Honors Physics Chapter 7 - Momentum and Collisions
A curling stone with a mass of 20.0 kg strikes a second stone with a mass of 16.0 kg. The second stone slides forward with a velocity of 1.52 m/s and the first continues forward with a velocity of 0.05 m/s. What was the original velocity of the first stone?
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A kickball with a mass of 0.85 kg moves at a speed of 12.0 m/s. Then the ball is kicked and rebounds in the opposite direction at a speed of 24.0 m/s. What is the change in momentum of the ball?
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Two bubbles of fluid with masses 0.3 kg and 1.7 kg collide head -on and combine to form a single bubble. The initial speed for each is 1.45 m/s. If the velocity of the new bubble with mass 2.0 kg is 1.10 m/s what is the decrease in kinetic energy?
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Impulse
A change in momentum. THE PRODUCT OF FORCE AND CHANGE IN TIME; SYMBOL IS J.
Inelastic Collision
A collision in which the colliding objects become distorted, generate heat, and possibly stick together.
Perfectly inelastic collision
A collision in which two objects stick together and move with a common velocity after colliding.
Momentum
A quantity defined as the product of the mass and velocity of an object. p = mv (momentum is measured in kg m/s)
Change in Momentum
An external force applied constantly to an object for a certain time interval will cause a change in the object's momentum equal to the product of the force and the time interval. Δp = FΔt
A 68-kg canoeist stands in the middle of her 32-kg canoe. Initially, both the canoeist and the canoe are at rest, and the canoe is pointing directly toward the shore. If the canoeist begins to walk toward one end of the canoe with a speed of 0.95 m/s relative to the shore, what is the speed of the canoe relative to the shore?
Both objects will accelerate and momentum will be conserved. m1v1 = m2v2 v2 = m1v1 / m2 = (68kg)(0.95m/s) / (32kg) --> v2 = 2.0m/s
Two canoes are touching and at rest on a lake. The occupants push away from each other in opposite directions, giving canoe 1 a speed of 0.58 m/s and canoe 2 a speed of 0.38 m/s . If the mass of canoe 1 is 325 kg , what is the mass of canoe 2?
Both objects will accelerate and momentum will be conserved. m1v1 = m2v2 --> m2 = m1v1 / v2 m2 = (325kg)(0.58 m/s) / (0.38 m/s) m2 = 500 kg or 5.0x10^2 kg
Four automobiles are initially traveling at the indicated velocities. The automobiles have different masses and velocities. The drivers step on the brakes and all automobiles are brought to rest.
Car A: 35,00.0 kg Car B: 1,000 kg 15.0 m/s 20.0 m/s Car C: 1,00.0 kg Car D: 1,500 kg 10.0 m/s 15.0 m/s
A 280-g ball falls vertically downward, hitting the floor with a speed of 2.5 m/s and rebounding upward with a speed of 2.0 m/s. (Let upward be the positive direction.) A: What was the ball's momentum just before it hit the floor? B: What was the ball's momentum just after it rebounded from the floor?
Convert g to kg. A: p = mv = (0.28kg)(-2.5m/s) --> downward momentum is -0.70 kg m/s B: p = mv = (0.28kg)(2.0 m/s) --> upward momentum is 0.56 kg m/s
A 92-kg astronaut and a 1800-kg satellite are at rest relative to a space station. The astronaut pushes on the satellite, giving it a speed of 0.14 m/s directly away from the station. Seven and a half seconds later the astronaut comes into contact with the station. What was the initial distance from the station to the astronaut?
First, find the velocity of the astronaut using: m1v1 = m2v2 v1 = m2v2/m1 = (1800kg)(0.14m/s) / (92kg) --> v1 = 2.7 m/s Next, use the velocity and time to find distance. s = d/t or d = s•t --> d = (2.7m/s)(7.5s) = 20 m (two sig. figs). 2.0x10^1 m
A safety helmet extends the time of impact from 0.005 s to 0.020 s. (a) By what factor is the average force that causes the impact reduced?
I = FΔt The Δt for the impulse increased from 0.005s to 0.0020s. Which is 4 times as long. (0.0020s / 0.005s ) = 4. Therefore: F = I/4Δt. Force is reduced by a factor of 4.0.
During a ballistics test a bullet is fired into a thick gel to bring it to a stop. A 5.5-g bullet traveling at 325 m/s is brought to a stop in the gel by an average force of 750 N . What amount of time is needed for the bullet to come to rest?
Impulse Theorem: FΔt = Δp --> Δt = Δp / F Convert 5.5 g into kg. Δt = (325 m/s) ( 0.0055kg) / 750 N --> Δt = 2.4x10^-3 s 2.4 ms
During an intense game of croquet, a 0.52-kg ball at rest on the grass is struck by a mallet with an average force of 190 N. If the mallet is in contact with the ball for 6.6 ×10^−3s , what is the ball's speed just after it is hit?
