Unit 4: Linear Momentum Name: - Rockwood School District Physics 1/Assignments... · Unit 4: Linear Momentum Name: ... The student is able to design an experimental test of an application

Unit 4: Linear Momentum Name: ____________________________

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Big Idea 1: Objects and systems have properties such as mass and charge. Systems may have

internal structure.

Prof-

icient

Essential Knowledge 1.A.1: A system is an object or a collection of objects. Objects are treated as

having no internal structure.

a. A collection of particles in which internal interactions change little or not at all, or in which

changes in these interactions are irrelevant to the question addressed, can be treated as an object.

Big Idea 3: The interactions of an object with other objects can be described by forces.

Essential Knowledge 3.D.1:

The change in momentum of an

object is a vector in the

direction of the net force

exerted on the object.

Learning Objective (3.D.1.1):

The student is able to justify the selection of data needed to

determine the relationship between the direction of the force

acting on an object and the change in momentum caused by that

force.

Essential Knowledge 3.D.2:

The change in momentum of an

object occurs over a time

interval.

a. The force that one object

exerts on a second object

changes the momentum of the

second object (in the absence of

other forces on the second

object).

b. The change in momentum of

that object depends on the

impulse, which is the product of

the average force and the time

interval during which the

interaction occurred.


The student is able to justify the selection of routines for the

calculation of the relationships between changes in momentum of

an object, average force, impulse, and time of interaction.


The student is able to predict the change in momentum of an

object from the average force exerted on the object and the interval

of time during which the force is exerted.


The student is able to analyze data to characterize the change in

momentum of an object from the average force exerted on the

object and the interval of time during which the force is exerted.


The student is able to design a plan for collecting data to

investigate the relationship between changes in momentum and the

average force exerted on an object over time.

Big Idea 4: Interactions between systems can result in changes in those systems.

Essential Knowledge 4.B.1:

The change in linear

momentum for a constant-mass

system is the product of the

mass of the system and the

change in velocity of the center

of mass.

Learning Objective (4.B.1.1):

The student is able to calculate the change in linear momentum of

a two-object system with constant mass in linear motion from a

representation of the system (data, graphs, etc.).


The student is able to analyze data to find the change in linear

momentum for a constant-mass system using the product of the

mass and the change in velocity of the center of mass.

Essential Knowledge 4.B.2: The change in

linear momentum of the system is given by

the product of the average force on that

system and the time interval during which

the force is exerted.

a. The units for momentum are the same as

the units of the area under the curve of a

force versus time graph.

b. The changes in linear momentum and

force are both vectors in the same direction.


The student is able to apply mathematical routines to

calculate the change in momentum of a system by

analyzing the average force exerted over a certain time

on the system.


The student is able to perform analysis on data

presented as a force-time graph and predict the change

in momentum of a system.

Unit 4: Linear Momentum Name: ____________________________

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Big Idea 5: Changes that occur as a result of interactions are constrained by conservation laws.

Essential Knowledge 5.A.2: For all systems under

all circumstances, energy, charge, linear momentum,

and angular momentum are conserved. For an

isolated or a closed system, conserved quantities are

constant. An open system is one that exchanges any

conserved quantity with its surroundings.

Learning Objective (5.A.2.1):

The student is able to define open and closed

systems for everyday situations and apply

conservation concepts for energy, charge,

and linear momentum to those situations.

Essential Knowledge

5.D.1: In a collision

between objects, linear

momentum is

conserved.

a. In a closed system,

the linear momentum is

constant throughout the

collision.


The student is able to design an experimental test of an application of the

principle of the conservation of linear momentum, predict an outcome of

the experiment using the principle, analyze data generated by that

experiment whose uncertainties are expressed numerically, and evaluate

the match between the prediction and the outcome.


The student is able to analyze data that verify conservation of momentum

in collisions with and without an external friction force.

Essential Knowledge 5.D.3: The velocity of the

center of mass of the system cannot be changed by an

interaction within the system.

a. The center of mass of a system depends upon the

masses and positions of the objects in the system. In

an isolated system (a system with no external forces),

the velocity of the center of mass does not change.

b. When objects in a system collide, the velocity of

the center of mass of the system will not change

unless an external force is exerted on the system.


The student is able to predict the velocity of

the center of mass of a system when there is

no interaction outside of the system but there

is an interaction within the system (i.e., the

student simply recognizes that interactions

within a system do not affect the center of

mass motion of the system and is able to

determine that there is no external force).

Impulse and Momentum Reading Assignment

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Directions: Read Chapter 9 sections 9.1-9.6. As you read answer all Stop to Think questions (Check your

answers on page282) and work through all example problems. Below is a list of what you need to take

away from your reading.

