1 Physics 107: Ideas of Modern Physics Exam 1 Feb. 8, 2006 Name ID # Section # On the Scantron sheet, 1) Fill in your name 2) Fill in your student ID # (not your social security #) 3) Fill in your section # (under ABC ofspecial codes) Fundamental constants: g= accel. of gravity on Earth = 10 m/s 2 G= gravitational constant = 6.7x10-11 N-m 2 /kg 2
2 1. A 2. On Earth, I throw a 1 kg ball upwards with a force of 100 N. It rises up, reaches it s maximum height of one meter and then falls back down. After the ball has left my hand, its acceleration is a. constant b. continually decreasing c. always zero d. zero only at the top e. different for upward and downward motion After the ball leaves my hand, the only force acting on it is the force of gravity. The acceleration is then constant. 3. A 1 kg baseball is thrown hard enough that it goes into a perpetual circular orbit around the Earth at head-height. The speed of the baseball is constant. Ignoring air-resistance, the acceleration of the baseball after it is thrown is a. 0 m/s 2 Again, the acceleration is that due to gravity, so b. 1 m/s 2 is 10 m/s 2 c. 5 m/s 2 d. 10 m/s 2 e. impossible to determine without knowing the speed. 4. Starting from rest, a 100 kg rollerblader propels herself along the floor with a fire extinguisher that produces a constant thrust of 50N. Four seconds after she starts the extinguisher, her velocity is a. 0.5 m/s b. 1.0 m/s c. 2 m/s d. 4 m/s e. 8 m/s The 50 N thrust produces an acceleration of 50 N / 100 kg = 0.5 m/s 2. So for every second of acceleration, the velocity increases by 0.5 m/s. After four seconds, the roller blader is going 2 m/s. 5. What property of an object is constant during the application of a constant force? a. velocity b. acceleration c. momentum d. all of the above e. none of the above Constant force leads to constant acceleration, a=f/m
3 6. A 2 kg ball moving at 3 m/s to the right collides with 4 kg ball moving at 2 m/s to the left. The two balls stick together when they collide. After the collision, the stuck balls are 3 m/s 2 m/s 2 4 a. moving to the right at constant speed b. moving to the left at constant speed Before c. accelerating to the right? d. accelerating to the left e. stationary 2 4 After The total momentum before the collision is (using pos. to the right, and neg. to the left) (2 kg) x (3 m/s) + (4 kg) x (-2 m/s) = -2 kg-m/s After the collision, we must have this same momentum. Since the balls are stuck together, they must move at the same speed. The mass is positive, so the speed is negative. The balls move to the left at constant speed. 7. An adventurer wants to hover stationary 5 meters above the Earth s surface. He does this by strapping thrusters to his body that each produce 10 Newtons of thrust. His mass is 100 kg. How many thrusters would he need to hover? a. 2 b. 10 c. 20 d. 50 e. 100 The gravitational force on the adventurer is mg =( 100 kg)x(10 m/s2) = 1000 N. To hover, the net force should be zero, so a thrust of 1000 N is required to cancel the gravitational force. So 100 thrusters are required. 8. An astronaut and his ship are at rest with respect to each other in outer space. The astronaut must return to his ship, but his thrusters are empty. He returns by throwing the 10 kg of moonrocks he has collected at a speed of 5 m/s. If the astronaut s mass without the moonrocks is 100 kg, at what speed does the astronaut return to his ship? a. 2 m/s b. 0.5 m/s c. 1 m/s d. 5 m/s e. 10 m/s Before the astronaut throws the rocks, the total momentum is zero. After he throws the rocks, it must also be zero. The momentum of the rocks is (10 kg) x (5 m/s) = 50 kg-m/s. The astronaut must have the same momentum but in the opposite direction. (100 kg) x (? m/s) = 50 m/s his speed is 0.5 m/s.
4 9. The figure shows a top view of a ball on the end of a string traveling counterclockwise in a circular path. The speed of the ball is constant. If the string should break at the instant circled, the ball would follow path A B C a. A b. B c. C d. D e. impossible to tell from the given information D 10. I push a 10 kg box along the floor so that it moves in a straight line at a constant velocity of 2 m/s. The total net force on the box is a. 0 N b. 5 N c. 10 N d. 20 N e. 50 N Since the box is moving at constant velocity, the net force on it must be zero. There must be a frictional force that exactly opposes the force I put on the box. 11. In outer space, an astronaut must get two stationary rocks moving at identical speeds. The bigger rock has three times the mass of the smaller rock. She uses the same 100 N thruster for both, but leaves it on for different times. The required times compare as a. time big rock = (time small rock ) x 3 b. time big rock = (time small rock ) / 3 c. time big rock = (time small rock ) x 9 d. time big rock = (time big rock ) / 9 e. time big rock = time small rock 12. Beginning at time=0, a constant vertical force is continually applied to a rocket by its engines so that it moves upward. Which of the following statements best describes the rocket s motion (use g=10 m/s 2 )? a. Its speed increases, then is constant after a short time. b. Its acceleration is zero c. Its acceleration increases proportional to time d. Its speed increases proportional to time. e. Its acceleration is equal to the acceleration of gravity.
