app1 unit 5: linear momentum and collisions...

APP1 – Unit 5: Linear Momentum and Collisions (1)

1 Dec 15

B > A > C > D = F > E Positive work is done in A, B, C, zero work in D and F since the force and displacement are perpendicular to each other, and negative work in E.

Warm Up

Linear Momentum

Hey, Mr. Nannini, what’s that “p” mean? "Momentum" derives from the old Aristotlean term “impetus,” which in turn comes from the Latin petere, hence the “p.” Petere means either to go to or to seek.

Newton’s second law, in the form of:

ΣF = ma (our usage as a = ΣF/m)

is only valid for objects that have constant mass. Newton originally captured this relationship as

ΣF = Δp / Δt

Momentum and N2L

Consider the mass and velocity of Objects A and B. Compared to Object B, Object A has _____ the momentum of Object B. a. two times b. four times c. eight times d. same e. one-half f. one-fourth g. impossible to know without know the F and the a.

Learning Check

Demo 1 and 2 Clay ball vs. rubber ball: which has greater Δp? Clay ball vs. rubber ball vs. Hulk: which has the greater effect?

Hulk not skairt of

puny human science!!

Impulse

https://www.youtube.com/watch?v=pQ9NiazPYI8

https://www.youtube.com/watch?v=zLcVTjiYmoM

Impulse

https://www.youtube.com/watch?v=vjQA3NrVvrk&feature=iv&src_vid=yUpiV2I_IRI&annotation_id=annotation_1352584259#t=5m

Impulse (Car Crash Physics)

Demo 3

Impulse and the egg

Practice For Wednesday: Read for Comprehension: Section 9-4 (pp. 248 - 252) Review: Intro and Section 9-1 and 9-2 (pp. 240 – 244) Conceptual questions (p. 273): 5, 7 Conceptual exercises (p. 274): 1, 3, 5 Problems: N/A

Goal time: 30 minutes

The next month in APP1

1

2

3 4

1 – 2D motion reassessment; 2 – Work/Energy assessment; 3 – Impulse/Momentum assessment; 4 – Work/Energy reassessment (?) Saturday Morning Physics Also note: Pacing guide updated for the rest of the school year; posted on PlusPortals

Begin Impulse/

Momentum


2 Dec 15

Warm Up

B > A = D > C Work done on the box will change its kinetic energy. Find work done by subtracting the initial kinetic energy from the final value for each 5 second interval. The external agent will do positive work in interval B, no work in intervals A and D (kinetic energy doesn’t change), and negative work in interval C

Gedankenexperiment

Gedankenexperiment

Using the impulse-momentum theorem: 1. If you throw a ball horizontally while standing on roller skates, you roll

backwards. Will you roll backwards if you go through the motions of throwing the ball, but hold on to it instead? Explain your reasoning.

Gedankenexperiment

Using the impulse-momentum theorem: 2. A Ford Escape and a Fiat 500c traveling at equal speeds have a head-on collision.

a. Which vehicle will experience the greater force of impact? Justify your answer. b. Which vehicle will experience the greater change in momentum? Justify your answer. c. Which vehicle will experience the greater acceleration? Justify your answer.

Impulse-Momentum Theorem

The force-time graph above shows the force vs. time for a tennis racket returning a serve. The mass of the tennis ball is 57g and it was travelling horizontally in the negative-x direction at 55 m/s when it was returned. (air resistance is negligible) Determine the impulse delivered on the ball by the return. Determine the velocity of the tennis ball when it was returned.


During break, you’re teaching your little brother how to ride a bike (combined mass of 55-kg). From rest, you start him off with a good push on a flat, horizontal street, and this is captured in the force-time graph above. (friction is negligible) Determine the impulse you delivered on your brother and his bike. Determine the velocity of your brother and his bike after you let go.

10

20

Gedankenexperiment

Suppose you are on a cart, initially at rest on a track with very little friction. You throw balls at a partition that is rigidly mounted on the cart. If the balls bounce back as shown in the figure above, is the cart put in motion? a. Yes, if moves to the right. b. Yes. It moves to the left. c. No, it remains in place.

