MOMENTUM(p)Recall: N2LMThe net force acting on a particle equals the time rate of change momentum of the particle.A rapid change in momentum requires a large net force, while a gradual change requires less net force

MOMENTUM(p)If a particle is moving obliquely and has velocity components vx, vy, vz, then its momentum components would be:

IMPULSE(J) - MOMENTUM(p) THEOREMv1 = 0v2 > 0t1 t2 The change in momentum is affected by the applied net force and how long it is applied!Impulse Momentum TheoremThe change in momentum of a particle during a time interval equals the impulse of the net force that acts on the particle during that interval

IMPULSE(J) - MOMENTUM(p) THEOREMIn specific problems, it is often easiest to use Impulse-Momentum Theorem in its component form:

IMPULSE(J) - MOMENTUM(p) THEOREMSuppose you have a choice between catching a 0.50-kg ball moving at 4.0 m/s or a 0.10-kg ball moving at 20 m/s. Which will be easier to catch?Example 1.A 0.16-kg hockey puck is moving on an icy, frictionless, horizontal surface. At t = 0 the puck is moving to the right at 3.0 m/s. a) Calculate the velocity of the puck(magnitude and direction) after a force of 25.0 N directed to the right has been applied for 0.05 s. b) If instead, a force of 12 N directed to the left is applied from t1 = 0 s to t2 = 0.05 s, what is the final velocity of the puck?Example 2.

IMPULSE(J) - MOMENTUM(p) THEOREMExample 3.

CONSERVATION OF MOMENTUMBefore CollisionDuring CollisionAfter CollisionThe total momentum of a system is conserved!

CONSERVATION OF MOMENTUMBefore CollisionDuring CollisionAfter Collision

COLLISIONElastic Collision - the total kinetic energy of the system before and after the collision is constant.

COLLISIONConservation of Momentumeqn. 1 eqn. 2Relative velocity of approachRelative velocity of separation

COLLISIONSo, Coefficient of Restitution, e for Elastic Collision:Summary:Elastic Collision K1 = K2 e = 1Inelastic Collision K1 > K2 e < 1CompletelyInelastic Collision K1 > K2 e = 0 uA = uB

COLLISIONA 5-gm bullet is fired from a 4-kg gun. The muzzle speed is 600 m/s. Find the speed of recoil of the gun.Example 4.A 100-gm block moving with a speed of 10 cm/s to the right collides with a 200-g block moving with a speed of 5 cm/s at the same direction. a) Find the speed of the two blocks right after the collision if the collision is inelastic with coefficient of restitution, e = 0.75. b) Find the change in kinetic energy of the system.Example 5.A hockey puck B rests on a smooth ice surface and is struck by a second puck A, which was originally travelling at 40 m/s and which is deflected 30o from its original direction. Puck B acquires a velocity at a 45o angle to the original direction of A. The pucks have the same mass. Compute the speed of each puck after the collision.Example 6.