name regents physics - johnson city high school...

Name__________________________ Regents Physics

Date_____________________

Unit Packet Contents Notes 1: Impulse Momentum

Concept Development: Momentum (pg 29)

Guided Practice: Impulse Momentum

Notes 2: Conservation of Momentum

Concept Development: Momentum Conservation (pg 30)

Guided Practice: Conservation of Momentum in Explosions

Guided Practice: Conservation of Momentum in Collisions

Unit Objectives: Forces / Vectors

At the end of this unit you will be able to:

1. Define the term momentum, and state its SI unit.

2. Solve problems involving mass, velocity, and momentum.

3. Define the term impulse, and state its SI unit.

4. Relate impulse to change in momentum.

5. Solve impulse-momentum problems.

6. State the law of conservation of momentum.

7. Solve problems involving momentum being conserved in explosions.

8. Explain the difference between an elastic and inelastic collisions.

9. Solve problems involving momentum being conserved in collisions.

10. Relate the law of conservation of momentum to Newton’s third law

Text Assignment: Due Friday February 1

Read pages 86 – 99

Do Review Questions 1-18

Do Plug N Chug 19 – 22

Do Think N Explain 24, 26, 29

Remember to write

complete sentences and

complete thoughts

when doing your

homework

Ph6_notes1key Page 1 of 4

Name__________________________ Regents Physics Date_____________________ Notes: Impulse/Momentum Thought question:

Even though the Volkswagon will suffer greater damage the forces exerted are

______________________ forces and are therefore equal.

Since the Mack truck possess much greater ______________ it also possesses more of a quantity

called ________________.

o Note that this assumes that the VW and the truck have the same ____________

Momentum

A vector quantity that is related to the ____________________________ of a moving object

Objects with larger mass have _______________________ than those with smaller mass and equal

velocity

Objects with greater velocity have _____________________ than those with a smaller speed and

equal mass.

Units for momentum -- _________________ (Not same as newtons Kg m/s2)

Example 1: Find the momentum of the following objects:

a. A baseball with a mass of 0.25 kg and a velocity of 20 m/s

b. A train with a mass of 90,000 Kg and a velocity of 5 m/s

c. A bullet with a mass of 0.100 kg and a velocity of 125 m/s

p = mv Where: p = momentum m= mass v = velocity

mass and speed

more momentum

more momentum

Kg m/s

action - reaction

mass

momentum

speed

p = mv = (0.25kg) (20 m/s) = 5 kg m/s

p = mv = (90,000kg) (5 m/s) = 450,000 kg m/s

p = mv = (0.100kg) (125 m/s) = 12.5 kg m/s


Impulse

A ______________ being exerted over a given _________________.

Causes a change in an object’s _____________________.

FtJ

Deriving Impulse vs. Momentum relationship

Remember Newton’s second Law

Which formula defines acceleration?

Substitute in Newton’s second law with this formula.

Check the dimensional analysis (do the units work out?)

Impulse / Momentum problems

The larger the ______________ and the greater the _______________ it is being exerted, the more it

will change the _______________ of an object

force time

momentum

force time

momentum

Where: J = impulse F = force

t = time

Fnet = m a

a = Δv / t

Fnet = m Δv / t Fnet t = m Δv Or J = Δp


Example 1: A force of 20 N acts on a 2.0 kg mass that starts out at rest for 10 s. Compute the impulse

and the final momentum of the mass. Calculate the velocity of the mass after the completion of the 10

seconds.

Example 2: A car that weighs 7840 N is accelerated from rest to a velocity of 25.0 m/s eastward by a

force of 1000 N. What was the car’s change in momentum? How long did the force act to change the

car’s momentum?

Example 3: A force of 6.00 N acts on a 3.00 kg object for 10.0 s. What is the object’s change in

momentum? What is its change in velocity?

