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Chapter 9 : Linear Momentum 8-5 The Law of Conservation of Energy Problem 38 38.(II) A 180-g wood block is firmly attached to a very light horizontal spring, Fig. 8–35. The block can slide along a table where the coefficient of friction is 0.30. A force of 25 N compresses the spring 18 cm. If the spring is released from this position, how far beyond its equilibrium position will it stretch on its first cycle? 8-7 Gravitational Potential Energy and Escape Velocity Far from the surface of the Earth, the force of gravity is not constant: The work done on an object moving in the Earth’s gravitational field is given by: 8-7 Gravitational Potential Energy and Escape Velocity Because the value of the work depends only on the end points, the gravitational force is conservative and we can define gravitational potential energy: 8-7 Gravitational Potential Energy and Escape Velocity Example 8-12: Package dropped from high-speed rocket. A box of empty film canisters is allowed to fall from a rocket traveling outward from Earth at a speed of 1800 m/s when 1600 km above the Earth’s surface. The package eventually falls to the Earth. Estimate its speed just before impact. Ignore air resistance. The radius of the earth is 6380km, and the mass of the earth is 5.98X1024kg 8-7 Gravitational Potential Energy and Escape Velocity Problem 50: (II) Two Earth satellites, A and B, each of mass of 950kg are launched into circular orbits around the Earth’s center. Satellite A orbits at an altitude of 4200 km, and satellite B orbits at an altitude of 12,600 km. (a) What are the potential energies of the two satellites? (b) What are the kinetic energies of the two satellites? (c) How much work would it require to change the orbit of satellite A to match that of satellite B? The radius of the earth is 6380km, and the mass of the earth is 5.98X1024kg 8-7 Gravitational Potential Energy and Escape Velocity If an object’s initial kinetic energy is equal to the potential energy at the Earth’s surface, its total energy will be zero. The velocity at which this is true is called the escape velocity; for Earth: it is also the minimum velocity that prevent an object from returning to earth. 8-8 Power Power is the rate at which work is done. Average power: Instantaneous power: In the SI system, the units of power are watts: 8-8 Power Power is the rate at which energy is transformed Units: Joules/s or Watts, W In the British system, the basic unit for power is the foot-pound per second, but more often horsepower is used: 1 hp = 550 ft·lb/s = 746 W. Puzzler: kilowatt·hours [kW·h] are units of what quantity? 8-8 Power Example 8-14: Stair-climbing power. A 60-kg jogger runs up a long flight of stairs in 4.0 s. The vertical height of the stairs is 4.5 m. (a) Estimate the jogger’s power output in watts and horsepower. (b) How much energy did this require? 8-8 Power Example 8-15: Power needs of a car. Calculate the power required of a 1400-kg car under the following circumstances: (a) the car climbs a 10° hill (a fairly steep hill) at a steady 80 km/h; and (b) the car accelerates along a level road from 90 to 110 km/h in 6.0 s to pass another car. Assume that the average retarding force on the car is FR = 700 N throughout. 9-1 Momentum and Its Relation to Force Momentum is the property of a moving object to continue moving Momentum is a vector symbolized by the symbol p and is defined as The rate of change of momentum is equal to the net force: This can be shown using Newton’s second law. Momentum, p Vector units: kg.m/s Bowling Ball vs. Tennis Ball p = mv Mass 7 kg 57 g Speed 9 m/s 60 m/s 63kg.m/s 3.42kg.m/s momentum 9-1 Momentum and Its Relation to Force Example: A system consists of three particles with these masses and velocities: mass 3.0 kg moving west at 5.0 m/s; mass 4.0 kg moving west at 10.0 m/s; and mass 5.0 kg moving east at 20.0 m/s. What is total momentum of the system? 9-1 Momentum and Its Relation to Force Example 9-1: Force of a tennis serve. For a top player, a tennis ball may leave the racket on the serve with a speed of 55 m/s (about 120 mi/h). If the ball has a mass of 0.060 kg and is in contact with the racket for about 4 ms (4 x 10-3 s), estimate the average force on the ball. Would this force be large enough to lift a 60-kg person? 9-1 Momentum and Its Relation to Force Example 9-2: Washing a car: momentum change and force. Water leaves a hose at a rate of 1.5 kg/s with a speed of 20 m/s and is aimed at the side of a car, which stops it. (That is, we ignore any splashing back.) What is the force exerted by the water on the car? 9-2 Conservation of Momentum During a collision, measurements show that the total momentum does not change: 9-2 Conservation of Momentum Conservation of momentum can also be derived from Newton’s laws. A collision takes a short enough time that we can ignore external forces. Since the internal forces are equal and opposite, the total momentum is constant. 9-2 Conservation of Momentum This is the law of conservation of linear momentum: when the net external force on a system of objects is zero, the total momentum of the system remains constant. Equivalently, the total momentum of an isolated system remains constant. 9-2 Conservation of Momentum Example 9-4: Rifle recoil. Calculate the recoil velocity of a 5.0-kg rifle that shoots a 0.020-kg bullet at a speed of 620 m/s. ( 9-2 Conservation of Momentum Problem 12:(I) A 130-kg tackler moving at 2.5m/s meets head-on (and tackles) an 82-kg halfback moving at 5.0m/s. What will be their mutual speed immediately after the collision?