Name: PHYS 110 Final Exam Prof. Finn 1

Transcription

1 Name: PHYS 110 Final Exam Prof. Finn 1

2 Constants: G = 6.67 x N m 2 /kg 2 M sun = 1.99 x kg R sun = 6.96 x 10 8 m M earth = 5.98 x kg R earth = 6.38 x 10 6 m Earth-Sun distance = 1.5 x m I sphere = 2/5 M R 2 I hoop = M R 2 I cylinder = ½ M R 2 R = J/(mol K) = L atm/(mol K) k = 1.38 x J/K 1 amu = x kg N A = 6.02 x atm = x 10 5 N/m 2 m H = 1.0 amu m O = 16.0 amu 2

3 Directions: Answer 6 out of the first 8 problems AND problems 9 and 10. Each problem is worth an equal amount of points. Write your solutions in the blue book. Be sure to show all your work and keep careful track of units! Good luck! 1. A soccer player, Madeline, is standing on the roof of building A, 50.0 m above the ground. Her friend Emily is standing on the roof of another building, building B, which is located 15.0 m away. The roof of building B is 2.0 m lower than the roof of building A. Madeleine wants to kick a ball to Emily. Madeleine kicks the ball with an initial velocity v 0 at an angle of 45.0 degrees above the horizontal. V 0 50 m 48 m 15 m a. With what velocity must Madeline kick the ball in order for the ball to reach Emily? b. How long does it take the ball to reach Emily? c. What is the magnitude and direction of the total velocity of the ball just as it reaches Emily? d. What is the maximum height reached by the ball relative to the ground? 2. A mass M 1 is on an inclined plane that makes an angle of 30.0 degrees with the horizontal. M 1 is attached by a string and frictionless pulley to M 2. Both masses are 5.0 kg, and the coefficient of kinetic friction of Ignore the mass of the string and pulley. a. Draw a free-body diagram for M 1. b. Draw a free-body diagram for M 2. c. Calculate the acceleration of the masses. d. If M 2 is initially 1.4 m above the ground, how long until it reaches the ground? 3

4 3. A lead bullet with mass m bullet =0.010 kg and initial velocity v 0 =90.0 m/s is fired at a block of wood at mass m wood =1.000 kg. Both the bullet and wood block are initially at a temperature of C. a. The bullet is embedded in the block of wood. What is the velocity of the bullet and block after the collision? b. What is maximum height, h, reached by the wood and bullet? c. How much energy was lost to heat during collision of bullet and pendulum? d. If the heat lost is completely transferred to the wood block, how much does its temperature increase? 4. A star with the same mass and size as the sun has only 1 planet orbiting it. The planet is twice the mass of earth and is located twice as far from its star as the earth is from the sun. a. Calculate the gravitational force between the star and the planet. b. How fast is the planet moving around its star? c. How long does it take for planet to complete one orbit around star? d. The star rotates on its axis once every 30. days. At the end of its life, the star will collapse to become a white dwarf which is the same size as earth. What is the white dwarf s period of rotation? 5. A cylinder and a hoop, both of mass M and radius R, are released from rest from the top of an inclined plane at a height h above the ground. The length of the incline is L. h L a. Calculate the final velocities of the cylinder and hoop when they reach the bottom of the incline. Which arrives at the bottom of the incline first? b. Calculate the linear acceleration of the hoop and the cylinder. c. Calculate the angular acceleration of the hoop and the cylinder. 4

5 6. This question consists of two unrelated sections. a. Calculate the true mass (in a vacuum) of a piece of aluminum whose apparent mass is kg when weighed in air. b. If wind blows with a velocity of 50.0 m/s over a house, what is the net force on the roof if its area is 250. m 2 and it is flat? 7. A window washer is cleaning the 2 nd -floor windows of Roger Bacon. The window washer is standing on a wood plank that is 2.0 m long and is 0.5 m from the left edge. The wood plank is supported by two ropes, which are tied to each end of the board. The washer has a mass of 65 kg and the wood plank has a mass of 7.0 kg. 0.5 m 2.0 m a. Draw a diagram of the board and label all the forces acting on it. b. What are the conditions that are required to keep the window washer and board in equilibrium? c. Find the tension in each rope. 8. A 2.5 kg mass is hung from a spring and the spring stretches 0.10 m m a. Draw a free-body diagram of the mass. b. Calculate the spring constant, k. c. The mass is then displaced 0.15 m from this equilibrium and released. Calculate the period of oscillation. d. Sketch the position of the mass as a function of time. e. When will the mass cross equilibrium position? f. What is total energy of the system? g. What is the velocity of the mass when it is 0.02 m from its equilibrium position? 5

6 You must complete questions 9 and A 100.-g block of ice at C is placed in an aluminum calorimeter with 1.20 kg of water. The mass of the aluminum is 1.00 kg. The water and aluminum are initially at 20 0 C, and the system then comes to equilibrium. a. What is the equilibrium temperature? b. At equilibrium temperature, how many molecules of liquid water are present? 10. Consider the following two-step process. Heat is allowed to flow out of one mole of ideal gas at constant volume so that its pressure drops from 4.05 x 10 5 N/m 2 (point a) to 1.52 x 10 5 N/m 2 (point b). Then the gas expands at constant pressure, from a volume 6.0 x 10-3 m 3 to 9.5 x 10-3 m 3. a. Calculate the temperature at points a, b, and c. b. Calculate the total change in internal energy as the gas goes from state a to c. c. Calculate the total work done by the gas from a to c. d. Calculate the total heat flow into or out of the gas as the gas goes from state a to c. e. Calculate the average for the three temperatures that you found in part a. Use this average temperature of points a, b, and c to estimate the total change in entropy of the gas as it goes from state a to state c. f. Assume that the highest and lowest temperatures from part a are the operating temperatures of an engine and that the engine operates at 40% of the ideal efficiency. Calculate is the efficiency of the engine. 6