Physics momentum impulse
If you topple from your tree house, you'll continuously gain momentum as you fall to the ground below. Doesn't this violate the law of conservation of momentum? Defend your answer.
If the system is you and the Earth, then your momentum toward Earth is equal and opposite to Earth's momentum toward you. There is no net change in momentum because while you're falling down, Earth is falling (much less noticeably) up.
Suppose the small fish is not at rest but is swimming toward the large fish at 2 m/s.
If we consider the direction of the large fish as positive, then the velocity of the small fish is -2 m/s.
A falling firecracker bursts into two pieces. Compared with the momentum of the firecracker when it bursts, the two pieces
combined have the same momentum.
When the speed of an object is doubled, its momentum
doubles.
Impulse Equation
impulse = F × t The greater the impulse exerted on something, the greater will be the change in momentum. impulse = change in momentum Ft = ∆(mv)
Momentum Equation
momentum = mass × velocity momentum = mv When direction is not an important factor, momentum = mass × speed
On roller blades you horizontally toss a ball away from you. The mass of the ball is one tenth your mass. Compared with the speed you give to the ball, your recoil speed will ideally be
one tenth as much.
The impulse-momentum relationship is a direct result of Newton's
second law.
A big fish swims upon and swallows a small fish at rest. After lunch, the big fish has less
speed.
A car with a mass of 1000 kg moves at 20 m/s. What braking force is needed to bring the car to a halt in 10 s?
F= ∆(mv)/ t 5 (1000 kg 3 20 m/s) / (10 s) 5 2000 kg?m/s2=2000 N
What impulse occurs when an average force of 10 N is exerted on a cart for 2.5 seconds?
10N x 2.5s= 25 N x s Impulse is force multiplied by time.
If the bowling ball rolls into a pillow and stops in 0.5 s, calculate the average force it exerts on the pillow.
16/.5=32 We know that it initial momentum was 16 and that if it stops then it loses all of that momentum, therefore the change in momentum is 16. Impulse is equal to the change in momentum. Impulse is also equal to force multiplied by time. Therefore if I divide my change in momentum by the time it takes to stop I will get the force it took to stop the ball. (change in momentum = impulse = force x time using this information I know that change in momentum / time = force)
Imagine that you are hovering next to the space shuttle in an Earth orbit. Your buddy of equal mass, who is moving at 4 km/h with respect to the shuttle, bumps into you. If he holds onto you, how fast do you both move with respect to the ship?
2 km/h faster than the ship. This is because the momentum of the system needs to be conserved. Momentum is equal to mass multiplied by velocity. The velocity for just one mass was 4. In order to have the same momentum once the mass is doubled the velocity will be cut in half.
The sliding carton skids onto a rough surface and stops in 3 s. Calculate the force of friction it encounters.
200/3=66.6N The change is momentum is equal to the impulse. The impulse is the force multiplied by the time. Therefore the force is equal to the change in momentum divided by the time.
What change in momentum does the cart undergo?
25 kg x m/s Change in momentum is equal to impulse.
If a the mass of the cart is 2 kg and the cart is initially at rest, calculate its final speed.
5 kg·m/s divided by 2kg = 12.5 m/s Momentum is equal to mass multiplied by velocity. The change in momentum is 25 kg·m/s and since it started at rest, then this is equal to its final momentum. To get velocity we divide momentum by mass.
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 totally inelastic collision occurs.
Air Track
An air track nicely demonstrates conservation of momentum. Many small air jets provide a nearly frictionless cushion of air for the gliders to slide on.
Distinguish between mass and momentum. Which is inertia and which is inertia in motion.
An objects inertia is basically defined by its mass. An objects momentum is its mass multiplied by its velocity. This means that Mass is Inertia and Momentum is inertia in motion.
In a car crash, why is it advantageous for an occupant to extend the time during which the collision takes place?
Because no matter how long it takes the impact will be the same because all of the momentum needs to be taken away. Since impact is force multiplied by time, we know that the longer you make that crash take, the less force needs to be exerted on you and your car to take away the momentum you had before the crash.
In terms of momentum conservation, why does a cannon recoil when fired?
Because the initial system had no momentum. If the cannonball has momentum after it is fired, then the momentum of the cannon must be equal to and opposite from that momentum otherwise momentum would not be conserved - and we know that momentum has to be conserved.
Why is more impulse delivered during a collision when bouncing occurs than during one when it doesn't?
Because there is the impulse that comes from stopping the balls downward momentum when it hits the ground and the impulse of giving the ball upward momentum as it goes back up.
Bouncing
Cassy imparts a large impulse to the bricks in a short time and produces considerable force. Her hand bounces back, yielding as much as twice the impulse to the bricks. The curved blades of the Pelton Wheel cause water to bounce and make a U-turn, producing a large impulse that turns the wheel.
Which impulse is greatest?
Catching it and throwing it out again because you experience the impulse of catching it and the impulse of throwing it.
Law of Conservation of Momentum
Describes the momentum of a system If a system undergoes changes wherein all forces are internal, the net momentum of the system before and after the event is the same. Examples are: atomic nuclei undergoing radioactive decay, cars colliding, and stars exploding.
