axis, subject to a constant net torque. The work done by the torque during the second 5s is as the work done during the first 5 s. the same twice as much half as much four times as much one-fourth as much 22. A wheel rolls without sliding along a horizontal road as shown. The velocity of the center of the wheel is represented by. Point P is painted on the rim of the wheel. The instantaneous velocity of point P is : zero 23. A solid wheel with mass M, radius R, and rotational inertia MR 2 /2, rolls without sliding on a horizontal surface. A horizontal force F is applied to the axle and the center of mass has an acceleration a. The magnitudes of the applied force F and the frictional force f of the surface, respectively, are: F = Ma, f = 0 F = Ma, f = Ma/2 F = 2Ma, f = Ma F = 2Ma, f = Ma/2 F = 3Ma/2, f = Ma/2 24. A hoop rolls with constant velocity and without sliding along level ground. kinetic energy is: half its translational kinetic energy the same as its translational kinetic energy twice its translational kinetic energy four times its translational kinetic energy one-third its translational kinetic energy

6 6 of 7 4/5/ :25 PM 25. A wheel with rotational inertia I, mounted on a vertical shaft with negligible rotational inertia, is rotating with angular speed ω 0. A nonrotating wheel with rotational inertia 2I is suddenly dropped onto the same shaft as shown. The resultant combination of the two wheels and shaft will rotate at: ω 0 /2 2ω 0 ω 0 /3 3ω 0 ω 0 /4 26. As an astronaut, you observe a small planet to be spherical. After landing on the planet, you set off, walking always straight ahead, and you find yourself returning to your spacecraft from the opposite side after completing a lap of 25.0 km. You hold a hammer and a falcon feather at a height of 1.40 m, release them, and observe they fall together to the surface in 29.2 s. Determine the mass of the planet. (5 points) 27. In an American football game, a 90.0 kg fullback running east with a speed of 5.00 m/s is tackled by a 95.0 kg opponent running north with a speed of 3.00 m/s. (a) Explain why the successful tackle constitutes a perfectly inelastic collision? (b) Calculate the velocity of the players immediately after the tackle. (c) Determine the mechanical energy that disappears as a result of the collision. Account for the missing energy. (8 points) 28. Two astronauts, each having a mass of 75.0 kg, are connected by a 10.0 m rope of negligible mass. They are isolated in space, orbiting their center of mass at speeds of 5.00 m/s. Treating the astronauts as particles, calculate (a) the magnitude of the angular momentum of the system and (b) the rottional energy of the system. By pulling on the rope, one astronaut shortens the distance

7 7 of 7 4/5/ :25 PM between them to 5.00 m. (c) What is the new angular momentum of the system? (d) What are the astronauts new speeds? (e) What is the new rotational energy of the system? (f) How much work does the astronaut do in shortening the rope? (12 points)

1. An object is dropped from rest. Which of the five following graphs correctly represents its motion? The positive direction is taken to be downward.

1. An object is dropped from rest. Which of the five following graphs correctly represents its motion? The positive direction is taken to be downward. Unless otherwise instructed, use g = 9.8 m/s 2 Rotational Inertia about an axis through com: Hoop about axis(radius=r, mass=m) : MR 2 Hoop about diameter (radius=r, mass=m): 1/2MR 2 Disk/solid cyllinder