PHY 1114: Physics I

Lecture 9: Linear Momentum &

Collisions

Fall 2012 Kenny L. Tapp

The linear momentum of an object is the product of its mass and velocity.

Note that momentum is a vector—it has both a magnitude and a direction.

SI unit of momentum: kg • m/s. This unit has no special name.

Linear Momentum

p = m v

Which has more linear momentum?(a) a 1500 kg car moving at 25.0 m/s

or

(b) a 40,000 kg truck moving at 1.00 m/s

Quick Question 1:

If an object’s momentum changes, a force must have acted on it.

The net force is equal to the rate of change of the momentum.

Linear Momentum

A loaded tractor-trailer with a total mass of 5,000 kg traveling at 3.0 km/h (Vo = 0.83 m/s) hits a concrete barrier in front of a super secret government facility

and comes to a stop in 0.64 s. What is the magnitude of the average force exerted on the truck by the

barrier?

Quick Question 2: Linear Momentum: Impulse

There are many situations when the force on an object is not constant.

Rain comes down with a velocity of -15 m/s and hits the roof of a car. The mass of rain per second that strikes the roof of the car is 0.060 kg/s. Assuming that rain comes to rest upon striking the car, find the average force exerted by the rain on the roof.

Neglecting the weight of the raindrops, the net force on a raindrop is simply the force on the raindrop due to the roof.

Linear Momentum: Impulse

For a system of objects, the total momentum is the vector sum of each.

Linear Momentum

The change in momentum is the difference between the momentum vectors.

Linear Momentum

If there is no net force acting on a system, its total momentum cannot change.

This is the law of conservation of momentum.

If there are internal forces, the momenta of individual parts of the system can change, but the overall

momentum stays the same.

Conservation of Linear Momentum

Collisions happen quickly enough that any external

forces can be ignored during the collision.

Therefore, momentum is conserved during a

collision.

Conservation of Linear Momentum

Starting from rest, two skaterspush off against each other onice where friction is negligible.

One is a 54-kg woman and one is a 88-kg man. The woman moves away with a speed of +2.5 m/s. Find the recoil velocity of the man.

Quick Question 3:

Quick Question 3:

A 60 kg astronaut floating at rest in space outside a space capsule throws his 0.50 kg hammer such that it moves with a speed of 10 m/s relative to the capsule.

Knowing the astronaut will move in the opposite direction of the hammer, due to the conservation of

momentum, what is the astronaut’s velocity?

Quick Question 4:

In an elastic collision, the total kinetic

energy is conserved.

Total kinetic energy is not conserved in an inelastic collision.

Elastic and Inelastic Collisions

A completely inelastic collision is one where

the objects stick together afterwards.

Elastic and Inelastic Collisions

Elastic and Inelastic Collisions

• Consider a collision in 2-D (cars crashing at a slippery intersection...no friction).

v1

v2$

V$

before a'er

m1

m2

m1$+$m2

For an elastic collision, both the kinetic energy and the momentum are conserved:

Elastic and Inelastic Collisions

Collisions may take place with the two

objects approaching each other, or with one overtaking the

other.

Elastic and Inelastic Collisions

Bobby Boucher (m = 115 kg) tackles his Professor in class with a running velocity of +4.5 m/s. The

two move off together with a velocity of +2.6 m/s. Find the mass of the Professor.

Quick Question 5:

An Audi (m = 1500kg) moving at 24 m/s collides inelastically with a Porsche(m = 2000kg) traveling at 18 m/s in the same direction. Find the velocity of the two-vehicle combination immediately after the collision.

Quick Question 6: Quick Question 6:

Example Diagram

James Bond (mass 91 kg) jumps down from a digger onto a train (mass 510 kg) in which a criminal is fleeing. The velocity of the train is initially 35 m/s. What is the velocity of the train after James Bond lands in it?

Quick Question 7:

If you blow up a balloon and then let it go, it zigzags away from you as the air shoots out. This is an example of jet propulsion. The

escaping air exerts a force on the balloon that pushes the balloon in the opposite direction.

Jet propulsion is another example of conservation of momentum.

Jet Propulsion and Rockets

The thrust of a rocket works the same way.

Jet Propulsion and Rockets

This same phenomenon explains the recoil of a gun:

Jet Propulsion and Rockets

A rifle with a weight of 30 N fires a 5.0 g bullet with a speed of 300 m/s.

Quick Question 8:

(a) Find the recoil speed of the rifle.

(b) If a 700 N hunter holds the rifle firmly against his shoulder, find the recoil speed of the man and rifle.