AP Physics B

Impulse and Momentum

Impulse = ∆MomentumConsider Newton’s 2nd

Law and the definition of acceleration

Units of Impulse: Units of Momentum:

Momentum is defined as “Inertia in Motion”

NsKg x m/s

ExampleA 100 g ball is dropped from a height of h = 2.00 m above the floor. It

rebounds vertically to a height of h'= 1.50 m after colliding with the floor. (a) Find the momentum of the ball immediately before it collides with the floor and immediately after it rebounds, (b) Determine the average force exerted by the floor on the ball. Assume that the time interval of the collision is 0.01 seconds.

Impulse is the AreaSince J=Ft, Impulse is the AREA of a Force vs.

Time graph.

How about a collision?Consider 2 objects speeding

toward each other. When they collide......

Due to Newton’s 3rd Law the FORCE they exert on each other are EQUAL and OPPOSITE.

The TIMES of impact are also equal.

Therefore, the IMPULSES of the 2 objects colliding are also EQUAL

21

21

2121

)()(

JJ

FtFt

ttFF

How about a collision?If the Impulses are equal then

the change in MOMENTUMS are also equal!

Momentum is conserved!The Law of Conservation of Momentum: “In the

absence of an external force (gravity, friction), the total momentum before the collision is equal to the total momentum after the collision.”

Several Types of collisionsSometimes objects stick together or blow apart.

In this case, momentum is ALWAYS conserved.

ExampleA bird perched on an 8.00 cm tall swing has a mass of 52.0 g, and the base of the swing has a mass of 153 g. Assume that the swing and bird are originally at rest and that the bird takes off horizontally at 2.00 m/s. If the base can swing freely (without friction) around the pivot, how high will the base of the swing rise above its original level?

Example Granny (m=80 kg) whizzes around the rink with a velocity of 6 m/s. She suddenly collides with Ambrose (m=40 kg) who is at rest directly in her path. Rather than knock him over, she picks him up and continues in motion without "braking." Determine the velocity of Granny and Ambrose.

What happens if we have two unknowns?At an amusement park, a 96.0 kg bumper

car moving with a speed of 1.24 m/s bounces elastically off a 135 kg bumper car at rest. Find the final velocities of the cars.

1 1 2 2 1 1f 2 2fm v m v m v m v

2 2 2 21 1 2 2 1 1f 2 2f

1 1 1 1.

2 2 2 2m v m v m v m v

1 1 1f

2 2f 2

( )1.

( )

m v v

m v v

Let subscript 1 refer to the 96.0kg car and subscript 2 refer to the 135 kg car.Use momentum conservation.

Use conservation of kinetic energy.

Rearranging the first equation gives

2 21 1 1f 1 1 1f 1 1f

2 22 2f 2 2f 22 2f 2

( ) ( )( )1 .

( )( )( )

m v v m v v v v

m v v v vm v v

1 1f

2f 2

( )1,

( )

v v

v v

2f 1 1f 2or .v v v v

Rearranging the second equation gives

Comparing these two equations implies that

2fv 1f .v

1 1 2 2 1 1f 2 1 1f 2

1 2 1 2 2 1 2 1f

( )( ) 2 ( )m v m v m v m v v vm m v m v m m v

1 2 21f 1 2

1 2 1 2

2m m mv v v

m m m m

2f 1 1f 2 1f 2f 2 1Since , .v v v v v v v v

Substitute for in the first equation and solve for

1fv 2f .v

1 1 2 2 1 2f 2 1 2 2f

1 1 2 1 2 1 2 2f

( )2 ( ) ( )m v m v m v v v m vm v m m v m m v

Substitute for in the first equation and solve for

2D Inelastic Collisions must rely on the Conservation of Momentum:Example: A car with a

mass of 950 kg and a speed of 16 m/s approaches an intersection, as shown. A 1300 kg minivan traveling at 21 m/s is heading for the same intersection. The car and minivan collide and stick together. Find the speed and direction of the wrecked vehicles just after the collision, assuming external forces can be ignored.

Collisions in 2 DimensionsThe figure to the left shows

a collision between two pucks on an air hockey table. Puck A has a mass of 0.025-kg and is moving along the x-axis with a velocity of +5.5 m/s. It makes a collision with puck B, which has a mass of 0.050-kg and is initially at rest. The collision is NOT head on. After the collision, the two pucks fly apart with angles shown in the drawing. Calculate the speeds of the pucks after the collision.

Collisions in 2 dimensions

vB

Collisions in 2 dimensions

For 2D Elastic Collisions, KE is also conserved:Example: The collision of two 7 kg curling stones.