Because all balls bounce back to the right, to conserve momentum to the cart must move forward (balls are no longer part of the cart system)

Practice For Monday: Read for comprehension: Sections 9-5 and 9-6 (pp. 253 - 263) Conceptual questions: N/A Conceptual exercises: N/A Problems: (p. 275) 15, 17, 19, 21

Goal time: 1 hour


1

2

3 4


Begin Impulse/

Momentum


3 Dec 15

Warm Up

D > A = B > C The change in kinetic energy will occur because of the energy transfer produced by the external agent working on the box. All boxes move the same distance under the action of the external force, only the magnitudes of the external forces determine the ranking.

Gedankenexperiment

Using the impulse-momentum theorem: 2. A Ford Escape and a Fiat 500c traveling at equal speeds have a head-on collision.

a. Which vehicle will experience the greater force of impact? Justify your answer. b. Which vehicle will experience the greater change in momentum? Justify your answer. c. Which vehicle will experience the greater acceleration? Justify your answer.


The force-time graph above shows the force vs. time for a tennis racket returning a serve. The mass of the tennis ball is 57g and it was travelling horizontally in the negative-x direction at 25 m/s when it was returned. (air resistance is negligible) Determine the impulse delivered on the ball by the return. Determine the velocity of the tennis ball when it was returned.


During break, you’re teaching your little brother how to ride a bike (combined mass of 55-kg). From rest, you start him off with a good push on a flat, horizontal street, and this is captured in the force-time graph above. (friction is negligible) Determine the impulse you delivered on your brother and his bike. Determine the velocity of your brother and his bike after you let go.

10

20

Gedankenexperiment

Suppose you are on a cart, initially at rest on a track with very little friction. You throw balls at a partition that is rigidly mounted on the cart. If the balls bounce back as shown in the figure above, is the cart put in motion? a. Yes, if moves to the right. b. Yes. It moves to the left. c. No, it remains in place.

Because all balls bounce back to the right, to conserve momentum to the cart must move forward (balls are no longer part of the cart system)

Battling Beetles

Long, long ago in a distant galaxy lived a thriving colony of battling beetles on the Planet Newtonia. These beetles fight each other for territory by using the principles of momentum.

Using our finely developed Battling Beetle simulators, explore the effect of mass and velocity in collisions of this ancient tribe of inveterate invertebrates.

Practice For Friday: Read for comprehension: N/A Conceptual questions: N/A Conceptual exercises: N/A Problems: N/A Video: Hewitt Drew It 24 and 25 (Momentum) https://youtu.be/2FwhjUuzUDg https://youtu.be/1-s8NZ8xKW0


https://youtu.be/2FwhjUuzUDg



https://youtu.be/1-s8NZ8xKW0





1

2

3 4


Begin Impulse/

Momentum


4 Dec 15

Warm Up

The student’s contention is wrong. Both p-t graphs have a straight line for the motion of the sailboats - they moved at constant speeds, so there was no change in their kinetic energy. No ΔK, no WTotal

1. Justin Verlander applies an average net force of 132 N while throwing a baseball (mass = 140 g) for a period of 4.5 x 10-2 sec. Determine the magnitude of the change in momentum of the ball.

2. If the initial speed of the baseball is v = 0.0 m/s, determine the ball’s speed when it leaves his hand.

3. Curtis Granderson hits the ball with an average net force of 1150 N, opposite to the direction of the ball's initial motion, acting on the ball for 9.0 x 10-3 s during the hit. Determine the final velocity of the ball.

4. Determine the magnitude of the force that the ball exerts on the bat. Explain.

Take me out to the ball game

A rocket being testing has a weight of 4.36 x 104N, and an engine that provides an upward force of 1.2 x 105N. It reaches a maximum speed of 860 m/s. a. Draw a force diagram for the rocket. b. Determine how much time the engine must burn during the

launch in order to reach this speed.

c. What assumption must you make to determine this?

Saturday Morning Physics is on for

Tomorrow!

10am – 12pm Student entrance will be open


1

2

3 4


Begin Impulse/

Momentum

Practice For Monday: Read for comprehension: Sections 9-5 and 9-6 (pp. 253 - 263) Conceptual questions: N/A Conceptual exercises: N/A Problems: (p. 275) 15, 17, 19, 21

Goal time: 1 hour

The prudent student will review their notes and practice problems from the Work-Energy Unit in preparation for Tuesday’s assessment. I also recommend making up problems for yourself and your friends and

solving. That’s a great way to master the material.


