1、Chapter 9 Momentum and the Conservation of Momentum,Linear Impulse and Momentum Impulse-Momentum Theorem and Conservation of Momentum N-II Law for the Motion of the Center of Mass Systems of Variable Mass,9-1 Linear Impulse-Momentum Theorem, the impulse(沖量)of force,1. Impulse-momentum theorem,研究力和運(yùn)動(dòng)

2、的時(shí)間積累過(guò)程關(guān)系。,Net linear impulse delivered to a particle equals the change in linear momentum of the particle (物體在運(yùn)動(dòng)過(guò)程中所受合外力的沖量，等于該物體動(dòng)量的增量).,Descriptions:,(1) F should be the sum of all external forces. When the force is constant, the direction of J is as same as the force; if F is variable, the direct

3、ion of J is determined by the integral of .,(2) Both and are vectors. They have same units and dimensions. This theorem is only hold for IRF.,(3) In reality, one often use its component form:,(4) The magnitude of the impulse is equal to the area under the F(t) curve.,Look at Problem 28 of P227!,A pi

4、tched 140g baseball, in horizontal flight with a speed of 39m/s, is struck by a bat and the ball leaves the bat with a speed of 45m/s, at an upward angle上偏 of 30o (a) what impulse act on the ball? (b) If the impact time is 1.2ms, what average force act on the baseball.,(b),Example:,Momentum theorem

5、of particle system,There are N particles in a system. The equation of motion for particle i is,for the whole system is,9-2 Conservation of Momentum (P202),note, impulse-momentum theorem of particle system,The impulse of external forces acting on a system = the change of momentum of the entire system

6、.,If no net external force acts on a particles system, total linear momentum of the system cannot change.,No exceptions to this law have been discovered. So it is considered to be more fundamental than Newtons second law in both macroscopic and microscopic physical worlds.,(1) Conditions of validity

7、:,Net forces can be neglected in the case of collision, strike, explosion, ,and so on.,(2) Conclusion: Only external force can change the state of motion of a system.,(3) If component of net external force on a system along an axis is zero, the component of momentum of the system along that axis doe

8、s not change.,(4) It is only suitable for inertial reference frame.,Solution:,A gun mounted on wheels of mass M shoots a projectile of mass m with muzzle (出口) velocity of v (對(duì)炮車)at an angle above the horizontal. Find the horizontal recoil (反沖) speed V of the gun (求：炮車反沖速度V). (neglect friction),The r

9、ecoil speed:,Example:,Answer:,A flatcar of weight W can roll without friction along a horizontal straight track. Initially, a man of weight w is standing on the car, which is moving to the left with speed vo. What is the change in velocity of the car if the man runs to right so that his speed relati

10、ve to the car is vrel.,The direction of it is as same as the one of vrel.,Example:,The center of mass of N-particle system is a point that moves as though all of mass were concentra-ted there and all external forces were applied there.,Define the position of the center of mass (CM) of N-particle sys

11、tem to be:,Similar relations to the y and z components.,9-3 The Center of Mass,質(zhì)心運(yùn)動(dòng)定理,If a particle system exerted by zero force, the velocity of mass center keep constant.,N-II Law for the motion of the center of mass:,The sum of all forces acting on a system = total mass of the system times of its

12、 center of mass.,The center of mass of all parts of the bodies moves like a single particle acted by the same net external force gravity.,As figure shown, a boat L=4m, M=150kg. It is initially rest on the water. When a men, m=50kg, walks from the head to the tail of the boat, what are the distances

13、of the men and boat relative to the beach, respectively (人和船對(duì)岸各移動(dòng)的距離)neglect the friction from water.,Initial:,Final:,=constant,質(zhì)心初始靜止,Example:,Let and denote the velocity of boat and men relative to the beach at any instant, then,9-4 Systems of Variable Mass: Rocket Propulsion,As Fig. 9-33 shown, a

14、 system has changed in mass from M to M+dM in time dt, we have,With a little algebra and note,Then a dynamic equation for this system should be:,Look at examples in 9-10 after class.,Where, the two terms on its right side represents the sum of external force on the mass M and the force exerted on it due to the addition of mass.,For a rocket propulsion, The thrust (推力) of the rocket engine.,It depends on the desi