1. Define/Know

a. Impulsive force

b. Impulse: formula, symbol, units

c. momentum: formula, symbol, units

d. total momentum

e. the law of conservation of momentum

f. explosion

g. perfectly inelastic collision

2. Explain:

a. how the magnitude of an impulsive force changes with time.

b. impulse and momentum theorem

c. how to use the impulse momentum theorem to decrease the force of impact in a collision

d. how conservation of momentum is used to solve collision problems

e. when momentum is conserved (and when it is not)

3. Be able to:

a. Calculate impulse in terms of time and force.

b. Interpret a Force vs. time graph, and what the area under the curve represents.

c. Calculate momentum if mass and velocity is known.

d. Calculate the change in momentum and relate that to the magnitude of the impulse.

e. calculate an initial (or final) velocity using conservation of momentum (see example 9.5)

Impulse and Momentum Problems

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42.0O

1.50 m

6.50 kg

Momentum

1. What is the momentum for a 0.05 kg paintball traveling 150 m/s?

2. What momentum does a 1400 kg automobile traveling 0.9 m/s (a few miles per hour) have?

3. A pair of 100,000 kg railroad cars move east; the first moving at 12.5 m/s, the second at 11.2 m/s. What is the magnitude of the total momentum of the system?

4. 6.50 kg block slides down a ramp that is elevated at 42.0° a distance of 1.50 m. The coefficient of kinetic friction is 0.235.

a. What is the acceleration of the block down the ramp?

b. What is the speed of the block when it reaches the bottom?

c. What is the momentum of the block at the bottom of the ramp? 5.


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6. 7. 8. Impulse 9.


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10. 11. 12. 13. A participant in the World’s Strongest Man competition exerts a force of 650 N on a 1,800 kg cable car for 25 seconds. Ignore friction between the wheels and the track.

(a) Calculate the Impulse exerted on the cable car. (b) If the cable car started from rest, what was its speed after the strongman pushed for 25 seconds?


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14. It takes you all of 0.018 s to initially touch and then catch a 0.600 kg football travelling at 16.0 m/s. (a) What is the change in momentum for the football? (b) What is the impulse? (c) What is the force that must be exerted to stop the ball?

15. A horizontal force of 25 N acts for 5 seconds on a 50 kg object that starts from rest on a frictionless horizontal surface.

(a) Calculate the impulse on the object? (b) How fast is the object moving at the end of the 5 second interval?

16. The front of 1400 kg car is designed to absorb the shock of a collision by having a “crumple zone” in which the front 1.20 m of the car collapses in absorbing the shock of the collision. If a car traveling 25.0 m/s stops uniformly in 1.20-m

(a) what is the acceleration of the car? (b) how long does the collision last? (c) Calculate the initial momentum of the car? (d) What is the magnitude of the average force on the car?


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17.

18.


9

18 (continued).

Conservation of Momentum 19.


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20.

21. At the lake out on a float is a water slide. You have been sliding down it and landing in the water with a velocity of Vw all morning. Then a large, very fast boat comes by that is making very large waves with causes the rope that anchors the floating slide to break so now it is free to move in the water. After the waves dissipate and the water is smooth you decide to slide down the slide again. If the water provides no resistance force to the motion of the floating slide, how does your velocity when you hit the water compare to Vw? Explain this result in terms of the law of conservation of momentum.


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22.


12

22 (continued)


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23. During practice, a quarterback throws a 0.43 kg football with a velocity of 8.2 m/s to the south into a 0.16 kg trash can laying on its side. The trash can travels with the ball after the collision. What is the final velocity of the combined mass?

24. A 2.15 kg ball (m1) moving at 5.00 m/s to the right hits a 1.15 kg ball (m2) head-on that is traveling at 3.50 m/s to the left. The second ball (m2) ends up going to the right with a velocity of 3.00 m/s. What is the velocity of the first ball after the collision?

25. A 3.50 kg object, object A, moving at 5.50 m/s to the right collides head on with a 5.00 kg object, object B, that is a rest. The 3.50 kg object ends up with a speed of 0.50 m/s in the opposite direction. What is the velocity of the two objects after the collision? 26. Dan (50 kg) is gliding on his skateboard (5 kg) at 4 m/s. He suddenly jumps off the skateboard, kicking the skateboard backward at 8 m/s. How fast is Dan going as his feet hit the ground?


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27. You find yourself stranded on this very slippery sheet of ice. There is so little friction that you can’t walk at all. No worries, you’ve got this lovely 2.5 kg physics book. You throw it away from yourself giving it a speed of 8.4 m/s. Figure your mass at 42.0 kg. (a) What is your speed after you let go of the book? (b) How much time does it take for you to reach the other side of the ice 15.5 m away? 28.


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.

29. Several students are riding in bumper cars at an amusement park. The combined mass of car A and its

occupants is 250 kg. The combined mass of car B and its occupants is 200 kg. Car A is 15 m away from car B

and moving to the right at 2.0 m/s, as shown, when the driver decides to bump into car B, which is at rest.

