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CH. 3 Energy and Conservation Laws 3.1 Conservation Laws: The total mass in an isolated system is constant 3.2 Linear momentum: The mass of an object times its velocity, P = mv 무거운 물체가 같은 속도로 움직이는 가벼운 물체보다 운동량이 더 크다 자전거와 사람의 질량: 80kg 자동차의 질량: 1,200kg 속력: 10m/s 자전거의 운동량: p mv 80kg 10m / s 800kgm / s 자동차의 운동량: p mv 1,200kg 10m / s 12,000kgm / s Newton’s second Law of Motion 운동량의변화 force 시간의 변화 (mv) F t If the mass of the object stays constant, (mv) v F m ma t t (mv) Ft : impulse The tennis racquet exerts a large force on the tennis ball for a short time. Ex 3.1 m = 0.06kg, v = 40m/s ( mv) mv 0 0.06kg 40m / s 2.4kg m / s t 0.005s (mv) 2.4kg m / s F 480 N t 0.005s Law of Conservation of Linear Momentum : The total linear momentum of an isolated system is constant. The total linear momentum of the objects in the system before the collision is the same as the total linear momentum after the collision. The most important use of the linear momentum conservation law is in the analysis of collisions. 당구공, 자동차, 스케이터 Ex 3.2 m1 1,000kg, m2 1,500kg m v 1,000kg v 1 1 1 v1 ?, v2 0 충돌후 v 4m/s (m1 m2 )v 2,500kg 4m / s 2,500kg 4m / s v1 10m / s 1000kg A bullet becomes embedded in a block of wood. If the speed of the block and the masses of the block and the bullet are measured, the initial speed of the bullet can be computed using the conservation of linear momentum. mv1 (m M )v2 m v2 v1 mM The mass of the cart on the right cart 2, is three times the mass of the cart on the left, cart 1. After the spring is released, the speed of the lighter cart is three times the speed of the more massive cart. (mv)전 (mv)후 (mv)전 0 (mv)후 0 m1v1 m2 v2 m1 v1 m2 v2 m2 v1 v2 m1 v1 m2 v2 m1 The ratio of the speeds of the two carts is the inverse of the ratio of their masses. Conservation of Liner Momentum: Newton’s third law of motion The skater and the snowball have the same amount of momentum but in opposite direction. 3.3 Work: The Key to Energy FL d L FR d R 들어올리는 힘 x 높이 = 굴리는 힘 x 경사로의 길이 Frolling d rolling Flifting d lifting Work: The force that acts times the distance moved in the direction of the force: 1J 1N m work = Fd Ex 3.3 Because of friction, a constant force of 100 N is needed to slide a box across a room. If the box moves 3 m, how much work is done? Work = Fd = 100N 3m = 300Nm = 300J Ex 3.4 The barrel has a mass of 30kg and the height of the dock is 1.2m. How much work would you do when lifting the barrel? F = W = mg = 30kg x 9.8m/s2 = 294N work = Fd = Wd = 294N x 1.2m = 353J Ex 2.2 v 27m / s 0m / s a 2.7m / s 2 t 10s F ma 1,000kg 2.7m / s 2 2,700 N Ex 3.5 How much work is done? 10초 동안 2.7m/s2로 가속되었으므로, 1 2 1 d at (2.7m / s)(10s ) 2 135m 2 2 work = Fd = 2,700N x 135m = 364,500J The force is always toward the center of the circle and perpendicular to the object’s velocity at each instant. Therefore, the force does not do work on the object. Work is also done when a force causes something to slow down. When you catch a ball, your hand exerts a force on the ball. As the ball slows down, it pushes your hand back with equal and opposite force. In this case, the ball does work on your hand. The work that the force of gravity does on an object as it falls is equal to the work that was done to lift the object the same distance. 3.4 Energy: The measure of a system’s capacity to do work. Kinetic Energy: Energy due to motion. 1 2 KE mv 2 Ex. 3.6 1,000kg의 차가 정지상태 에 27m/s로 가속된다 The car’s kinetic energy when it is traveling 27m/s is 1 KE 2 mv 2 1 1,000kg (27m / s ) 2 2 500kg 729m 2 / s 2 364,500 J A spinning dancer(far left) has kinetic energy, even though she stays in one place. This transparent toy car (left) and shaver (right) use rotational kinetic energy stored in spinning flywheels. Potential Energy: Energy due to an object’s position or orientation. PE= work done = weight x height = Wd=mgd Ex 3.7 3kg brick is lifted to a height of 0.5m above a table. Its positional energy relative to the table is PE = mgd = 3kg 9.8m / s 2 0.5m 14.7 J Its potential energy to the floor is PE=mgd= 3kg 9.8m / s 2 1.5m 44.1J The potential energy of golf ball A is positive relative to the ground. The potential energy of B is zero and that of c is negative because it is below ground level. Balls A and b can move horizontally while C is restricted to the hole. Elastic potential energy Olympic archer Joanne Edens. While pulling the bowstring back, she does work bending the bow. This gives the bow elastic potential energy. This mechanical bird uses energy stored in the rubber band inside. Patricia is holding the crank used to wind it up. 3.5 The Conservation of Energy Energy cannot be created or destroyed, only converted from one form to another. Therefore, the total energy in an isolated system is constant. This wind generator converts kinetic energy of the wind into electrical energy plus some internal energy because of friction. A basketball rolls off the rim and falls to the floor. Initially, it has potential energy only. As it falls, its potential energy decreases as its kinetic energy increases. Just before it hits the floor, it has kinetic energy only. At each point as it falls, its total energy, kinetic plus potential, is the same, 18 joules. E KE PE 일정 공이 떨어지기 시작할 때( KE 0) E KE PE PE PE mgd 공이 마루에 닿는 순간( PE 0) E KE PE KE KE 1 2 mv 2 The potential energy the object had when it was released equals the kinetic energy it has just before impact. 