PHSC-Chapter 5 Momentum
For the same force, which cannon imparts the greater speed to a cannonball-a long cannon or a short one? Explain.
A cannonball will have more momentum coming from the long cannon due to the force acting for more time.
elastic collision
A collision in which collision objects rebound without lasting deformation or the generation of heat.
inelastic collision
A collision in which the colliding objects become distorted, generate heat, and possibly join together.
If the equally massive cars of the previous question stick together after colliding inelastically, how does their speed after the collision compare with the initial speed of car A?
Again, the momentum of car A is transferred, this time to both cars. Since twice the mass is moving after collision, the speed is half.
In terms of impulse and momentum, why do air bags in car reduce the chances of injury in accidents?
Air bags lengthen the time of contact thereby reducing the force of contact.
If you're in a car with faulty brakes and you have to hit something to stop, the momentum will change to zero whether you hit a brick wall or a haystack. So why is hitting a haystack a safer bet?
Although the change in momentum, and therefore the impulse will be the same for both, hitting the haystack means a small force and long time (rather than a big force and short time hitting the wall).
Distinguish between an elastic collision and an inelastic collision. For which type of collision is momentum conserved?
An elastic collision is one where rebound is without lasting deformation or the generation of heat. An elastic collision is one where deformation does occur, or heat is generated. Momentum is conserved for both types.
Why is it a good idea to extend your hand forward when catching a fast-moving baseball with your bare hand?
An extended hand has room to move backward when the ball is caught. This stretches the time, which results in less force.
When you are traveling in a car at highway speed, the momentum of a grasshopper is suddenly changed as it splatters onto your windshield. Compared to the change in momentum of the grasshopper, by how much does the momentum of the car change?
By Newton's third law, the force on the grasshopper is equal in magnitude and opposite in direction to the force on the car windshield. The rest is logic: Since the time of impact is the same for both, the amount of impulse is the same for both, which means they both undergo the same change in momentum. The change in momentum of the grasshopper is evident because of its large change in speed. The same change in momentum of the considerably more massive car is not evident, for the change in speed is correspondingly very small. Nevertheless, the magnitude of m •V for the grasshopper is equal to M •v for the car!
To impart the greatest momentum to an object, what should you do in addition to exerting the largest force possible?
Extend the time during which the force acts for more impulse.
Calculate the impulse that occurs when an average force of 10N is exerted on a cart for 5s.
Ft = (10N)(5s) = 50Ns
A car with a mass of 1000 kg moves at 20 m/s. Show that the braking force needed to bring the car to a halt in 10 s is 2000 N.
Ft = change in mv F = change mv/ t (100kg)(20m/s)/10s = 2000N
A car carrying a 75-kg test dummy crashes into a wall at 25 m/s and is brought to rest in 0.1 s. Show that the average force exerted by the seat belt on the dummy is 18,750 N.
Ft = change in mv F = change mv/ t (75kg)(25m/s)/0.1s = 18750N
Why is it incorrect to say that impulse equals momentum?
Impulse equals a change in momentum, not momentum itself.
impulse-momentum relationship
Impulse is equal to the change in the momentum of the object that the impulse acts on. In symbol notation, Ft = change in mv.
How can a supertanker have a huge momentum when it moves relatively slowly?
It has a huge momentum because its mass is so huge.
What does it mean to say that momentum (or any quantity) is conserved?
It means that in any interaction where external impulses don't occur, the momentum of a system remains the same before and after the interaction. In general it means that the magnitude of the quantity remains unchanged while other changes may take place.
A lunar vehicle is tested on Earth at a speed of 10km/h. When it travels as fast on the Moon, is its momentum more, less, or the same?
Its momentum is the same (its weight might change, but not its mass).
A railroad diesel engine weighs four times as much as a freight car. If the diesel engine coasts at 5 km/h into a freight car that is initially at rest, show that the speed of the coupled cars is 4 km/h.
Let m be the mass of the freight car, and 4m the mass of the diesel engine, and v the speed after both have coupled together. Before collision, the total momentum is due only to the diesel engine, 4m (5 km/h), because the momentum of the freight car is 0. After collision, the combined mass is (4m + m), and combined momentum is (4m + m)v. By the conservation of momentum equation: Momentumbefore = momentumafter 4m (5 km/h) + 0 = (4m + m)v (20 ·km/h) = =4 km/h.
Railroad A rolls at a certain speed and makes a perfectly elastic collision with car B of the same mass. After the collision, car A is observed to be at rest. How does the speed of car B compare with the initial speed of car A?
Momentum is completely transferred from car A to car B. Since the masses are the same, the speed of car B is equal to the initial speed of car A.
When a cannonball is fired, is momentum conserved for the cannon-cannonball system as a whole?
