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Physics Work, Energy, and Momentum Unit Day 1: Objective 7.2.1 1. Example: During winter break you enter a dogsled race across a frozen lake. To get started, you pull the sled (m = 80 kg) with a force of 180 N at20° above the horizontal. You pull the sled 5 m. Find the amount of work you do on the sled. 2. A truck of mass 3000 kg is to be loaded onto a ship by a crane that exerts an upward force of 31 kN on the truck. This force is applied over a distance of 2 m. Find the work done by the crane on the truck. Homework: Day 2: Chapter 7: E 1 – 3, 5 Objective 7.3.1 3. A 4-kg block on a frictionless table is attached to a horizontal spring with a force constant of 400 N/m. The spring is initially compressed with the block at x1 = -5 cm. Find the work done on the block as the block moves to its equilibrium position x2 = 0 4. To stretch a spring 3.00 cm from its unstretched length, 12.0 J of work must be done. How much work must be done to compress this spring 4.00 cm from its unstretched length? Homework: Chapter 7: Q 1 – 3; E 10 Days 3 and 4: Objective 7.4.1 5. During your winter break you enter a dogsled race across a frozen lake. To get started you pull the sled (m = 80 kg) with a force of 180 N at 20° above the horizontal. You pull the sled for 5 m. Find the work you do and the final speed of the sled. 6. A truck of mass 3000 kg is to be loaded onto a ship by a crane that exerts an upward force of 31 kN on the truck. This force is applied over a distance of 2 m. Find a) the work done by the crane on the truck, b) the total work done on the truck, and c) the upward speed of the truck after the 2 m if it started from rest 7. A 4-kg block on a frictionless table is attached to a horizontal spring with a force constant of 400 N/m. The spring is initially compressed with the block at x1 = -5 cm. Find a) the work done on the block as the block moves to its equilibrium position x2 = 0 and b) the speed of the block at x2=0 Homework: Chapter 7: Q 5, 11; E 13, 15, 17 Physics Work, Energy, and Momentum Unit Days 5 and 6: Objective 7.5.1, 7.6.1 8. Example: Standing near the edge of the roof of a 12-m high building, you kick a ball with an initial speed of vi = 16 m/s at an angle of 60° above the horizontal. Neglecting air resistance, use conservation of energy to find how high above the height of the building the ball rises and its speed just before it hits the ground. 9. You try: You throw a 0.200-kg ball straight up in the air, giving it an initial upward velocity of 20.0 m/s. Use conservation of energy to find how high it goes. 10. Example: A child of mass 40 kg goes down an 8.0 m long slide inclined at 30° above the horizontal. The coefficient of kinetic friction between the slide and the child is 0.35. If the child starts from rest at the top of the slide, how fast is she traveling when she reaches the bottom? 11. On your own: A pendulum consists of a bob of mass m attached to a string of length L. The bob is pulled aside so that the string make an angle q0 with the vertical, and is released from rest. Find an expression for its speed as it passes through the bottom of the arc. 12. Example: A 1.20-kg piece of cheese is placed on a vertical spring of negligible mass and force constant k = 1800 N/m that is compressed 15.0 cm. When the spring is released, how high does the cheese rise from its initial position? (The spring and the cheese are not attached.) 13. On your own: A 2000-kg elevator with broken cables is falling at 25 m/s when it first contacts a cushioning spring at the bottom of the shaft. The spring is supposed to stop the elevator, compressing 3.00 m as it does so. During the motion, a safety clamp applies a constant 17,000 N frictional force to the elevator. What is the force constant of the spring? Homework: Day 9: Chapter 7: Q 6, 9, 10; E 23, 24, 26, 28, 29, 36, 38, 40, 42 Objective 7.8.1 14. Example: Force A does 5 J of work in 10 s. Force B does 3 J of work in 5 s. Which force delivers greater power? 15. On your own: A 5-kg box is being lifted upward at a constant velocity of 2 m/s by a force equal to the weight of the box. What is the power input of the force? How much work is done by the force in 4 s? Homework: Day 11: Chapter 7: E 44, 46, 47 Objective 8.1.1, 8.1.2, 8.2.1 16. Example: A 45-g golf ball initially at rest is given a speed of 25.0 m/s when a club strikes. If the club and ball are in contact for 2.00 ms, what average force acts on the ball? Physics Work, Energy, and Momentum Unit 17. On your own: A 0.160-kg hockey puck is moving on an icy, frictionless, horizontal surface. At t = 0 the puck is moving to the right at 3.00 m/s. Calculate the velocity of the puck after a force of 12.0 N directed to the left has been applied for 0.050 s. 18. A runaway 14,000 kg railroad car is rolling horizontally at 4 m/s toward a switchyard. As it passes by a grain elevator, 2000 kg of grain are suddenly dropped into the car. How long does it take the car to cover the 500-m distance from the elevator to the switchyard? Neglect friction and air drag. Homework: Day 12: Chapter 8: Q 1, 3, 4; E 1, 2, 4, 7, 9 Objective 8.2.1 19. On your own: During repair of the Hubble Space Telescope, an astronaut replaces a damaged solar panel. Pushing the detached panel away into space, she is propelled in the opposite direction. The astronaut’s mass is 60 kg and the panel’s mass is 80 kg. The astronaut is at rest relative to the spaceship when she shoves away the panel, and she shoves it at 0.3 m/s relative to the spaceship. What is her subsequent velocity relative to the spaceship? 