7 Dec 15

Warm Up

Since the velocity has doubled, the final Kf will be four times larger than the Ko. Positive work must have been done on the tugboat.

5. Three identical blocks take a different path from height h to the ground. Block A is

released from rest and falls vertically. Block B is released from rest and slides down a

frictionless incline. Block C is projected horizontally with an initial velocity v. Air

resistance is negligible. (PMPM 03)

a. Rank order the blocks from the longest time to reach the ground to the shortest time to

reach the ground. Explain why you selected this ranking.

_______ _______ _______

longest time least time

b. Rank order the blocks from the greatest overall velocity (not just components) at the

instant they hit the ground. Explain why you selected this ranking.

_______ _______ _______

greatest velocity least velocity

From 2D Motion Reassessment

B > A = C

C > A = B

From 2D Motion Reassessment 6. Jim and Sara stand at the edge of a 50 m high cliff on the moon. Jim extends

his arm over the cliff edge and throws a ball straight up with an initial velocity of

20 m/s. Sara throws an identical ball with the same initial velocity, but she throws

the ball at a 30 degree angle above the horizontal. Air resistance is negligible. No

calculations needed, assess qualitatively based on what you know about projectile

motion. (PMPM 03)

a. Consider each ball at the highest point in its flight. At this point:

i. Which ball has the greater vertical velocity? Circle your answer and explain briefly.

Sara’s Jim’s Both are the same

ii. Which ball has the greater horizontal velocity? Circle your answer and explain briefly.


iii. Which ball's velocity vector has greater magnitude? Circle your answer and explain

briefly.


b. Now consider each ball just before it hits the ground, 50 m below where the balls were

initially released. At this point, which ball has the greater vertical velocity? Circle your

answer and explain briefly.


Inelastic Collisions

Collision: two objects strike one another.

In general: the external forces are much smaller than the

internal forces between the colliding objects such that

external forces may be ignored.

Inelastic collision: ρ conserved, but not K

ρo = ρf Ko = Kf

Completely inelastic collision: objects stick together after

collision.

ρo = ρf Ko = Kf

In the general case of an inelastic collision between

two masses m1 and m2, with velocities of v1,i and v2,i

respectively:

Inelastic Collisions

1. Specify the impulsive force event that separates initial and final situations.

2. Designate objects in the system by listing the object, its mass, and its velocity in the

chart -- use variables for unknown quantities.

3. Draw a horizontal bar to represent the size and direction of the momentum for each

object.

4. Write the conservation of momentum equation for the bars and solve for the

unknown quantity.

– + 0

final

object/mass/velocity

– + 0

initial

object/mass/velocity

event:

Conservation of Momentum Bar Graphs

CoM Practice #1 1. In a railroad yard, a train is being assembled. An empty boxcar, coasting at 3.0 m/s, strikes a

loaded car that is stationary, and the cars couple together. Each of the boxcars has a mass of 9000

kg when empty, and the loaded car contains 55,000 kg of lumber.

a. Complete the momentum conservation diagram.

b. Momentum conservation equation:

c. Find the speed of the coupled boxcars.

– + 0

final object/mass/velocity

– + 0

initial object/mass/velocity

event:

CoM Practice #2 2. An astronaut of mass 80.0 kg is trying to block an oxygen tank of mass 10.0 kg drifting towards the

International Space Station at a velocity of 2 m/s. The astronaut catches the oxygen tank in an

attempt to block it from doing damage.



c. Find the speed with which the astronaut and oxygen tank moves after the collision.

– + 0


– + 0


event:

ETM 02: I identify when the total energy of a system is changing or not changing, and I can identify the reason for the change in the form of a general equation.

ETM 03: I can construct a mathematical expression to describe energy changes in a system.

ETM 04: I can use the conservation of energy to solve problems, starting from a general conservation of energy equation.

ETM 05: I can use the relationship between the force applied to an object (or system) and the displacement of the object to calculate the work done on that object (or system).

