MOMENTUM: Inertia in motion Linear momentum of an object equals the product

of its mass and velocity Moving objects have momentum Vector quantity

The momentum vector points in the same direction as the velocity vector

Proportional to mass and velocity

p = mv

p = momentum (kg * m/s)m = mass (kg)v = velocity (m/s)

Collisions:Momentum- Useful concept when applied to

collisions

In a collision, two or more objects exert forces on each other for a brief instant of time, and these forces are significantly greater than any other forces they may experience during the collision

What is the taxi cab’s momentum?* Mass of the taxi = 0.14 kg* Velocity of the taxi = 1.2 m/s

Answer: p = mv p = (0.14 kg)(1.2 m/s)

p = 0.17 kg * m/s to the left

v = 1.2 m/s

p = 0.17 kg * m/s

ΣF = Δp/Δt **Net force equals the change in momentum per unit time Rearranging this equation Δp = ΣFΔt

Impulse (J) The change in momentum is called the impulse of the force

(Impulse- momentum theorem) Vector quantity Units: kg * m/s

J = Δp = FΔt p = Momentum J = Impulse F = Force Δt = Elapsed time

The greater the net force, or the longer the interval of time it is applied, the more the object’s momentum changes the same as saying the impulse increases

Changing Momentum: Scenario 1 if you want to decrease a large

momentum, you can have the force applied for a longer time.If the change in momentum occurs over a long

time, the force of impact is small.Examples:

Air bags in cars. Crash test video

Ft

Changing Momentum: Scenario 2

If the change in momentum occurs over a short time, the force of impact is large.

Ft

Baseball player swings a bat and hits the ball, the duration of the collision can be as short as 1/1000th of a second and the force averages in the thousands of newtons

The brief but large force the bat exerts on the ball = Impulsive force

A long jumper's speed just before landing is 7.8 m/s. What is the impulse of her landing? (mass = 68 kg) J = pf – pi

J = mvf – mvi

J = 0 – (68kg)(97.8m/s) J = -530 kg * m/s

*Negative sign indicates that the direction of the impulse is opposite to her direction of motion

Impulse = Change in momentum J = Δp = FavgΔt

Change in momentumΔp = mΔv

** In conclusion, there are different equations for impulse• J = F Δt• J = Δp = mΔv = mvf – mvi

F Δt = mΔv

Conservation of momentum: The total momentum of an isolated system

is constantNo net external force acting on the systemMomentum before = Momentum after

Momentump = mv

Conservation of momentumMomentum before = Momentum afterpi1 + pi2 +…+ pin = pf1 + pf2 +…+ pfn

m1vi1 + m2vi2 = m1vf1 + m2vf2

m1, m2 = masses of objects vi1, vi2 = initial velocities vf1, vf2 = final velocities

Elastic collisionObjects start apart and end apart

Inelastic collisionObjects start apart and end togetherObjects start together and end apart

Momentum is conserved in any collision Elastic or inelastic

A 55.0 kg astronaut is stationary in the spaceship’s reference frame. She wants to move at 0.500 m/s to the left. She is holding a 4.00 kg bag of dehydrated astronaut chow. At what velocity must she throw the bag to achieve her desired velocity? (Assume the positive direction is to the right.)

VARIABLES: Mass of astronaut ma = 55 kg

Mass of bag mb = 4 kg

Initial velocity of astronaut via = 0 m/s

Initial velocity of bag vib =0 m/s

Final velocity of astronaut vfa = -0.5 m/s

Final velocity of bag vfb = ? EQUATION:

m1vi1 + m2vi2 = m1vf1 + m2vf2

mavia + mbvib = mavfa + mbvfb

0 = mavfa + mbvfb

Vfb = - (mavfa / mb)

Vfb = - ((55kg)(-0.5m/s))/(4kg) = 6.875 m/s

Collisions

Momentum is always conserved in a collision

Classification of collisions: ELASTIC

Both energy & momentum are conserved

INELASTIC Momentum conserved, not energy Perfectly inelastic -> objects stick Lost energy goes to heat

• Catching a baseball• Football tackle• Cars colliding and sticking• Bat eating an insect

Examples of Examples of Perfectly Perfectly

Elastic CollisionsElastic Collisions• Superball bouncing• Electron scattering

Examples of Examples of Perfectly Inelastic Perfectly Inelastic

CollisionsCollisions