Transcript Momentum
Momentum and Impulse Collisions Center of Mass http://ia300128.us.archive.org/2/it ems/AP_Physics_C_Lesson_11/Cont ainer.html Momentum and Newton’s Second Law F ma F F F dv m dt d ( mv ) dt dp dt Net Force is the rate change of momentum! Momentum Defined Linear momentum is the product of mass and velocity. p mv Impulse The impulse of the net force, denoted by J, is defined to be the product of the net force and the time interval. Impulse is equivalent to change in momentum. This equation assumes constant net force. J Ft Non-uniform Net Force The force equation is time dependent. J t2 t1 Fdt Collisions Elastic Objects bounce off of each other Kinetic energy is conserved if the collision is completely elastic Inelastic Objects stick to each other Kinetic Energy is not conserved Elastic Collision Momentum Conservation Momentum is conserved if the vector sum of the external forces acting on the system of particles is zero. If this is not the case you cannot use conservation of momentum. Problem A marksman holds a rifle of mass 3.00 kg loosely in his hands, so as to let it recoil freely when fired. He fires a bullet of mass 5.00 g horizontally with a velocity relative to the ground of 300 m/s. What is the recoil velocity of the rifle? What are the final momentum and kinetic energy of the bullet? Of the rifle? Inelastic Collision Boxing and Brain Injury In boxing matches of the 19th century, bare fists were used. In modern boxing, fighters wear padded gloves. How do gloves protect the brain of the boxer from injury? Also, why do boxers often “roll with the punch”? Explanation The brain is immersed in a cushioning fluid inside the skull. If the head is struck suddenly by a bare fist, the skull accelerates rapidly. The brain matches this acceleration only because of the large impulsive force exerted by the skull on the brain. This large and sudden force (large Fav and small Δt) can cause severe brain injury. Padded gloves extend the time over which the force is applied to the head. For a given impulse, a glove results in a longer time interval than a bare fist, decreasing the average force. Explanation The brain is immersed in a cushioning fluid inside the skull. If the head is struck suddenly by a bare fist, the skull accelerates rapidly. The brain matches this acceleration only because of the large impulsive force exerted by the skull on the brain. This large and sudden force (large Fav and small Δt) can cause severe brain injury. Padded gloves extend the time over which the force is applied to the head. For a given impulse, a glove results in a longer time interval than a bare fist, decreasing the average force. Example Problem In a crash test, a car of mass 1.50 x 103 kg collides with a wall and rebounds. The initial and final velocities of the car are vo=-15.0 m/s and v =2.60 m/s, find a) the impulse delivered to the car due to the collision and b) the size and direction of the average force exerted on the car. Injury in Automobile Collisions The main injuries that occur to a person in an accident occur when the person hits the interior of the car. They include: brain damage, bone fracture, trauma to the skin, blood vessels and internal organs. Continued If a collision lasts for less than 70 ms a person will survive if the whole-body impact pressure (F/A) is less than 1.9 x 105 N/m2 (28 lb/in2). Death results in 50% of cases in which the whole-body impact pressure reaches 3.4 x 105 N/m2 (50 lb/in2). Example A 75 kg person not wearing a seat belt traveling at 27 m/s (60 mi/h) who comes to rest in 0.010 sec after striking an unpadded dash board. What is his whole-body impact pressure? Answer mv mvo Fav t 0 27m / s Fav 0.010s 5 Fav 2.0 x10 N v a t 0 27m / s a 0.010s a 2700m / s2 2700m / s2 / 9.8m / s2 280 g ' s Answer Continued 5 Fav 2.0 x10 N 5 2 4 x10 N / m 2 A 0.5m What happens to him? This exceeds the threshold—an unprotected collision at 60 mi/h is almost certainly fatal. This force is twice the force to break the tibia, the acceleration can cause serious brain damage even in the absence of a skull fracture. What happens to him? This exceeds the threshold—an unprotected collision at 60 mi/h is almost certainly fatal. This force is twice the force to break the tibia, the acceleration can cause serious brain damage even in the absence of a skull fracture.