LECTURE 15 MOMENTUM AND IMPULSE. Lecture Instructor: Kazumi Tolich

Transcription

1 LECTURE 15 MOMENTUM AND IMPULSE Lecture Instructor: Kazumi Tolich

2 Lecture 15 2 Reading chapter 9-1 to 9-4 Momentum n Newton s 2 nd law with momentum n Conservation of momentum Impulse n Impulse-momentum theorem

3 Momentum 3 Linear momentum or just momentum is defined to be p = mv Momentum of a particle can be thought of as its quantity of motion, or amount of effort needed to bring the particle to rest. If a system consists of multiple particles, the total momentum of the system is the vector sum of momentum of each particle: p %&%'( = p ) + p ) + p +

4 Quiz: 1 4 Which of the following statements regarding kinetic energy and linear momentum is/are true? Choose all that apply. A. The total kinetic energy of two moving objects can be zero. B. The total momentum of two moving objects can be zero. C. The kinetic energy of a system can be transformed into other forms of energy. D. The kinetic energy of a system can be transformed into linear momentum. E. The linear momentum can be transformed into kinetic energy. F. If the kinetic energy of a system increases, the momentum of the system also must increase.

5 Quiz: 15-1 answer 5 A. The total kinetic energy of two moving objects can be zero. The kinetic energy of a moving object is always a positive scalar. B. The total momentum of two moving objects can be zero. Momentum is a vector. If the momenta are pointing in the opposite directions with the same magnitude, the total momentum is zero. C. The kinetic energy of a system can be transformed into other forms of energy. The kinetic energy of an object can be transformed into potential energy, internal energy etc. D. The kinetic energy of a system can be transformed into linear momentum. E. The linear momentum can be transformed into kinetic energy. Momentum and kinetic energy are both associated with moving objects, but do not transform into each other. F. If the kinetic energy of a system increases, the momentum of the system also must increase. Can you keep the number of oranges in the basket constant while you keep eating the apples in it? Of course you can.

6 Law of conservation of momentum/demo: 1 6 In Principia (1687), Newton presents the second law of motion in terms of momentum. - F = p t This is equivalent to F = ma in less general case where m is constant. The law of conservation of momentum states: If F = 0, then p is constant Multiple particles in a system can exert internal forces on each other, but since they always sum up to zero, the total momentum of the system is conserved as long as there is no external force acting on the system. Demo: Reaction Gliders on Air Track

7 Example: 1 7 Meteor Crater in Arizona is thought to have been formed by the impact of a meteor with Earth some 50,000 years ago. The mass of the meteor is estimated at m 6 = kg, and its speed at v 6 = m/s. What speed would such a meteor impart to Earth in a head-on collision? Meteor Crater: 1200 m in diameter, 170 m deep

8 Example 2 8 A railroad flatcar of weight W can roll without friction along a straight horizontal track. Initially a man of weight w is standing on the car, which is moving to the right with speed v :. What is the change in velocity of the car if the man runs to the left so that his speed relative to the car is v ;<(?

9 Example 3 9 A radioactive nucleus, initially at rest, decays by emitting an electron and a neutrino perpendicular to each other. The linear momentum of the electron is p < = kg m/s y>, and that of the neutrino is p? = kg m/s x>. Find the direction and magnitude of the linear momentum of the nucleus as it recoils from the decay.

10 Impulse 10 When two objects collide, they usually exert very large forces on each other for a very brief time, and such forces are called impulsive forces. The impulse applied to an object during a collision changes its momentum (Momentumimpulse theorem). I = F 'B t = p

11 Quiz: 2 A paratrooper whose chute fails to open lands in snow. Had he landed on bare ground, the collision would be lethal. Which of the following statements is/are correct? Choose all that apply. A. The stopping time is longer for landing in snow. B. The stopping time is shorter for landing in snow. C. The stopping time is unchanged for landing in snow. D. The impulse to the paratrooper is greater for landing in snow. E. The impulse to the paratrooper is smaller for landing in snow. F. The impulse to the paratrooper is unchanged for landing in snow. G. The average force on the paratrooper is greater for landing in snow. H. The average force on the paratrooper is smaller for landing in snow. I. The average force on the paratrooper is unchanged for landing in snow.

12 Quiz: 15-2 answer/demo: 3 The stopping time is longer for landing in snow. The impulse to the paratrooper is unchanged for landing in snow. The average force on the paratrooper is smaller for landing in snow. The duration of the collision is elongated by the snow. The impulse is the change in momentum: I = p. The initial momentum is the momentum of the paratrooper just before he hits the snow, and the final momentum is zero because he eventually stops. The average force by the snow on him is smaller because p = F 'B t. Demo: Egg in Sheet Air bags increase the time interval during which the passenger is brought to rest, decreasing the force on (and resulting injury to) the passenger.

13 Quiz: 3 13 A basket ball flew toward your face and collided with it. And a few seconds later a bowling ball flew toward your face at the same speed as the basket ball and collided with your face. Assuming the collision times are the same, which of the following statements is/are correct? Choose all that apply. A. The impulse to your face is greater for the bowling ball. B. The impulse to your face is smaller for the bowling ball. C. The impulse to your face is the same for both balls. D. The average force on your face is greater for bowling ball. E. The average force on your face is smaller for bowling ball. F. The average force on your face is the same for both balls.

14 Quiz: The impulse is greater for bowling ball. The average force on your face is greater for bowling ball. Having more mass, bowling ball would have more momentum when flying: p = mv. To stop the balls you need to apply impulse to the ball. Since impulse is equal to change in momentum, the greater impulse is required to stop the bowling ball: I = p. You need to exert more force on the bowling ball: I = F 'B t. From Newton s 3rd law, the bowling ball would exerting the same force on you. This is why you are (or at least you should be) more scared if someone throws a bowling ball at you than a basket ball at the same speed.

15 Long legs and jumping 15 A frog making a jump wants to gain as much momentum, therefore impulse, I = F 'B t, delivered to it, as possible before leaving the ground. There is a maximum force that the muscle can exert, limiting F 'B. The time interval t over which the force is exerted can be increased by having long legs. Many good jumpers have long legs.

16 Example: 4 16 In a typical golf swing, the club is in contact with the ball for about 1.0 ms. If the 45-g ball acquires a speed of 67 m/s, estimate the magnitude of the force exerted by the club on the ball.