Momentum/Energy Unit-Momentum Sub-Unit
Regents Physics
3.1.1 Momentum & Impulse
Definitions
• momentum: a property of ___________________________ objects o Depends on: ________________and ____________________ o vector : same direction as ____________________
Example #1
• What is the momentum of a 2000 kilogram car that is moving east with a speed of 5.0 meters per second?
Comparing Momentum • Which has greater momentum?
Definitions
• impulse: _____________________________________________________ o Caused by a change in ______________
o vector : same direction as ______________________
Example #2 – Starting
• A 1000 kilogram drag racing car accelerates from 0 to 330 miles per hour (148 meters per second) in 5.0 seconds.
o What is the impulse experienced by the drag racer?
o What is the net force experience by the drag racer?
Equation Units for impulse
Equation Units for momentum
2000 kg car with v = 5 m/s
10000 kg bus with v = 1 m/s
or or
30 kg player with v = 2 m/s
60 kg referee with v = 0 m/s
• An F-4 aircraft with a mass of 2.7 x 104 kilograms lands while moving at 100 meters per second. The aircraft deploys a parachute that slows the aircraft to a speed of 40 meters per second in 8.0 seconds
o What force does the parachute exert on the F-4? o Solution Method #1
o Solution Method #2
PRACTICE
1) Which has the greatest inertia? Which has the greatest momentum? (1) a parked 1000 kg car
(2) a 0.02 kg fly moving at 8.0 m/s (3) a 50 kg sprinter running at 7.5 m/s (4) a 1.0 kg ball rolling down a hill at 0.6 m/s
following objects.
a. A 10 kilogram object that begins from rest and accelerates to a speed of 2.0 meters per second.
pi = _________
pf = _________
J = __________
b. A 5.0 kilogram object initially moving at 3.0 meters per second that comes to a stop in 1.5 seconds.
pi = _________
pf = _________
J = __________
c. A 15.0 kilogram object that is moving east at 1.0 meter per second and is subjected to a net force of 10 newtons to the east for 3.0 seconds. pi = _________
pf = _________
J = __________
d. A 2.0 kilogram object that is moving west at 4.0 meters per second that is slowed down to 0.5 meter per second.
pi = _________
pf = _________
Momentum/Energy Unit-Momentum Sub-Unit
Regents Physics
3) A 5.0 kilogram wooden block is sliding to the right on a wooden table with an initial velocity of 6.0 meters per second. The block eventually comes to a stop.
a. Draw an arrow to show the direction of the block’s initial velocity above the block and label it “v”. Draw and label the THREE forces (weight, normal, and friction) that are acting on the block.
b. Calculate the net force acting on the block.
c. Determine the block’s initial momentum.
d. How long will it take for the block to come to a stop?
Review Questions
3.1.1 – Use equations to calculate impulse; momentum; initial velocity; final velocity; force; and/or time.
- What is the momentum of an object with a mass of 5 kilograms that is moving at 3.0 meters per second.
[15 kg·m/s]
- An object with a mass of 3 kilograms begins with a speed of 2.0 meters per second and increases its speed to 5.0 meters per second in 10 seconds.
o Determine the impulse experienced by the object.
o Determine the net force applied to the object in speeding it up.
[9 kg·m/s; 0.9 N]
- A 2.0 kilogram object at rest is subjected to a net force of 5.0 newtons for 4.0 seconds. What final speed will the object reach?
[10 m/s]
- A 4.0 kilogram object moving west at 8.0 meters per second is subjected to a force to the east for 1.5 seconds, slowing it down to a speed of 2.0 meters per second. Determine the net force that was applied.
Law of Conservation of Momentum
The total amount of momentum in a system must remain constant.
Equation
Elastic Collision
A collision in which two objects hit one another and bounce off with NO STICKING.
Equation
Example #1
• A 2.0 kilogram ball moving at +3 meters per second collides with a 3.0 kilogram ball at rest. Assuming that the 2.0 kilogram ball stops after the collision, what is the velocity of the 3.0 kilogram ball after the collision?
A collision in which two objects collide and stick together to form a single object.
Equation
Example #2
• A 50 kilogram football player moving at +2.0 meters per second collides with a 70 kilogram football player moving at -4.0 meters per second. At what speed will the two players be moving if they are locked together after they collide?
Stopped Crash
A collision in which two objects collide and come to a stop.
Equation
Example #3
• A 1000 kilogram car moving east at 3.0 meters per second collides with a 1500 kilogram car moving west. If the two cars stop after the collision, what velocity did the 1500 kilogram car have before the collision?
before after
before after
Momentum/Energy Unit-Momentum Sub-Unit
Regents Physics
Pop ApartAn interaction in which two objects start from rest and are launched apart with equal momentum.
Equation
Example #4
• A 100 kilogram cannon has a 5.0 kilogram cannonball inside it. If the cannonball is fired with an initial velocity of +20 meters per second, what is the recoil velocity of the cannon?
PRACTICE
1) A 30 kilogram child is running at 12.0 meters per second when she jumps on a stationary, 150 kilogram sled. What is the speed of the sled after the child jumps on board?
2) A 2.0 kilogram block moving east at 5.0 meters per second collides elastically with a 3.0 kilogram block moving west at 5.0 meters per second. After the collision, the 2.0 kilogram ball is moving west at 7.0 meters per second.
a. Determine the total momentum of the system before the collision.
b. Determine the final velocity of the 3.0 kilogram block.
3) A 5.0 kilogram cart and a 2.5 kilogram cart are placed with a spring between them so that both carts are free to move when the spring is released. The 5.0 kilogram cart moves off to the west with a speed of 1.2 meters per second when the spring is released. What will the velocity of the 2.5 kilogram cart be after the spring is released?
Review Questions
3.1.2a – Determine an unknown in an elastic collision.
- A 3.0 kilogram object moving at 2.0 meters per second collides with a 1.0 kilogram object that is initially at rest and comes to a stop. Determine the speed of the 1.0 kilogram object after the collision.
[6m/s]
- A 2.0 kilogram object moving east at 3.0 meters per second collides (with no sticking) with a 4.0 kilogram object moving west at 1.0 meters per second. If the 2.0 kilogram object moves west at 0.5 meter per second after the collsion, determine the direction and speed of the 4.0 kilogram object.
[+0.75m/s]
3.1.2b – Determine an unknown in an inelastic collision.
- A 2.0 kilogram object moving east at 4.0 meters per second collides with a 5.0 kilogram object moving west at 6.0 meters per second. The two objects stick together after the collision. Determine the speed of the two objects after the collision.
[-3.1m/s]
- A 2000 kilogram railroad car moving at 3.0 meters per second rolls under a chute through which a 500 kilogram load of coal is dropped into the car. Determine the speed of the railroad car after the coal is dropped into it.
[2.4m/s]
momentum is zero.
- A 1000 kilogram car moving east collides with a 3000 kilogram truck moving west and both come to aa stop. Before the collision the truck is moving at 2.0 meters per second. What speed was the car moving with before the collision?
[6m/s]
- A 4.0 kilogram cart and a 3.0 kilogram cart are pushed up against opposite sides of a spring and held motionless. When the carts are released, the 3.0 kilogram cart moves west at 10 meters per second. What is the direction and speed of the 4.0 kilogram cart after the release?
[7.5m/s]
- A pair of lab carts, A and B collide and come to a stop. Before the collision, cart A, which has a mass of 2.5 kilograms was moving at 4.0 meters per second. What is the mass of cart B if its speed before the collision was 2.0 meters per second?
