1 PPMF102– Lecture 3 Linear Momentum

2 Linear momentum (p) Linear momentum = mass x velocity Linear momentum = mass x velocity p = mv p = mv SI unit: kgm/s SI unit: kgm/s It is a vector quantity. It is a vector quantity. The direction of p is the same as the direction of v. The direction of p is the same as the direction of v. A body at rest has zero momentum. A body at rest has zero momentum.

3 Illustrations 1. What is the momentum of a 5.0 kg body that moves at 10 m/s? 1. What is the momentum of a 5.0 kg body that moves at 10 m/s? p = mv p = mv = (5.0)(10) = (5.0)(10) = 50 kg m/s = 50 kg m/s 2. What is the momentum of a 1500 kg car moving at 110 km/h? 2. What is the momentum of a 1500 kg car moving at 110 km/h?

4 Conservation of linear momentum The total momentum of an isolated system of bodies remains constant The total momentum of an isolated system of bodies remains constant Total momentum before collision = Total momentum after collision Total momentum before collision = Total momentum after collision p before = p after p before = p after m 1 u 1 + m 2 u 2 =m 1 v 1 + m 2 v 2 m 1 u 1 + m 2 u 2 =m 1 v 1 + m 2 v 2

5 Momentum is conserved in collisions

6 Eg. 1 Railroad cars collide momentum conserved A boxcar traveling 24.0 m/s strikes a second car initially at rest. The two stick together after the collision. If the two boxcars have the same mass, what is their final velocity?

Elastic collision Total momentum is conserved. Total momentum is conserved. p before = p after p before = p after In an elastic collision, total kinetic energy is also conserved. In an elastic collision, total kinetic energy is also conserved. Total kinetic energy before collision = Total kinetic energy after collision Total kinetic energy before collision = Total kinetic energy after collision 7

8 Inelastic collision Total momentum is conserved. Total momentum is conserved. p before = p after p before = p after In an inelastic collision, some kinetic energy is lost. In an inelastic collision, some kinetic energy is lost. Total kinetic energy before collision > Total kinetic energy after collision Total kinetic energy before collision > Total kinetic energy after collision With inelastic collisions, some of the initial kinetic energy is lost to thermal or potential energy. With inelastic collisions, some of the initial kinetic energy is lost to thermal or potential energy. In a completely inelastic collision, the two objects stick together after the collision. In a completely inelastic collision, the two objects stick together after the collision.

Inelastic Collisions Example 2: Ballistic pendulum. The ballistic pendulum is a device used to measure the speed of a projectile, such as a bullet. The projectile, of mass m, is fired into a large block of mass M, which is suspended like a pendulum. As a result of the collision, the pendulum and projectile together swing up to a maximum height h. Determine the relationship between the initial horizontal speed of the projectile, v, and the maximum height h.

10 Eg. 2 A 10-kg wheelbarrow moves with a constant speed of 2.0 m/s. An additional 6.0 kg load is dropped into the wheelbarrow. What then will be its speed? Assume no friction. A 10-kg wheelbarrow moves with a constant speed of 2.0 m/s. An additional 6.0 kg load is dropped into the wheelbarrow. What then will be its speed? Assume no friction.

11 Eg. 3 A kg bullet traveling 190 m/s hits a 2.0-kg block of wood and embedded in it. If the block is stationary on a frictionless surface when hit, how fast does it move together with the bullet? A kg bullet traveling 190 m/s hits a 2.0-kg block of wood and embedded in it. If the block is stationary on a frictionless surface when hit, how fast does it move together with the bullet?

Impulse Impulse = change in linear momentum J =  p = mv – mu J =  p = mv – mu Since the time involved in a collision is usually short, average force can be used. Impulse = Average Force x time J = F t J = F t Unit for impulse is kgm/s; same unit as momentum 12