1 2 mv mgd 2 2 v 2 gd v 2 gd Ex 3.8 The height of the falls is about 53m.Estmiate their speed when they hit the water at the bottom of the falls. v 2 gd 2 9.8m / s 2 53m 1039m 2 / s 2 32.2m / s As a roller coaster travels down a hill, its potential energy is converted into kinetic energy. If there is no friction, its kinetic energy at the bottom equals its potential energy at the top. Its speed at the bottom is the same as that of an object dropped from the same height. 1 2 mv mgd 2 v 2 2 gd v 2 gd The motion of a pendulum involves the continuous conversion of gravitational potential energy in kinetic energy and back again. A golf ball at rest in the small valley has negative potential energy. Hitting the golf ball gives it kinetic energy but it oscillates inside the valley if its total energy is negative, (a) and (b). If the golf ball is given enough kinetic energy to make its total energy zero, it rolls out of the valley and stops (c). 3.6 Collisions: An Energy Point of View An Elastic Collision is one in which the total kinetic energy of the colliding bodies after the collision equals the total kinetic energy before the collision. An Inelastic Collision is one in which the total kinetic energy of the colliding bodies after collision is not equal to the kinetic energy before. The total kinetic energy after can be greater than, or less than, the total kinetic energy before. Ex 3.9 Compare the amount of kinetic energy in the system before and after the collision. 1 KE전 1,000kg (10m / s ) 2 2 50,000 J 1 2 KE후 2,500kg (4m / s ) 2 20,000 J 30,000J (60%) of the kinetic energy before the collision was converted into other forms of energy. A cart 2 has energy stored in its spring-loaded plunger. When this cart is struck by cart 1, this potential energy is converted into kinetic energy, which then shared by both carts. The total kinetic energy after the collision is greater than the total kinetic energy before the collision. Elastic collisions involving the force of gravity (and no physical contact) are used in the space exploration. Called the slingshot effect or gravity assist, the technique involves having a spacecraft overtake a planet and pass it on its side away from the Earth. Gravitational Slingshot Effect - YouTube.url 3.3 Power: The rate of doing work. The rate at which energy is transferred or transformed. Work done divided by the time. Energy transferred divided by the time. P[watt] =W[J]/t[s] 예) 지게차로 1ton의 벽돌을 1.2m의 높이에 싣는 경우 m 1ton 103 kg d 1.2m W Fd 103 kg 9.8m / s 2 1.2m 11,760 J t 10 s, W 11,760 J P t 10 s 1,176 J / s 1,176W A 60W light bulb uses electrical energy at the rate of 60 J each second. A 1,600 W hair dryer uses 1,600 J of energy each second. 1 hp=746W Ex 3.10 We can determine the required power output of the engine. The work, 364,500 J, is done in 10 s. Hence the power is P=일/시간 = 364,500J/10s =36,450W=48.9hp The human body has a maximum power output that varies greatly from person to person. In the act of jumping, an outstanding athlete can develop more than 8,000 W, but only for a fraction of a second. The same person would have a maximum of less than 800W if the power level had to be maintained for an hour. The average person can produce 800W or more for a few seconds and perhaps 100-200 W for an hour or more. The Gossamer Albatross, 2시간 49분 동안 250W의 출력 To measure your power output when going up a flight of stairs, multiply the height of the stairs by your weight, and divides this by the times it takes you to climb the stairs. P=mgh/t 3.5 Rotation and Angular Momentum Law of Conservation of Angular Momentum: The angular momentum of an isolated system is constant. L= rxP=mvr(원궤도) A satellite in orbit about the Earth is twice as from the Earth’s center at point A as it is at point B. Conservation of angular momentum then tells us that its speed at A is one-half its speed at B. Conservation of angular momentum L mvr The person spins faster when the weight are pulled in closer to the body because angular momentum is conserved. Ch. 3 1. Questions: 3, 6 2. Problems: 6, 8, 15, 21, 22, 28, 33 3. Challenges: 4