Momentum and Collisions
Mass A, 2.0kg, is moving with an initial velocity of 15m/s in the +x-direction, and it collides with mass B, 4.0kg, initially moving 7.0m/s in the +x-direction. After the collision, the two objects stick together and move as one. What is the change in kinetic energy of the system as a result of the collision, in Joules?
-42.66667
Which of the following statements is true about the center of mass of a system?
-The velocity of the center of mass of the system cannot be changed by an interaction within the system. -In an isolated system that is initially stationary, the location of the center of mass is fixed. -When two objects collide, the velocity of their center of mass will not change.
A 30,000kg freight car is coasting at 0.850m/s with negligible friction under a hopper that dumps 111,000kg of scrap metal into it. What is the final velocity of the loaded car, in m/s?
.18
A 2.5kg block slides across a frictionless table toward a horizontal spring. As the block bounces off the spring, a probe measures the velocity of the block (initially negative, moving away from the probe) over time as follows: What is the average force exerted on the block by the spring over the entire 0.60s time interval of the collision?
100 N
What is the momentum of a 5kg ball dropped out of a 45m high window the instant before it hits the ground, in kg∗m/s?
150
A baseball and a ball of clay are approaching each other. The mass of the baseball is 145g and it is moving due west 5.00m/s at 180∘. The ball of clay is 290g and it is moving Northwest at 135∘ at 4.00m/s. What is the magnitude of their combined velocity after they collide and stick together?
4.02 m/s
A 7.77kg mass is moving due west 180∘ at 7.77m/s. A second mass of 8.88kg is moving due south 270∘ at 8.88m/s. What is the magnitude of their combined velocity, in m/s, after they collide and stick together?
5.96
A tennis ball traveling at 25.0m/s has a mass of 58.5g and bounces off a wall with a speed of 22.5m/s. The impact took 3.33ms. What is the magnitude of the average force exerted by the wall on the tennis ball?
834 N
Tennis racquets have "sweet spots." If the ball hits a sweet spot then the player's arm is not jarred as much as it would be otherwise. How does the "sweet spot" change the impact time of the ball?
It increases impact time
A small force and a large force impart the same change in momentum. What does this imply about the time interval over which each force acts?
The time interval is greater for the small force
What is true about linear momentum and kinetic energy for an isolated system?
Total momentum is always conserved
impulse
change in momentum Δ(mv) = Fnet Δt equal to the are under an Fnet vs. time graph
elestic collisions
conserve kinetic energy and also conserve momentum
when is momentum conserved
in all collisions as long as the system of analysis is large enough to include all of the objects that exert net force during the collision
Which of the following must you know to calculate momentum?
mass and velocity
momentum
mass x velocity or p = mv vector units are kg*m/s slow massive object could have same as fast low mass object
With a mass of 111.1kg, m1 is moving to the right with a velocity of 3.000m/s. m2 is moving at 5.52m/s to the LEFT and has a mass of 222.2kg. After the elastic collision, mass1 bounces off with a velocity of 8.000m/s to the LEFT. Calculate the magnitude of the velocity of m2 after the collision, in m/s.
0.0200
A 50g hockey puck is slapped with an initial velocity of 50m/s at an angle of 60∘ from the x-axis. What is the x-component of the momentum, in kg∗m/s?
1.25
With a mass of 111.1kg, m1 is moving to the right with a velocity of 3.000m/s. m2 is initially at rest and has a mass of 222.2kg. After the elastic collision, m1 bounces off with a velocity of 1.000m/s TO THE LEFT. Calculate the velocity of m2 after the collision.
2.000 m/s to the right
A car moving at 10m/s crashes into a tree and stops in 0.26s. Calculate the force, in N, that the seat belt exerts on a 70kg passenger in the car to bring him to a halt.
2692.3
A 7.77kg pumpkin falls from a height of 12.3m. It hits the ground and comes to an abrupt stop in about 444ms. What is the average force imparted by the ground (aka 'Normal Force') on the pumpkin? HINT: Use the conservation of energy to find the velocity of the pumpkin at the moment just before it hits the ground
272 Using vf^2 = v0^2 + 2ad works as well and is more efficient
Lee Majors, a professional stuntman, is preparing to run off a dock and dive into a large kayak. The stuntman has a mass of 80.8kg and the kayak has a mass of 29.9kg. If Lee dives horizontally with a velocity of 5.50m/s... What is his velocity in m/s immediately after he jumps into the kayak? To simplify things, ignore any velocities in the y-direction.