60.0 kg m/s 20.0 m/s

F = 20 N J = F t = Δp m = 2.0 kg J = (20 N) (10s) t = 10 s J = Δp = 200 N s Δp = m Δv = m(vf – vi) 200 N s = 2.0 kg (vf – 0) vf = 100 m/s


Example 4: What force is needed to bring a 1.10 x 103 kg car moving at 22.0 m/s to a halt in 20.0 s.

Example 5: A net force of 2.00 x 103 N acts on a rocket of mass 1.00 x 10

3 kg. How long does it take

this force to increase the rocket’s velocity from 0.0 m/s to 2.00 x 10 2 m/s?

Example 6: A car weighing 15680 N and moving at 20.0 m/s is acted upon by a 6.40 x 10

2 N force until

it is brought to a halt.

a. What is the car’s mass?

b. What is its initial momentum?

c. What is the change in the car’s momentum?

d. How long does the braking force act on the car to bring it to a halt?

-1210N

100 sec

1600 kg 32000 kg m/s 32000 kg m/s 50.0 seconds

Ph6_CDMntmIntroKey Page 1 of 1

Name ______________________ Regents / Honors Physics

Date ____________

Concept Development: Momentum Intro

Name____________________________________ Regents Physics

Date_________________________

Guided Practice: Impulse / Momentum

1. A fullback of mass 120 kg traveling at 20.0 m/s collides with another player and comes to rest in

1.5 seconds. What was the force of the impact?

2. A golf ball of mass 0.050 kg acquires a speed of 80.0 m/s when hit with a force of 3.0 x 103 N.

How long was the club in contact with the ball?

3. What force, acting for 1.35 x 10-3

seconds, will change the velocity of a 95-gram baseball from

50.0 m/s eastward to 45.0 m/s westward?

4. A 10,000-kg freight car is rolling along a track at 3 m/s. Calculate the time needed for a force of

1000 N to stop the car.

1600 N

1.3 x 10-4

s

6.7 x 103 N

30 s

5. A 0.25 kg soccer ball is rolling at 6.0 m/s toward a player. The player kicks the ball back in the

opposite direction and gives it a –14.0 m/s velocity. What is the average force during the

interaction between the player’s foot and the ball if the interaction lasts 2.0 x 102 sec?

6. Wayne hits a stationary 0.12 kg hockey puck with a force that lasts for 1.0 x 10-2

seconds and

makes the puck shoot across the ice with a speed of 20.0 m/s, scoring a goal for the team. With

what force did Wayne hit the puck?

7. A tennis ball traveling at 10.0 m/s is returned by Venus Williams. It leaves her racket with a

speed of 36.0 m/s in the opposite direction from which it came.

a. What is the change in momentum of the tennis ball?

b. If the 0.060 kg ball is in contact with the racket for 0.020 s, with what average force has

Venus hit the ball?

8. Auto companies frequently test the safety of automobiles by putting them through crash tests to

observe the integrity of the passenger compartment. If a 1000.-kg car is sent toward a cement

wall with a speed of 14 m/s and the impact brings it to a stop in 8.00 x 10-2

s, with what average

force is it brought to rest?

-250 N

240 N

2.8 kg m/s

140 N

175,000 N

Name__________________________ Regents Physics

Date_____________________

Notes: Cons. of Momentum

Newton’s 2nd

Law Revisited

According to Newton’s second law in order to __________________ an object a ________________

must be exerted.

The impulse momentum relationship is another way of describing the same phenomenon but we say

that an ____________________ must be exerted to change ______________________.

Internal vs. External Forces

Imagine that you have run out of gas in your car and you want to push the car to the side of the road.

Sitting the front seat and pushing on the dashboard will not help; this would be considered

_______________________ on the car.

Getting out and pushing on the bumper while standing on the road would be considered

_____________________ on the car.

Law of Conservation of Momentum

If a system has no _______________________ acting on it then the

______________________________ of the system remains constant.

Now consider a cannonball being fired from a cannon.