(a) Car A accelerates at 1.5 m/s2 to a speed of 5.0 m/s and then continues at constant velocity until it strikes

car B. Calculate the total time for car A to travel the 15 m.

(b) After the collision, car B moves to the right at a speed of 4.8 m/s.

i. Calculate the speed of car A after the collision.

ii. Indicate the direction of motion of car A after the collision.

____ To the left ______ To the right ____ None; car A is at rest.

Explain your answer


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30. A model rocket of mass 0.250 kg is launched vertically with an engine that is ignited at time t = 0, as

shown above. The engine provides an impulse of 20.0 N•s by firing for 2.0 s. Upon reaching its maximum

height, the rocket deploys a parachute, and then descends vertically to the ground.

(a) On the figures below, draw and label a free-body diagram for the rocket during each of the following

intervals.

(b) Determine the magnitude of the average acceleration of the rocket during the 2 s firing of the engine.

(c) What maximum height will the rocket reach? (caution….there are two different phases of motion)

(d) At what time after t = 0 will the maximum height be reached?


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31. A 70 kg woman and her 35 kg son are standing at rest on an ice rink, as shown above. They push against

each other for a time of 0.60 s, causing them to glide apart. The speed of the woman immediately after they

separate is 0.55 m/s. Assume that during the push, friction is negligible compared with the forces the people

exert on each other.

(a) Calculate the initial speed of the son after the push.

(b) Calculate the magnitude of the average force exerted on the son by the mother during the push.

(c) How do the magnitude and direction of the average force exerted on the mother by the son during the push compare with those of the average force exerted on the son by the mother? Justify your answer.

(d) After the initial push, the friction that the ice exerts cannot be considered negligible, and the mother comes to rest after moving a distance of 7.0 m across the ice. If their coefficients of friction are the same, how far does the son move after the push?


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32.

33. 34. 35.


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36. A 23,000 kg cannon mounted on a railway car fires at 45 kg shell at a velocity of 650 m/s at an angle of

34 above the horizontal. What is the recoil velocity of cannon/railroad car after the cannon is fired?

37. Object A of mass 1 kg traveling with a speed of 25 m/sec to the right collides with an identical object B

which was initially at rest. After the collision, object A moves with a velocity of 20 m/s at an angle of 37

above the horizontal while object B moves at an angle of 53 degrees below the horizontal. Determine the speed of object B after collision.

vBf

vA fA

B

After53

37

38. A 2.0 kg puck travelling at 5.0 m/s to the right collides obliquely with a 3.0 kg puck initially at rest. After

the collision the 2.0 kg puck travels at 2.5 m/s at an angle of 34 above the horizontal. What is the velocity (speed & direction) of the 3.0 kg puck after collision?


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Answers

1) 7.5 kg m/s

2) 1260 kg m/s

3) 2,370,000 kg m/s

4) a) 4.86 m/s2 b) 3.8 m/s c) 24.7 kg m/s

5) 2>1=3=5>4

6)

7)

8) a) + b) - c) +

9a) 1 Ns b) -2 Ns c) 1 Ns

10) a) 1.5 m/s b) 0

11) Block B

12) Equal

13) a) 16,250 kg b) 9 m/s

14) a) 9.6 kg m/s b) 9.6 kg m/s c) 533-N

15) a) 125 Ns b) 2.5-m/s

16) a) -260.4 m/s2 b) 0.096-s c) 35,000-kg m/s

d) 364,600-N

17) a) Bouncy b) CB = 0 RB = -Pxi c) CB= Pxi RB =

2(Pxi) d) Rubber e) Rubber f) totally stoked!

18) a) equal b) same c) same graph just mirror

images (second graph is negative of first graph)

d) equal e) equal f) VL < Vs

19) a) no b) yes

20) a) no b) yes

21) Less

22) (answers at bottom of page…use a mirror)

23) 5.98-m/s

24) + 1.52 m/s

25) +4.2-m/s

26) 5.2 m/s

27) a) 0.5-m/s b) 31-s

28) a) yes b) yes c) no d) no

29) a) 3.6 s b) i) 1.2 m/s ii) right

30) b) 30.2 m/s2 c) 244 m d) 8.1 s

31) a) 1.1 m/s b) 64.2 N c) equal d) 27.5 m

32) missing vector needs -2 py and -1 px

33) missing vector needs -3px

34) vector needs -3py

35) vector needs +3px and +2py

36) 1.05 m/s

37) 5 m/s

38) 2.2 m/s at 30 SofE


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Unit 4: Linear Momentum Name: - Rockwood School District Physics 1/Assignments... · Unit 4: Linear Momentum Name: ... The student is able to design an experimental test of an application