Momentum And Impulse

Bell Ringer What happens when two cars collide? How does the impact affect the motion of each vehicle? How do rockets work? Why is it when you fire a gun, the gun kicks back?

Objectives Define Impulse and Momentum Equations for Momentum and Impulse Boxing and Brain Injuries

Momentum Momentum is a quantity associated with an objects mass and velocity. It is measured in kg m/s

Momentum The equation for momentum is: p = m v

Momentum Let’s look at the equation: What happens to an objects momentum if we double the mass of the object? What happens to the objects momentum if we double the objects velocity?

Momentum Momentum is a vector quantity. Remember that a vector has magnitude and direction! Therefore, momentum is in the same direction as the velocity component.

Momentum Therefore: px = m vx AND py = m vy

Therefore P = (px2 + py2)1/2

Momentum Changing the momentum of an object requires the application of a force.

Momentum An objects change in momentum over a period of time is equal to the sum of the forces applied to the object.

Impulse Changing an object’s momentum requires the continuous application of a force over a period of time. This is the definition of Impulse.

Impulse If a constant force acts on an object, the impulse (J) delivered to the object over a time interval is: J = F Δ t

Momentum-Impulse Theorem J = FΔt = Δp = mvf - mvi

Momentum-Impulse Theorem This is a special case that shows that the impulse of the force acting on an object equals the change in momentum of the object.

The truth In real life situations, the force on an object is only rarely constant. Therefore, we will use the theorem to define an average Force!

Kinetic Energy and Momentum Kinetic energy and momentum are related. Look: K = ½ mv2 We can express K in terms of momentum: K = (mv)2/2m So, K = p2/2m

Example A golf ball with mass 5.0 x 10-2 kg is struck with a club. The force on the ball varies from zero when contact is made up to some maximum value and then back to zero when the ball leaves the club. Assume the ball leaves the club with a velocity of 44 m/s.

Continued Find the magnitude of the impulse due to the collision.

Example 2 In a crash test a car of mass 1,500 kg collides with a wall and rebounds. The initial velocity of the car is -15.0 m/s and the final velocity is 2.60 m/s. The collision lasts for 0.15 seconds.

Continued Find the impulse delivered to the car due to the collision. Find the size and direction of the average force exerted on the car.