The cannon exerts a ______________ on the ball and the ball exerts a _____________________ on

the cannon.

Momentum is a _______________________ so we consider the momenta of the cannon and the ball

as vectors in ___________________ directions.

Momentum is conserved here because the momentum of the ball is ________________________ to

the momentum of the cannon but in the opposite direction.

Conservation of momentum in explosions.

If an object or system _________________ into smaller pieces the sum of the resulting momentum

vectors is _________________.

external forces

breaks up

zero

accelerate force

impulse momentum

internal forces

external forces

total vector momentum

force reaction force

vector quantity

opposite

equal in magnitude

This can be summed up by the formula:

Pbefore = Pafter

Example 1: Two ice skaters are standing, face to face, at rest in the middle of a skating rink. They push

off from one-another. The first skater has a mass of 65 kg and is moving away at 5.0 m/s. The second

skater has a mass of 75 kg. How fast is the second skater sliding away?

Example 2: A 4.0 kg shotgun shoots a slug with a mass of 0.010 kg with a velocity of 300 m/s. What is

the recoil velocity of the shotgun?

EventtheAfter

VectorsMomentum

allofSumThe

EventtheBefore

VectorsMomentum

allofSumThe

Example 3: Upon launching a 4.0 kg model rocket expels 50.0 g of oxidized fuel from its exhaust at an

average velocity of 600 x 102 m/s. What is the vertical velocity of the model rocket after the launch?

Example 4: Two campers dock a canoe. One camper steps onto the dock. This camper has a mass of

80.0 kg and moves forward at a speed of 4.0 m/s. With what speed and direction will the canoe and the

other camper move if their combined mass is 110 kg?

Conservation of momentum in collisions

Perfectly Elastic Collisions

A collision between two objects where __________________________ in the collision

Not possible in real physical problems but can come close.

When object(s) rebound, their ______________________________is the same as before they

collided

ΣPbefore= ΣPafter Still holds

Example 6: A 0.50 kg ball traveling at 6.0 m/s collides head-on with a 1.00 kg ball moving in the

opposite direction at a velocity of –12.0 m/s. The 0.50 kg ball moves away at –14 m/s after the

collision. Find the velocity of the 1.00 kg ball after the collision.

no KE is lost

combined momentum

Perfectly Inelastic Collisions:

A collision between two objects where _________________________ in the collision

After the collision there is __________________ but rather the objects begin new motion as a

___________________________.

The momentum of the combined system is equal

to the sum of the momentum vectors of

______________________________

Example 7: Moving at 20.0 m/s a car of mass 7.00 x

102 kg collides with a stationary truck of mass 1.40 x

103 kg. If the two vehicles interlock as a result of the

collision, what is the velocity of the car-truck system?

no KE is lost

no rebound combined system

the individual objects

Example 8: A bullet of mass 50.0 g strikes a wooden block of mass 5.0 kg and becomes embedded in

the block. The block and bullet then flies off at 10.0 m/s. What was the original velocity of the bullet?

Example 9: A 75 kg man is ice skating in a straight line at a speed of 0.50 m/s. A 60 kg woman is

sneaking up behind him in the same straight line at a speed of 0.80 m/s. When she reaches him she

throws her arms around him and they continue to move in the same straight line. What was their speed

after they connected?

Ph6_CDMntmConsKey Page 1 of 1

Name ______________________ Regents / Honors Physics

Date ____________

Concept Development: Momentum Conservation

New speed =


Date_________________________

Guided Practice: Conservation of Momentum

In Explosions

1. A 40.0-kg projectile leaves a 2.00 x 103 kg launcher with a velocity of +8.00 x 10

2 m/s. What is

the recoil velocity of the launcher?

2. A thread holds two carts together on a frictionless surface. A compressed spring acts upon the

carts. After the thread is burned, the 1.5 kg cart moves with a velocity of 27 cm/s to the left.

What is the velocity of the 4.5 kg cart?