What is the force of impact on the car?
F =∆(mv)/ t; but we don't know t! Without knowledge of the impact time, we can't solve for the force of impact
Decreasing Momentum
If you were in a car that was out of control and had to choose between hitting a haystack or a concrete wall, you would choose the haystack. Physics helps you to understand why hitting a soft object is entirely different from hitting a hard one. If the change in momentum occurs over a long time, the force of impact is small. If the change in momentum occurs over a short time, the force of impact is large.
Distinguish between impact and impulse. Which designates a force and which is the force multiplied by time.
Impact is basically just the force applied to an object and impulse is the force multiplied by the amount it is applied for. This means that the force is impact and the impulse is force multiplied by time.
Does impulse equal momentum or a change in momentum?
Impulse is equal to the change in momentum.
Distinguish between impulse and momentum. Which is force x time and which is inertia in motion.
Impulse is how long a force is applied for and momentum is mass multiplied by velocity. This means that impulse is force multiplied by time and momentum is inertia in motion
In terms of impulse and momentum, why are air bags in automobiles a good idea?
In a crash you lose all momentum. Your change in momentum is equal to impulse. Impulse is force multiplied by time. The air bag makes your collision with the dashboard take longer so there is less force to hurt you.
Distinguish between an elastic and an inelastic collision.
In an elastic collision the objects basically bounce off of each other (they are not permanently deformed and do not generate heat). In an inelastic collision the objects do not bounce off of each other, but instead become attached or tangled in some way.
For a constant force, suppose the duration of impact on an object is doubled. How much is the impulse increased?
It is doubled
How much is the resulting change in momentum increased?
It is doubled
If the time of impact in a collision is extended by four times, how much does the force of impact change?
It is reduced to one fourth of what it was before the time was reduced.
What does it mean to say that momentum is conserved?
It means that the momentum before and after the collision is the same.
Momentum Vectors
Momentum is a vector quantity. The momentum of the wreck is equal to the vector sum of the momenta of car A and car B before the collision. The momentum of car A is directed due east and that of car B is directed due north. If their momenta are equal in magnitude, after colliding their combined momentum will be in a northeast direction with a magnitude (root 2) times the momentum either vehicle had before the collision. When the firecracker bursts, the vector sum of the momenta of its fragments add up to the firecracker's momentum just before bursting.
Consider a 6-kg fish that swims toward and swallows a 2-kg fish that is at rest. If the larger fish swims at 1 m/s, what is its velocity immediately after lunch?
Momentum is conserved from the instant before lunch until the instant after (in so brief an interval, water resistance does not have time to change the momentum).
What is the momentum of an 8-kg bowling ball rolling at 2 m/s?
Momentum is equal to force multiplied by velocity, so 8 kg x2 m/s = 16 kg·m/s
What is the momentum of a 50-kg carton that slides at 4 m/s across an icy surface?
Momentum is mass multiplied by velocity, so 50 x 4 = 200
A 2-kg blob of putty at 3 m/s slams into a 2 kg blob of putty at rest Calculate the speed of the two stuck-together blobs of putty immediately after colliding.
Momentum of the system before the collision was 6 kg·m/s, and since momentum has to be conserved the momentum after collision has to be 6 kg·m/s. The mass after the collision is 4 kg, so the velocity after the collision is 1.5 m/s
A 1000-kg car moving at 20 m/s slams into a building and comes to a halt. Which of the following questions can be answered using the given information, and which one can- not be answered? Explain.
Multiply units of N, kgm/s2, by s and get N?s 5 kg?m/s.
Net Momentum Equation
Net momentum (before)= Net momentum (after)
Why is it advantageous for a boxer to ride with the punch? Why should he avoid moving into an oncoming punch?
Saying that a boxer rides with a punch implies that he moves away as the punch hits him, this is one way to make the impact of the force take longer, thus decreasing the amount of force that he feels. He should avoid moving into an oncoming punch because this would do the opposite and would make the impact of the punch take less time and so it would increase the amount of force that he feels.
When you ride a bicycle at full speed and the bike stops suddenly, why do you have to push hard on the handlebars to keep from flying forward?
So that the reaction force of the handlebars on you will produce a backward-acting impulse.
A group of playful astronauts, each with a bag full of balls, form a circle as they free-fall in space. Describe what happens when they begin tossing balls simultaneously to one another.
The astronauts would recoil and the circle would widen.
Impulse Changes Momentum
The change in momentum depends on the force that acts and the length of time it acts. If the momentum of an object changes, either the mass or the velocity or both change. The greater the force acting on an object, the greater its change in velocity and the greater its change in momentum. A glass dish is more likely to survive if it is dropped on a carpet rather than a sidewalk. The carpet has more "give." Since time is longer hitting the carpet than hitting the sidewalk, a smaller force results. The shorter time hitting the sidewalk results in a greater stopping force. The safety net used by circus acrobats is a good example of how to achieve the impulse needed for a safe landing. The safety net reduces the stopping force on a fallen acrobat by substantially increasing the time interval of the contact.