Momentum is conserved for the canon-cannonball system, where the forces are internal to the system. Both forces act within the system, whereas if the system in question is only the cannon (or cannonball), force is from outside the system.
Your friend says that the law of momentum conservation is violated when a ball rolls down a hill and gains momentum. What is your response?
Momentum is conserved in the absence of a net force. Gravity on the ball provides the force that gives an impulse to the ball.
Two football players have a head-on collision and both stop short in their paths. if one player is twice, as heavy as the other, how does this speed compare to the smaller player?
Momentum is the same for both, so the twice-as-heavy player would have to be moving at half the speed of the higher player.
A 5-kg fish swimming 1 m/s swallows an absent-minded 1-kg fish swimming toward it at a speed that brings both fish to a halt immediately after lunch. Show that the speed of the approaching smaller fish before lunch must have been 5 m/s.
Momentumbefore = momentumafter (5kg)(1m/s) + (1kg)v = 0 5m/s + v = 0 v = -5 m/s So if the little fish approaches the big fish at 5 m/s, the momentum after will be zero.
When a cannonball is fired, its momentum does change. Is momentum conserved for the cannonball?
No, momentum is not conserved, for an impulse acts on the cannonball.
When a cannonball is fired, the cannon recoils. Is momentum conserved for the cannon?
No, the momentum is not conserved, for an opposite impulse acts on the cannon.
Which requires the greater impulse, stopping something dead in its tracks or stopping it and then reversing its direction?
Stopping and then reversing direction is a greater change in momentum and therefore requires a greater impulse.
Which is the greater change in momentum, stopping something dead in its tracks or stopping it and then reversing its direction?
Stopping and then reversing direction is a greater change in momentum.
In boxing, why is it advantageous to roll with the punch?
The force of impact will be less if momentum changes over a long time. By making t long, F will be smaller.
Why do 6-ounce boxing gloves hit harder than 16-ounce gloves?
The lighter gloves have less padding, and less ability to extend the time of impact, and therefore result in greater forces of impact for a given punch.
impulse
The product of the force acting on an object and the time during which it acts. In an interaction, impulses are equal and opposite.
momentum
The product of the mass of an object and its velocity.
In karate, why is a short time for the applied force advantageous?
The shorter time is accompanied by a greater force when the momentum of the arm is reduced.
In terms of impulse and momentum, why are nylon ropes (which stretch considerably under tension) favored by mountain climbers?
The time is extended while momentum decreases, thereby decreasing the jolting force of the rope. Note that in bringing a person to stop more gently does not reduce the impulse. It only reduces the force.
Why is it less damaging if you fall on a mat than if you fall on a solid floor?
The time to come to a stop will be longer on the mat. This means a longer time to stop and a smaller force.
Which has a greater momentum, a heavy truck at rest or a moving automobile?
The truck at rest has no speed, hence no momentum. So the moving automobile has greater momentum.
A fully dressed person is at rest in the middle of a pond on perfectly frictionless ice and must get to shore. How can this be accomplished?
To get to shore, the person may throw keys or coins or an item of clothing. The momentum of what is thrown will be accompanied by the thrower's oppositely directed momentum. So one can recoil towards shore. (Or inhale facing the shore and exhale facing away.)
law of conservation of momentum
When no external net force acts on an object or a system of objects, no change of momentum takes place. Hence, the momentum before an event involving only internal forces is equal to the momentum after the event: mv(before event) = mv(after event).
When can the momentum of two moving objects be canceled?
When their momentum is equal and opposite and they comprise the same system.
If Fast Freddy doubles his running speed, what else doubles?
a. His momentum
Standing on a skateboard, you toss a ball horizontally away from you. The mass of the ball is one-tenth your mass. Compared with the speed you give to the ball, your ideal recoil speed will be
a. one-tenth as much
If the mass of a cart full of groceries decreases to half and its speed doubles, the momentum of the cart
a. remains unchanged
A big fish swims upon and swallows a small fish at rest. After lunch, the momentum of the big fish is
a. the same as before
The impulse-momentum relationship is a direct result of Newton's
b. second law
Which of the following equations best illustrates the usefulness of automobile air bags?
b.Ft = change in mv
A 1-kg has the same speed as a 10-kg ball. Compared with the 1-kg ball, the 10-kg ball has
c. 10 times as much momentum
Two iron balls, one twice the mass of the other, are dropped from rest from the top of a one-story building. Compared with the lighter ball, the twice-as-heavy ball when hitting the ground below has
c. twice the momentum
When you jump from an elevated position to the ground below, the force you experience when landing depends on
d. All of the above
Your friend says the impulse equals momentum. You disagree and say the friend is missing an important word, which is
d. change
Calculate the momentum of a 50-kg carton that slides at 3m/s across an icy surface.
mv = (50kg)(3m/s) = 150kgm/s