Chapter 8 Momentum
8.1 Momentum
Its harder to stop a large truck than a small car when both are moving at the same speed. We say the truck has more momentum than the car. By momentum, we mean inertia in motion. More specifically, momentum is the mass of an object multiplied by its velocity.
Momentum = Mass x Velocity
P = mv
When direction is not an important factor, we can say:
Momentum = Mass x Speed
A moving object can have a large momentum if it has a large mass, a high speed, or both.
A moving truck has more momentum than a car moving at the same speed because the truck has more mass. But a fast car can have more momentum than a slow truck. And a truck at rest has no momentum at all.
8.2 Impulse Changes Momentum
If the momentum of an object changes, either the mass or the velocity changes (or both). The greater the force acting on an object, the greater its change in velocity, and hence, the greater its change in momentum.
Impulse
The change in momentum depends on the force that acts and the length of time it acts.
Ex. apply a brief force to a stalled automobile, and you produce a change in its momentum. Apply the same force over an extended amount of time and you produce a greater change in the automobiles momentum.
A force sustained for a long time produces more change in momentum than does the same force applied briefly. So both force and time are important in changing an object momentum.
The quantity force x time interval is called impulse. The greater the impulse exerted on something, the greater will be the change in momentum.
Impulse = change in momentum
Ft=â(mv)
Increasing Momentum
To increase momentum of an object it makes sense to apply the greatest force possible for as long as possible. The forces involved in impulses usually vary from instant to instant.
Ex. A golf club that strikes a golf ball exerts zero force on the ball until it comes in contact with it; then force increases rapidly as the ball becomes distorted.
Decreasing Momentum
In the case of hitting either the wall or the haystack and coming to a stop, your momentum is decreased by the same impulse. The same impulse does not mean the same amount of force or the same amount of time; rather it means the same product of force and time.
A longer contact time reduces the force and decreases the resulting deceleration.
Ex. if the time is extended 100 times, the force of impact would be reduced 100 times. Whenever we wish the force to be small, we extend time.
8.3 Bouncing
If a flower pot falls from a shelf to your head, you may be in trouble. If it bounces from your head, you may be in serious trouble. Because impulses are greater when an object bounces.
The impulse required to being an object to a stop and then to âthrow it back againâ is greater than the impulse required merely to bring the object to a stop.
Ex. you catch the falling pot with your hands. You provide an impulse to reduce its momentum to zero. If you throw the pot upward again, you provide additional impulse.
It takes greater impulse to catch the pot and throw it back up than merely catching it.
8.4 Conservation of Momentum
If you wish to change the momentum of an object, exert an impulse on it. The impulse must be exerted on the object by something outside the object. Internal forces wont work. To change the momentum of the basketball or a car, an outside push or pull is required.
Momentum is a vector quantity and it can be canceled. So although the cannonball in the preceding example gains momentum when fired and the recoiling cannon gain momentum in the opposite direction, the cannon-cannonball system does not.
The momentum of the cannon and the cannonball are equal in magnitude and opposite in direction, therefore, these momentums would cancel each other out for the system as a whole. No external forces acted on the system before or during the firing. Since no net force acts on the system, there is no net impulse on the system and there is no net change in the momentum.
A system will have the same momentum before some internal interaction as it has after the interaction occurs. When momentum or any quantity in physics doesnât change, we can say it is conserved.
The law of conservation of momentum describes the momentum of a system.
The law of conservation of momentum states that, in the absence of an external force, the momentum of a system remains unchanged.
8.5 Collisions
Whenever objects collide in the absence of external forces, the net momentum of both objects before the collision equals the net momentum of both objects after the collision.
net momentum (before collision) = net momentum (after collision)
Elastic Collisions
When a moving ball collides head on with a ball at rest, the first ball comes to rest and the second ball moves away with a velocity equal to the initial velocity of the first ball. We see that momentum is transferred over from the first ball to the second.
When object collide without being permanently deformed and without generating heat, the collision is said to be an elastic collision.
Inelastic Collisions
A collision in which the colliding objects become distorted and generate heat during the collision is an inelastic collision. Momentum conservation holds true even in inelastic collisions. Whenever colliding objects become tangled or couple together, a total inelastic collision occurs.
8.6 Momentum Vectors
Momentum is conserved even when interacting objects donât move along the same straight line.
The vector sum of the momentum is the same before and after a collision.