20. A 2.0-kg ball, A, is moving at a velocity of 5.0 m/s. It collides with a stationary ball, B, also of mass 2.0 kg. After the collision, ball A moves off in a direction of 30° to the left of its original direction. Ball B moves off in a direction of 90° to the right of ball A’s final direction. Find the speeds of the balls after the collision. 30 ° A B 90° Physics Work, Energy, and Momentum Unit 21. A hockey puck B rests on a smooth ice surface and is struck by a second puck, A, which was originally traveling at 40.0 m/s and which is deflected 30.0° from its original direction. Puck B acquires a velocity at a 45.0° angle to the original direction of A. The pucks have the same mass. Compute the speed of each puck after the collision. 30 ° A B Homework: Day 13: 45° Chapter 8: Q 5, 6; E 8, 10, 11, 16 Objective 8.4.1 22. Example: In a feat of public marksmanship, you fire a bullet of mass m1 into a hanging block of mass m2. The block, with the bullet embedded, swings upward. Noting the height, h, reached at the top of the swing, you inform the crowd of the bullet’s speed. How fast was the bullet traveling before it hit the block? 23. On your own: In Dallas, the morning after a winter ice storm, a 1400-kg automobile going west at 35.0 km/h collides with a 2800-kg truck going south at 50.0 km/h. If they become coupled on collision, what are the magnitude and direction of their velocity after colliding? 24. On your own: A neutron of mass mn and speed vn1 collides elastically with a carbon nucleus of mass mc initially at rest. What are the final velocities of both particles? Homework: Day 14: Chapter 8: E 17, 21, 22, 24, 25 Objective 8.4.1 25. Example: Find the center of mass of the Earth-Sun system. The distance between 11 30 their centers is 1.49 x 10 m. The mass of the Sun is 1.99 x 10 kg. The mass of 24 the Earth is 5.98 x 10 kg. Homework: Chapter 8: Q 7, 8; E 27 – 29 Physics Work, Energy, and Momentum Unit Review: Chapter 7: P 55, 56, 58, 61, 70 Chapter 8: 1. A 2300 kg car, moving at 15 m/s, collides with a bridge abutment, which stops it in 0.56 s. What is the average force that acts on the car during impact? 2. It is well known that bullets and other missiles fired at Superman simply bounce off his chest. Suppose that a gangster sprays Superman’s chest with 3 g bullets at the rate of 100 bullets/min, and the speed of each bullet is 500 m/s. Suppose too that the bullets rebound straight back at 500 m/s. What is the magnitude of the average force on Superman’s chest from the stream of bullets? 3. A 4-kg block moving right at 6 m/s collides elastically with a 2-kg block moving right at 3 m/s. Find their final velocities. 4. An alpha particle with a mass of 4.0 amu (atomic mass units) collides with an oxygen nucleus with a mass of 16 amu that is initially at rest. The alpha particle is scattered at an angle of 64.0 degrees from its initial direction of motion, and the oxygen nucleus recoils at an angle of 51.0 degrees on the opposite side of that initial direction. The final speed of the nucleus is 1.20 x 105 m/s. Find the final and initial speeds of the alpha particle. 5. In a pool game, the cue ball, which has an initial speed of 10 m/s, makes an elastic collision with the eight ball, which is initially at rest. After the collision, the cue ball moves at an angle of 60° to the left of its initial velocity. The eight ball moves at an angle of 30° to the right of the cue ball’s initial velocity. What is the speed of each ball after the collision? Each ball has a mass of 0.17 kg. 6. You are at the wheel of a 1200-kg car traveling east through an intersection when a 3000-kg truck traveling north through the intersection crashes into your car. Your car and the truck stick together after impact, and skid at an angle of 59° north of east. The driver of the truck claims that you were at fault because you were speeding. You look for evidence to disprove this claim. First, there were no skid marks, indicating that neither you nor the truck driver saw the accident coming and braked hard; second, there is a sign reading “Speed limit 80 km/h” on the road you were driving on; and third, the speedometer of the truck was smashed with the needle stuck at 50 km/h, indicating that the truck’s speed at impact was 50 km/h. Does this evidence support or disprove the claim that you were speeding? 7. Three particles with masses 1.2 kg, 2.5 kg, and 3,4 kg form an equilateral triangle of edge length a = 140 cm. Where is the center of mass of this three particle system? 8. A distance of 1.131 x 10-10 m lies between the centers of the carbon and oxygen atoms in a carbon monoxide molecule. Locate the center of mass of the molecule relative to the carbon atom. Carbon has a mass of 12 amu (atomic mass units) and oxygen has a mass of 16 amu.