CHAPTER 9

Momentum and Its Conservation

WHAT’S THE RELATIONSHIP BETWEEN FORCE AND VELOCITY? What happens when the

baseball is struck by the bat? _______________tells us that

the forces on the bat and ball are equal.

_______________tells us that both bat and ball will experience an acceleration proportional to their masses.

But what is the relationship between the velocities of the ball and the bat and the forces they experience?

“THE BIG MO”: MOMENTUM

The ________________ of an object of mass m moving with a velocity is defined as the __________ of the ______ and the __________.SI Units are kg m/s (Dimensions = ML/T)Vector quantity, the direction of the

momentum is the same as the velocity’s.

p

v

mp v

MORE ABOUT MO Momentum components:

px = m vx and py = m vy Applies to two-dimensional motion. Again the direction of momentum and velocity are the

same.

Momentum is related to ________________. We can derive an equation that relates KE and

momentum. More on kinetic energy in chapter 10.

CHANGING THE BIG MO How does an object change its acceleration?

How would an object change its momentum?

In order to change the momentum of an object, a _______________ must be applied.

IMPULSE The _________of change of momentum

of an object is equal to the __________acting on it.

Just like with acceleration, when the __________is zero, no change occurs to momentum.

Gives an alternative statement of Newton’s second law.

( )finet

m v vt t

p

F

IMPULSE

When a single, constant force acts on the object, there is an ____________ delivered to the object.

is defined as the impulse. ____________________, the direction is the same as

the direction of the __________. The impulse is also described using the letter J. Impulse is useful for describing ______________

that do not last a long time. (More on this later.)

t I F

I

IMPULSE-MOMENTUM THEOREM The theorem states that the ___________

acting on the object is equal to the ___________________ of the object.

This theorem holds for _________ and ____________ forces.

If the force is not constant, use the average force applied.

fit m mI F p v v

SAMPLE PROBLEM

Rico strikes a 0.058 kg golf ball with a force of 272 N and gives it a velocity of 62.0 m/s. How long was Rico’s club in contact with the ball?

AVERAGE FORCE IN IMPULSE The ______________can be thought of as the

constant force that would give the same impulse to the object in the time interval as the actual time-varying force gives in the interval.

av t F p

AVERAGE FORCE AND COLLISIONS

IMPULSE AND COLLISIONS Impulse is most useful in describing _________

of _______________. The impulse-momentum theorem allows us to

study the effects that the ________________of a collision has on the _________ felt by the ____________.

For example, why is it important for boxers to wear boxing gloves?

CHANGING IMPULSE AND COLLISIONS

_____________ the contact time increases the ___________ but reduces the _________ during the collision.

Increasing force increases the impulse as well.

IMPULSE APPLIED TO AUTO COLLISIONS The most important factor is the

___________or the time it takes the person to come to a rest. Increasing the collision time is the key factor. This will reduce the chance of dying in a car

crash.

WAYS TO INCREASE THE TIME

Crumple zones Air bags

Seat belts

TYPICAL COLLISION VALUES

For a 75 kg person traveling at 27 m/s and coming to stop in 0.010 s.F = -2.0 x 105 Na = 280 g

Almost certainly fatal:F = 90 kN fractures bone.a = 150 g for 4 ms causes spinal cord

damage (causes the nerves to enter the base of the brain)

COLLISIONS ______________ is conserved in any _________. ______________is not always conserved.

Some KE is converted to other forms of energy (i.e. internal energy, sound energy, etc.) or is used to do the work needed to deform an object.

Two broad categories of collisions:Elastic collisions Inelastic collisions: Perfectly inelastic and

inelastic Elastic and perfectly inelastic collisions

represent ideal cases of collisions. Most real world cases fit somewhere

between these two extremes.

CONSERVATION OF MOMENTUM Momentum in an

isolated system in which a collision occurs is conserved. A collision may be the

result of _______________ between two objects.

“Contact” may also arise from the ______________ interactions of the electrons in the surface atoms of the bodies.

An isolated system will have no external forces acting on the objects.

CONSERVATION OF MOMENTUM The principle of conservation of momentum

states when no external forces act on a system consisting of two objects that collide with each other, the total momentum of the system remains constant in time. Specifically, the total momentum before the

collision will equal the total momentum after the collision.

F

FORCES IN A COLLISIONThe force with

which object 1 acts on object 2 is equal and opposite to the force with which object 2 acts on object 1.

Impulses are also equal and opposite.

CONSERVATION OF MOMENTUM FORMULA Mathematically:

Momentum is conserved for the system of objects.

The system includes _____________________ interacting with each other.

Assumes only internal forces are acting during the collision.

Can be generalized to any number of objects.

1 1 2 2 1 1 2 2i i ffm m m m v v v v

SAMPLE PROBLEM

A 1875 kg car going 23 m/s rear-ends a 1025 kg compact car going 17 m/s on ice in the same direction. The two cars stick together. How fast do the two cars move together immediately after the collision?

RECOIL AND PROPULSION IN SPACE

Xe atoms are expelled from the ion engine. vatoms = 30km/h; Fatoms = 0.092 N Advantage: runs for a very long time

GLANCING COLLISIONS

For a general collision of two objects in three-dimensional space, the conservation of momentum principle implies that the total momentum of the system in each direction is conserved.

Use subscripts for identifying the object, initial and final velocities, and components.

We will examine collisions in two-dimensions.

fy22fy11iy22iy11

fx22fx11ix22ix11

vmvmvmvm

andvmvmvmvm

GLANCING COLLISIONS

The “after” velocities have x and y components. Momentum is conserved in the x direction and in

the y direction. Apply conservation of momentum separately to

each direction.

SAMPLE PROBLEM A 1,500 kg car traveling east with a speed of 25.0 m/s collides at an intersection with a 2,500 kg van traveling north at a speed of 20.0 m/s as shown in the figure. Find the direction and magnitude of the velocity of the wreckage after the collision, assuming that the vehicles undergo a perfectly inelastic collision and assuming that friction between the vehicles and the road can be neglected.

CHAPTER 9

Momentum and Its Conservation

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