4.01 Use conservation of momentum to solve this problem. The total mass multiplied by the final velocity must be equal to Lee's initial velocity multiplied by his mass.
Arden and Emory are identical twins. They each have a mass of 19.5kg. Thay are both wearing ice skates and are facing each other. Arden tosses a bowling ball to Emory with a velocity of 3m/s. Arden then moves backwards with a velocity of −0.700m/s. What is the mass of the ball?
4.55 kg
Suppose you are playing billiards and you find yourself behind the eight ball. You want to hit the cue ball at the eight ball, which is at rest, and have the cue ball bounce off at an angle of 40∘ to the left of the initial direction you hit the cue ball. At what angle will the eight ball recoil?
50 degree to the right
Which of the following is an example of a perfectly inelastic collision?
A bullet is shot and lodges into a wooden block. Two bumper cars collide and are coupled. you throw a ball of clay onto a hanging bowling ball and it sticks
Which of the following is true regarding collisions?
An elastic collision describes a collision in which kinetic energy and momentum are conserved
A boy standing on a frictionless ice rink is initially at rest. He throws a snowball in the +x-direction, and it travels on a ballistic trajectory, hitting the ground some distance away. Which of the following is true about the boy while he is in the act of throwing the snowball?
He feels a backward force exerted by the snowball he is throwing.
Which of the following is true of linear momentum in an isolated system?
Linear momentum is a conserved quantity Linear momentum is a vector quantity Linear momentum is dependent on mass Linear momentum is dependent on velocity
Mass A, 2.0kg, has an initial velocity of 4m/s in the +x-direction. Mass B, 2.0kg, has an initial velocity of 5m/s in the -x-direction. If the two masses have an elastic collision, what will be the final velocities of the masses after the collision?
Mass A will move 5m/s in the -x-direction; mass B will move 4m/s in the +x-direction.
Two steel balls collide and bounce apart in an isolated system. If the final kinetic energy is less than the initial kinetic energy, what of the following is true?
Momentum is conserved in this inelastic collision
Most day care centers have carpeted floors instead of tile floors. What does this imply about the relationship between collision time and padding?
Padding increases collision time
An object that has a small mass and an object that has a large mass have the same momentum. Which moving object has the largest speed?
The small mass
A 1200kg test car is driving toward a solid crash-test barrier with a speed of 45mi/h. Two seconds prior to impact, the car begins to brake, but it is still moving when it hits the wall. After the collision with the wall, the car crumples somewhat and comes to a complete stop. In order to estimate the average force exerted by the wall on the car, what information would you need to collect?
The velocity of the car just before impact and the duration of the collision with the wall.
A 2500kg test car is driving toward a solid crash-test barrier with a speed of 45mi/h. Two seconds prior to impact, the car begins to brake, but it is still moving when it hits the wall. After the collision with the wall, the car crumples somewhat and comes to a complete stop. In order to estimate the average force exerted by the wall on the car, what information would you need to collect?
The velocity of the car just before impact and the duration of the collision with the wall.
This graph shows the positions of two colliding objects measured before, during, and after a collision. Mass A is 1.0kg. Mass B is 3.0kg. Which of the following statements is true?
This is an elastic collision, with a total momentum of 0kg•m/s.
conservation of momentum in collisions
When no external forces act on a system of objects, the system's momentum can not change. The total momentum of two objects before a collision is equal to the objects' total momentum after the collision. Momentum is a vector: that is, total momentum of two objects moving in the same direction adds together; total momentum of two objects moving in opposite directions subtracts. A system's center of mass obeys Newton's second law: that is, the velocity of the center of mass only changes when an external net force acts on the system.
What is true about the momentum vector?
When you muliply mass (a scalar) by velocity (a vector), the result is momentum (a vector) The direction of the momentum vector is the same as the velocity vector The magnitude of the momentum vector is dependent on the mass
A train car passes under a grain silo and is filled with grain. What will happen to the car's speed due to the increase in mass? Neglect any effects due to friction.
decrease because of conservation of momentum
inelestic collisions
dissapate energy and also conserve momentum
Suppose a particle of known mass and velocity collides with a second particle of known mass that is at rest. You try to solve for the final velocities of both particles in the plane of collision, but when you apply the equations of conservation of momentum along the x-axis and y-axis, you realize that there are too many unknowns. How many pieces of information do you need to solve for each particle's final velocity?
two