Ch 6-- Linear Momentum & Impulse

Lillian (mass 40kg) standing on slippery ice catches her leaping dog (mass 15kg) moving at 3 m/s. What is the speed of Lillian and her dog after the catch?

(15kg x 3 m/s to the right) + (40kg x 0 m/s left)= 55 kg x ___ m/s 0.8 m/s

In terms of impulse and momentum, why do padded dashboards make automobiles safer?

Padded dashboards are safer than unpadded dashboards because the padded dashboard will increase the time required to stop your head from moving forward during an accident. The increased stopping time results in a smaller force being applied to the person's head. Force is inversely proportional to stopping time.

If a mack truck and a ford escort have a head-on collision, which vehicle will experience the greater force of impact? The greater change in momentum? The greater acceleration?

Same amount of force on both vehicles. Same size impulse on both vehicles. Same size change in momentum on both vehicles. The ford escort will have a much larger acceleration than the truck. Acceleration kills! a= f/m From newton's second law, we can see that acceleration is inversely proportional to the object's mass. Small mass, larger acceleration.

In terms of impulse and momentum, why do air bags in cars reduce the chances of injury in car accidents?

The airbag increases the stopping time and therefore decreases force applied to your face.

When you are traveling in your car at highway speed, the momentum of a bug is suddenly changed as it splatters onto your windshield. Compared to the change in momentum of the bug, by how much does the momentum of the car change?

The car has the same amount of change in momentum as the bug does. (conservation of momentum)

Definition of momentum

inertia in motion (inertia= an object's resistance to change speed or direction) momentum (P)= mass x velocity

A 5kg fish swimming at 1 m/s swallows an absent minded 1kg fish swimming toward it at a velocity that brings both fish to a halt immediately after they collide. What is the velocity of the smaller fish before lunch?

(Conservation of momentum) Pbefore= Pafter (5kg x 1m/s right) + (1kg x __m/s left)= 6kg x 0 m/s 5m/s left

To bring a supertanker to a stop, its engines are typically cut off about 25km from port. Why is it so difficult to stop a supertanker?

A moving supertanker will have a lot of momentum even when it is moving slowly because it has a lot of mass. Momentum = mass x velocity.

What does it mean to say that a quantity is conserved?

A quantity is conserved when its total amount never changes. Even if you can't find all the pieces, you know that they are somewhere.

Would you care to fire a gun with a bullet that is ten times as massive as the gun?

No. The gun would recoil with a speed ten times the muzzle velocity. Firing such a gun in the conventional way would not be a good idea!

Joanne drives her car with a mass of 1000kg, moves at 20 m/s. What braking force is needed to bring the car to a halt in 10 seconds?

FΔT=ΔP=MΔV F= MΔV/ΔT= 1000KG (-20m/s)/10 s= 2000N backward

What is the impulse to stop a 10kg bowling ball moving at 6m/s?

FΔT=ΔP=MΔV 10kg(-6 m/s)= -60 kg m/s= 60 kg m/s backward

In terms of impulse and momentum, why are nylon ropes, which stretch considerably under tension, favored by mountain climbers?

If the climber falls, he hopes that the rope will apply the force that stops him. The stretching of the nylon rope increases the stopping time, which decreases the force on his body.

How does impulse differ from force?

Impulse is the product of force and time, its not just force. Impulse= (F)(ΔT)

Why might a wine glass survive a fall onto a carpet floor but not onto a concrete floor?

The carpet floor provides a larger stopping time than a concrete floor. This will result in a smaller force for any given change in momentum. From FΔT=ΔP we get F=ΔP/ΔT. There is an inverse relationship between force and time. A large stopping time results in a small force applied to the glass.

Would a head-on collision between two cars be more damaging to the occupants if the cars stuck together or if the cars rebounded upon impact?

The occupants in a head on collision will experience an impulse equal to their change in momentum. If the vehicles bounce, there is a larger change in momentum and therefore a larger impulse.

A fully dressed person at rest in the middle of a pond on perfectly frictionless ice must get to shore. How can this be accomplished?

The person could take off their shoe and throw it in the opposite direction that they want to go in. Conservation of momentum demands that they will move slowly in the opposite direction on the frictionless ice.

It is generally much more difficult to stop a heavy truck than a skateboard when they move at the same speed. State a case where the moving skateboard could require more stopping force (consider relative times).

The skateboard could require a larger stopping force than the truck if the stopping time for the skateboard was very small. (force and time are inversely proportional)

Which has the greater momentum, a heavy truck at rest or a moving skateboard?

The skateboard. Momentum= mass x velocity, since the truck is not moving, its momentum is zero because its velocity is zero

Why can we say that when we fire a bullet from a gun, that momentum is conserved?

The total momentum of the gun and bullet before the trigger is pulled is zero. If we add the momentum of the bullet to the momentum of the gun after the trigger is pulled, we expect to get zero. Remember that momentum is a vector, meaning that it has both magnitude and direction. As an example, pretend that the bullet has a momentum of +2 kg m/s. The gun will have a -2 kg m/s momentum. +2 + -2= 0.

Why would it be a bad idea to have the back of your hand against the outfield wall when you catch a fly ball?

The wall would prevent your hand from moving backward as it applies the force to stop the ball. The result is a short stopping time, which would produce a large force on your hand. It would probably sting and may pop the ball out of your glove. From FΔT=ΔP, we get F=ΔP/ΔT. There is an inverse relationship between force and time. a small stopping time results in a large force applied to the hand.

For the same force, which cannon imparts a greater speed to a cannonball-- a long barrel or a short barrel cannon?

a long barrel imparts more speed than a short barrel because the projectile is in the barrel for more time. Remember, impulse = FΔT. More time means more impulse, which means a larger change in momentum, which means a faster moving cannon ball.

What are the two ways to increase impulse?

increase the force or increase the time the force is applied

If a ball is projected upward from the ground with 10 kg m/s momentum, what is the momentum of recoil of the world? Why do we not feel this?

the earth must recoil with 10 units of momentum. The earth has o much mass that it would have a very tiny change in velocity. ΔP= MΔV therefore ΔV= ΔP/M The earth's change in velocity is inversely proportional to its mass.