A proton from an accelerator strikes an atom. An electron is observed flying forward in the same direction the proton was moving and at a speed much greater than the speed of the proton. What conclusion can you draw about the relative mass of a proton and an electron?
The electron has much less mass than the proton.
If the time it takes the pillow to stop the ball is the same as the time of contact of the ball with the spring, how do the average forces on the ball compare?
The force of the spring is twice as big. We know this because we found in part a that the impulse is double. Impulse is time multiplied by force. If the time is the same and the impulse is double that means that the force has to be double.
A bug and the windshield of a fast-moving car collide. Indicate whether each of the following statements is true or false.
The forces of impact on the bug and on the car are the same size. True The impulses on the bug and on the car are the same size. True The changes in speed of the bug and of the car are the same. False the changes of speed are very different due to the different masses and resulting accelerations. The changes in momentum of the bug and of the car are the same size. True, since the impulses are of the same size.
Why is it difficult for a firefighter to hold a hose that ejects large amounts of water at high speed?
The hose tends to recoil from the ejected water.
When the force of impact on an object is extended in time, does the impulse increase or decrease?
The impulse increases.
Conservation of Momentum
The momentum before firing a cannon is zero. After firing, the net momentum is still zero because the momentum of the cannon is equal and opposite to the momentum of the cannonball.
Calculate the speed of the two blobs is the one at rest was 4 kg.
The momentum of the system before the collision was 6 kg·m/s, and since momentum has to be conserved, the momentum after the collision has to be 6 kg·m/s. The total mass after the collision in this case would be 6 kg, making the velocity 1 m/s.
Impulse
The quantity force × time interval is called impulse. A force sustained for a long time produces more change in momentum than does the same force applied briefly. Both force and time are important in changing an object's momentum. When you push with the same force for twice the time, you impart twice the impulse and produce twice the change in momentum.
Can you think of a case where a roller skate and a truck would have the same momentum?
The roller skate and truck can have the same momentum if the speed of the roller skate is much greater than the speed of the truck. For example, a 1000-kg truck backing out of a driveway at 0.01 m/s has the same momentum as a 1-kg skate going 10 m/s. Both have momentum = 10 kg•m/s.
Which has the greater momentum?
The rolling skateboard
You can't throw a raw egg against a wall without breaking it, but you can throw it at the same speed into a sagging sheet without breaking it. Explain.
The sheet makes the collision take longer, and therefore there is a smaller force on the egg. Remember that the impulse is equal to the change in momentum. The change in momentum is defined by the mass and velocity, neither of which are changed by how you stop the egg. So this means that the only way to decrease the force on the egg is to increase the time it takes to change the momentum, the sheet does this nicely.
Suppose you roll a bowling ball into a pillow and the ball stops. Now suppose you roll it against a spring and it bounces back with an equal and opposite momentum. Which object exerts a greater impulse, the pillow or the spring?
The spring because the forward momentum is stopped and an equal and opposite backward momentum is created, making the impulse twice as big because there is twice as much change in momentum.
Which has the greater mass, a heavy truck at rest or a rolling skateboard?
The truck as the greater mass
What difference in recoil would you expect in firing a solid ball versus firing a hollow ball from the same cannon? Explain.
There is more kick from the solid ball because of a greater change in momentum for the solid ball.
Increasing Momentum
To increase the momentum of an object, apply the greatest force possible for as long as possible. A golfer teeing off and a baseball player trying for a home run do both of these things when they swing as hard as possible and follow through with their swing. The force of impact on a golf ball varies throughout the duration of impact.
What average force does the pillow exert on the ball?
We know from Newton's Third law that the action force equals the reaction force so the force of the pillow on the ball is the same as the force of the ball on the pillow which is 32.
Elastic Collisions
When a moving billiard 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. Momentum is transferred from the first ball to the second ball. When objects collide without being permanently deformed and without generating heat, the collision is an elastic collision. Colliding objects bounce perfectly in perfect elastic collisions. The sum of the momentum vectors is the same before and after each collision.
Do you experience an impulse when you catch a ball of the same speed?
Yes because when you catch the ball it exerts a force on you. This force has an impulse.
Visualize yourself on a skateboard. When you throw a ball, do you experience an impulse?
Yes because when you push on the ball the ball pushes back on you. This force has an impulse.
Do you experience an impulse when you catch it and throw it out again?
Yes you experience the impulse that was described in b when you catch it and the one described in a when you throw it.
Is momentum conserved for colliding objects that are moving at angles to each other?
Yes, this is explained in section 7.6. In order to see this you need to use vectors and vector addition. However, no matter what the angles are, the total (or net) momentum before the collision must equal the total (or net) momentum after.
Momentum
the mass of an object multiplied by its velocity. A moving object can have a large momentum if it has a large mass, a high speed, or both. It is harder to stop a large truck than a small car when both are moving at the same speed. The truck has more momentum than the car. By momentum, we mean inertia in motion.
What impulse acts on the car?
∆(mv) 5 (1000 kg)(20 m/s)=20,000 N/s
