1984 chapter summaries

Force is equal to the rate of change of momentum. An unbalanced force F causes a mass m to accelerate with acceleration a given by F = ma. The impulse p of a force F acting for a time t is Ft and is equal to the change in momentum. The change in momentum is calculated from the difference between the final momentum and the initial momentum. Momentum is always conserved in collisions but kinetic energy is not necessarily conserved.The following worked examples will illustrate some of these points.ExampleA car of mass 1200 kg is brought to rest from a speed of 20 m s"1 by a constant braking force 3000 N. Calculate the retardation and the time the car takes to come to rest.F= -3000 N m= 1200 kg a = ?ExampleAn ice hockey puck of mass 0.1 kg travelling at 20 ms"1 is struck by a stick so as to return it along its original path at 10 ms"1. Calculate the impulse of the force applied by the hockey stick.Let p be the impulse produced by the Force F applied by the stick for the time t.m = 0.1 kg u = +20 m s 1 i/=-10ms_1 F=1 t = ?P = Ft = mv — mu= 0.1 x(-10) -0.1 x (+20) = - 1 -2 = -3NsThe impulse applied by the stick is -3 N s. The minus sign indicates that the direction of the impulse is in the opposite direction to the original direction of motion of the puck.ExampleA rifle pellet of mass 5 g is fired horizontally into a block of wood fixed to a model truck which runs freely on a straight track. The mass of the truck and the block is 495 g and these move with a velocity of 0.8 m s"1 when the pellet embeds itself into the wood. Calculate the initial velocity of the pellet.m = 0.005 kg u = l M = 0.495 kg v= 0.8 ms"1mu = (m + M\v 0.005 x u = (0.005 + 0.495) x 0.8_ 0.5 x 0.8 u 0.005u- 80 ms"1The initial velocity of the pellet is 80 m s-1.ExampleA bullet of mass 0.01 kg travelling horizontally at 100 ms"1 penetrates a fixed block of wood and comes to rest in 0.02 s. Calculate (a) the distance of penetration x of the bullet into the wood and (b) the average retarding force exerted by the wood on the bullet.(a)u= 100ms"1 f=0ms_1 a = ? /=0.02s v=u +at 0 = 100 + a x 0.02 0.02a = -100 a = -100/0.02 a = -5000 ms"2v2 = u2 + 2 ax 0= 1002-2x5000* 10 000 x = 10 000 *=lmThe bullet penetrates 1 m into the block (note the deep penetration).(b)F=? m = 0.01 kg a = -5000 ms"2 F= maF= 0.01 x (-5000) F= -50 NThe average retarding force exerted by the wood is -50 N.