3. What is the recoil velocity of a 1.20 x 103 kg launcher if it projects a 20.0 kg mass at a velocity

of 6.00 x 102 m/s?

10 m/s

9.1 cm/s

16 m/s

4. Sergie, a 75 kg ice skater stands face to face with Margarite, a 62 kg ice skater. They push off

from one another and Sergie coasts away with a velocity of 3.2 m/s. What is the velocity of

Margarite?

5. A 5.00 g projectile is launched with a horizontal velocity of 647 m/s from a 4.65 kg launcher

moving at 2.00 m/s. What is the velocity of the launcher after the projectile is launched?

6. An astronaut is on a space walk repairing a satellite. After completing the repair the astronaut

pushes off from the satellite and floats away with a velocity of 2.5 m/s while the satellite floats

away with a velocity of 0.175 m/s. The astronaut and all of his gear has a mass of 225 kg. What

is the mass of the satellite?

5 m/s


Date_________________________

Guided Practice: Conservation of Momentum

In Collisions

1. Moving at 20.0 m/s, a car of mass 7.00 x 102 kg collides with a stationary truck of mass 1.40 x

103 kg. If the two vehicles interlock as a result of the collision, what is the velocity of the car-

truck system?

2. A bullet of mass 50.0 g strikes a wooden block of mass 5.0 kg and becomes embedded in the

block. The block and bullet then flies off at 10.0 m/s. What was the original velocity of the

bullet?

3. A 0.50 kg ball traveling at 6.0 m/s collides head on with a 1.00 kg ball moving in the opposite

direction at a velocity of –12.0 m/s. The 0.50 kg ball moves away at –14 m/s after the collision.

Find the velocity of the 1.00 kg ball after the collision.

4. Jamal is at the state fair playing some of the games. At one booth he throws a 0.50 kg ball

forward with a velocity of 21.0 m/s in order to hit a 0.20 kg bottle sitting on a shelf, and when he

makes contact the bottle goes flying forward at 30.0 m/s.

a. What is the velocity of the ball after it hits the bottle?

b. If the bottle were more massive, how wou8ld this affect the final velocity of the ball?

6.67 m/s

1.0 x 103

m/s

-2.0 m/s

a. 9.0 m/s

b. the ball’s final velocity

would be less

5. Jeanne rolls a 7.0 kg bowling ball down the alley for the league championship. One pin is still

standing, and Jeanne hits it head-on with a velocity of 9l m/s. The 2.0 kg pin acquires a forward

velocity of 14.0 m/s. What is the new velocity of the bowling ball?

6. Running at 2.0 m/s, Dirk, the 45.0 kg quarterback, collides with Biff, the 90.0 kg tackle, who is

traveling at 7.0 m/s in the other direction. Upon collision, Biff continues to travel forward at 1.0

m/s. How fast is Bruce knocked backwards?

7. Anthony and Sissy are participating in the “Roll-a-Rama” roller skating dance championship.

While 75.0 kg Anthony roller skates backwards at 3.0 m/s, 60.0 kg Sissy jumpsinto his arms with

a velocity of 5.0 m/s in the same direction.

a. How fast does the pair roll backwards together?

b. If Anthony is skating toward Sissy when she jumps, would their combined final velocity

be larger or smaller than your answer to part a? Why?

8. Tyrrell throws his 0.20 kg football in the living room and knocks over his mother’s 0.80 kg

antique vase. After the collision, the football bounces straight back with a speed of 3.9 m/s,

while the vase is moving at 2.6 m/s in the opposite direction.

a. How fast did Tyrrell throw the football?

b. If the football continued to travel at 3.9 m/s in the same direction it was thrown, would

the vase have to be more or less massive than 0.80 kg?

5.0 m/s

10 m/s

a. 3.9 m/s

b. Smaller b/c their total momentum

would be less.

a. 6.5 m/s

b. Less b/c the football would not have had as

much change in momentum

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