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PPMF102– Lecture 3PPMF102– Lecture 3

Linear MomentumLinear Momentum

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Linear momentum (p)Linear momentum (p)

Linear momentum = mass x velocityLinear momentum = mass x velocity

pp = m = mvv SI unit: kgm/sSI unit: kgm/s It is a vector quantity.It is a vector quantity. The direction of p is the same as the The direction of p is the same as the

direction of v.direction of v. A body at rest has zero momentum.A body at rest has zero momentum.

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IllustrationsIllustrations

1. What is the momentum of a 5.0 kg 1. What is the momentum of a 5.0 kg body that moves at 10 m/s?body that moves at 10 m/s?

p = mvp = mv

= (5.0)(10)= (5.0)(10)

= 50 kg m/s= 50 kg m/s 2. What is the momentum of a 1500 2. What is the momentum of a 1500

kg car moving at 110 km/h?kg car moving at 110 km/h?

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Conservation of linear Conservation of linear momentummomentum

The total momentum of an isolated The total momentum of an isolated system of bodies remains constantsystem of bodies remains constant

Total momentum before collision = Total momentum before collision = Total momentum after collisionTotal momentum after collision

ppbeforebefore = p = pafterafter

mm11uu11 + m + m22uu22 = = mm11vv11 + m + m22vv22

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Momentum Momentum is conserved is conserved in collisionsin collisions

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Eg. 1 Railroad cars collideEg. 1 Railroad cars collide momentum conserved 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 collisionElastic collision•Total momentum is conserved.Total momentum is conserved.•ppbeforebefore = p = pafterafter

•In an elastic collision, total kinetic energy In an elastic collision, total kinetic energy is also conserved.is also conserved.

•Total kinetic energy before collision = Total kinetic energy before collision = Total kinetic energy after collisionTotal kinetic energy after collision

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Inelastic collisionInelastic collision Total momentum is conserved.Total momentum is conserved. ppbeforebefore = p = pafterafter

In an inelastic collision, some kinetic energy is In an inelastic collision, some kinetic energy is lost.lost.

Total kinetic energy before collision > Total Total kinetic energy before collision > Total kinetic energy after collisionkinetic energy after collision

With With inelasticinelastic collisions, some of the initial collisions, some of the initial kinetic energy is lost to kinetic energy is lost to thermalthermal or or potential potential energyenergy..

In a completely inelastic collision, the two In a completely inelastic collision, the two objects stick together after the collision.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.

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Eg. 2Eg. 2

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

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Eg. 3Eg. 3

A 0.012-kg bullet traveling 190 m/s A 0.012-kg bullet traveling 190 m/s hits a 2.0-kg block of wood and hits a 2.0-kg block of wood and embedded in it. If the block is embedded in it. If the block is stationary on a frictionless surface stationary on a frictionless surface when hit, how fast does it move when hit, how fast does it move together with the bullet? together with the bullet?

ImpulseImpulseImpulse = change in linear momentumImpulse = change in linear momentum

J = J = p = mv – mup = mv – mu

Since the time involved in a collision is usually Since the time involved in a collision is usually short, average force can be used. short, average force can be used.

Impulse = Average Force x timeImpulse = Average Force x time

J = F tJ = F t

Unit for impulse is kgm/s; same unit as Unit for impulse is kgm/s; same unit as momentummomentum

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