Impulse Theorem: FΔt = Δp Since the ball was at rest initial mv = 0 kg m/s. FΔt = mv(f) ---> v = FΔt/m v = (190N)(6.6x10^-3 s) / (0.52kg) ---> v = 2.4 s.
In every interaction between isolated objects, the change in momentum of the first object is _________ to the change in momentum of the second object.
In every interaction between isolated objects, the change in momentum of the first object is EQUAL AND OPPOSITE to the change in momentum of the second object.
Rank these automobiles based on the magnitude of the impulse needed to stop them, from largest to smallest.
Largest Smallest
Rank these automobiles based on the magnitude of their momentum before the brakes are applied, from largest to smallest.
Largest Smallest
Which is preserved in an elastic collision, Momentum or Kinetic Energy?
Momentum and Kinetic energy are both conserved in an elastic collision.
Conservation of momentum
Momentum can be transferred from one object to another without a change in the total momentum of the entire "system".
Which is conserved in a perfectly inelastic collision, Momentum or Kinetic Energy?
Momentum is conserved but Kinetic Energy is not conserved because some of the Kinetic Energy is converted to sound and internal energy as the objects deform.
Elastic Collision
Occurs when two objects collide and return to their original shapes with no change in the total kinetic energy. After an elastic collision the two object move separately.
Rank the automobiles based on the magnitude of the force needed to stop them, from largest to smallest.
The correct ranking cannot be determined. The more momentum an object has, the more impulse is needed to stop it. However, this impulse can be provided via a large force acting over a short time interval or a relatively small force acting over a relatively long time interval.
What happened to the momentum of an object when it is brought to rest.
The momentum is brought to zero because the opbject no longer has any velocity.
A large tractor bumps into a less massive wagon. The momentum of the tractor _____ while the momentum of the wagon ____.
The momentum of the tractor DECREASES while the momentum of the wagon INCREASES.
A skier with a mass 33.0 kg uses skies with a combined mass of 6.0 kg at slides at a velocity of 2.8 m/s. Compare the momentum of the skier to the momentum of the skies.
The skier has a greater momentum than the skies because the skier has a greater mass.
If the mass of the canoe were increased, would the speed found be greater than, less than, or the same as before?
The speed would be less.
Two skaters stand facing each other. One skater's mass is 70 kg, and the other's mass 94 kg. If the skaters push away from each other: a) the 70 kg skater travels at a lower momentum b) the 904 kg skater travels at a lower momentum c) their momentum decreases d) their momenta are equal but opposite.
Two skaters stand facing each other. One skater's mass is 70 kg, and the other's mass 94 kg. If the skaters push away from each other: *d) their momenta are equal but opposite.*
Which two factors can be changed to increase your momentum?
Your mass and your velocity.
In a collision between two unequal masses, which mass receives a greater magnitude impulse? a) The smaller mass b) The larger mass c) They receive equal impulses.
c) They receive equal impulses.
A young hockey player stands at rest on the ice holding a 1.5-kg helmet. The player tosses the helmet directly in front of him with a speed of 5.5 m/s and recoils with a speed of 0.20 m/s . What is the mass of the hockey player?
m1v1 = m2v2 --> m1 = m2v2/v1 m1 = (1.5 kg)(5.5 m/s) / (0.20 m/s) --> m1 = 41 kg
Conservation of Momentum Formula
m1v1i + m2v2i = m1v1f + m2v2f
A 58.0 kg ice skater standing on a friction-less ice throws a 0.25 kg snowball horizontally at a speed of 28 .0 m/s. At what velocity does the skater travel backwards.
m1v1i + m2v2i = m1v1f + m2v2f 0 = m1v1f + m2v2f Neither object is in motion at first. m1v1f = m2v2 (58.0kg)v1f = (0.25kg)(28.0m/s) v = 0.12 m/s
Two air-track carts move toward one another on an air track. Cart 1 has a mass of 0.35 kg and a speed of 1.2 m/s. Cart 2 has a mass of 0.61 kg and a speed of 0.85 m/s. What is the total momentum of the system, assuming that cart 1 moves in the positive direction?
p1 = m1v1 = (0.35kg)(1.2m/s) = 0.42 kg m/s p2 = m2v2 = (0.61 kg)(-0.85) = -0.52 kg m/s p total = p1 + p2 = 0.42 + (-0.52 kg m/s) = - 0.099 kg m/s
A 280-g ball falls vertically downward, hitting the floor with a speed of 2.5 m/s and rebounding upward with a speed of 2.0 m/s. (Let upward be the positive direction.) What was the ball's change in momentum during its impact with the floor?
Δp = p(final) - p(initial) = (0.56kg m/s) - (-0.70 kg m/s) --> Δp = 1.26 kg m/s