5 13. An astronaut weighs 50 N on the surface of the Earth. When she is 10 Earth radii from the center of the Earth, her weight is a. The same as on Earth b. 10 times less than on Earth c. 9 times less than on Earth. d. 100 times less than on Earth. e. 50 times less than on Earth. On the surface of the Earth, the astronaut is one Earth radii from the center. So she is ten times further away at 10 Earth radii. Since the gravitational force drops off as the square of the distance, 10 times further distance gives 100 times less force. 14. An object is moving to the right in a straight line at a constant speed. Which one of the following statements best describes forces acting on it? a. No forces are acting on the object. b. A larger number of forces are acting on the object to the right than to the left. c. The net force acting on the object is to the right. d. Just one force is acting on the object. e. No net force is acting on the object. 15. You have a 2000 kg car that can produce 400 horsepower (300,000 Watts). You use it at this power to accelerate from 10 m/s to 20 m/s. How long will this take? a. 1.0 second b. 2.0 seconds c. 3.4 seconds d. 4.7 seconds e. 7.1 seconds To accelerate from 10 m/s to 20 m/s requires a change in kinetic energy of ½(2000kg)(20 m/s) 2 - ½(2000kg)(10 m/s) 2 = 300,000 J. Your engine produces 300,000 Watts = 300,000 J / s. So it will take 1.0 second to do 300,000 J of work.
6 16. A monkey produces electrical power by dropping coconuts from the top of a 20 meter tall tree. Each coconut has a mass of 2 kg, and the monkey drops them at a rate of 2 coconuts / second. Assuming the energy of the coconuts is converted entirely into electrical power, how many 100 watt light bulbs can be lit? a. 1 b. 2 c. 4 d. 6 e. 8 The potential energy of each coconut = mgh = (2kg)x(10 m/s2)x(20 m) = 400 J. At two coconuts per second, the monkey produces 800 J/s = 800 Watts. So 8 bulbs can be powered. 17. In class, a brave physics professor did not flinch when a bowling ball pendulum swung to within millimeters of his nose, because it swung back exactly to its release position. This illustrated the a. conservation of energy b. principle of superposition c. conservation of momentum d. principle of inertia e. stupidity of the professor 18. In outer space, an astronaut applies a 2 Newton force to a 5 kg object for 10 meters. How much work did the astronaut do? a. 10 Joules b. 20 Joules c. 50 Joules d. 100 Joules e. 250 Joules Work = Force x Distance, so the work done is 2 Newtons x 10 meters = 20 N-m = 20 Joules.
7 19. Two people move identical 200 kg barbells a vertical distance of 2 meters. One is a power-lifter who jerks the barbell in 0.9 seconds from the floor to above his head. The other is a physics 107 student who rolls the barbell up a ramp 10 meters long in 30 minutes. The work and power output of the power lifter compare to the student as a. Work same, Power same b. Work same, Power greater c. Work greater, Power same d. Work greater, Power greater e. Work less, power greater The work done is only against gravity, and so only the vertical distance matters. The work is the same. The power-lifter does the work much faster, so the power is greater. 20. You are designing a roller coaster, and want the cars to make it over the top of a 5 meter tall hill in the track. Which answer is closest to the minimum speed required for the 1000 kg roller coaster at the base of the hill? a. 21 m/s b. 50 m/s c. 100 m/s d. 7 m/s e. 10 m/s As the coaster rides up the hill, it s kinetic energy is converted into potential energy. At the top of the hill, it s potential energy would be mgh = (1000 kg)x(10 m/s2)x(5 m) = 50,000 J. It s kinetic energy is ½ (1000 kg) x (velocity) 2. (velocity) 2 =2x(50,000 J)/(1000 kg)=100 m 2 /s 2 So velocity = 10 m/s 21. A pendulum swings back and forth. At the top of the swing, a. both potential and kinetic greater than at bottom. b. both potential and kinetic smaller than at bottom. c. potential greater, kinetic smaller than at bottom. d. potential smaller, kinetic greater than at bottom. e. potential and kinetic same as at bottom.