ETM 06: I can create an energy bar graph (L-O-L chart) to describe the changes in the energy of a system.

Standards for Tomorrow’s Fiesta!

Do not fret on springs

The next two weeks in APP1

1

2

3 4

1 – 2D motion reassessment; 2 – Work/Energy assessment; 3 – Impulse/Momentum assessment; 4 – Work/Energy reassessment Saturday Morning Physics Also note: Pacing guide updated for the rest of the school year; posted on PlusPortals

Begin Impulse/

Momentum

Practice For Tuesday: Review: Sections 9-5 and 9-6 (pp. 253 - 263) Conceptual questions: N/A Conceptual exercises: N/A Problems: N/A

The prudent student will review their notes and practice problems from the Work-Energy Unit in preparation for Tuesday’s assessment. I also recommend making up problems for yourself and your friends and

solving. That’s a great way to master the material.

Session information: The Third High School Science and Technology Program session of the 2015-2016 school year will be held at the Research and Innovation Center (RIC) in Dearborn on Saturday, December 12th , 2015. This session will be held on Saturday morning from 9 a.m. - 11:30 a.m. and the topic is " Career Day". This special session of the HSSTP is an annual workshop for students and teachers interested in learning more about careers in technical fields. A number of Ford scientists and engineers will be present to speak about their experiences, to offer advice about fields of interest, colleges, and courses of study, and to provide encouragement. This session is an informal "open house" and depends strongly on participant involvement. As a result, students will get more out of the session if they come prepared with questions about careers in sciences and engineering that they would like to have them answered. Participants will be encouraged to talk to Ford volunteers from a variety of disciplines to get a broad perspective on technical careers.

Next Ford HSSTP Event is Saturday

Physics Student Coaches

Teammates: I am looking for volunteers to support our comrades 1:1. My intent is to link up volunteers to support out teammates as they master physics. Let me know and I’ll put together a roster. We’re all going to make it through.


9 Dec 15

"Dear brothers and sisters, I have often thought about how the Church might make clear its mission of being a witness to mercy. It is a journey that begins with a spiritual conversion. For this reason, I have decided to call an extraordinary Jubilee that is to have the mercy of God at its center. It shall be a Holy Year of Mercy. We want to live this Year in the light of the Lord's words: 'Be merciful, just as your Father is merciful' (cf Lk. 6:36)."

— Pope Francis

“Every one to whom much is given, much will be required.” -- Luke 12:48

Physics Student Coaches

I am looking for volunteers to support our teammates 1:1. My intent is to link up volunteers to support out teammates as they master physics. Let me know and I’ll put together a roster. We’re all going to make it through.

Warm Up

Same time interval for all four cases, so the magnitudes of the momentum changes - equal to the impulses applied to the boxes - is proportional to the net forces acting.

D > A = B > C

CoM Practice #2 2. An astronaut of mass 80.0 kg is trying to block an oxygen tank of mass 10.0 kg drifting towards the

International Space Station at a velocity of 2 m/s. The astronaut catches the oxygen tank in an

attempt to block it from doing damage.



c. Find the speed with which the astronaut and oxygen tank moves after the collision.

– + 0


– + 0


event:

CoM Practice #3 3. A 50.0 kg cart is moving across a frictionless floor at 2.0 m/s. A 70.0 kg boy, riding in the cart,

jumps off so that he hits the floor with zero velocity.



c. How large an impulse did the boy give to the cart?

d. What was the velocity of the cart after the boy jumped?

– + 0


– + 0


event:

CoM Practice #4 4. Two girls with masses of 50.0 kg and 70.0 kg are at rest on frictionless in-line skates. The 70-kg

girl pushes the 50-kg girl so that the 50-kg girl rolls away at a speed of 10.0 m/s.

a. Show the effect of the push on both girls with a momentum conservation diagram.


c. Calculate the impulse that each girl imparts to the other.

– + 0


– + 0


event:

Elastic Collisions Elastic collisions: ρ and K conserved

ρo = ρf Ko = Kf

Very uncommon in the macroscopic world, very common at

the atomic / molecular level.

Do not try to memorize the equations on p. 259

(it’s good to understand them, though)

For elastic collisions, be able to use this:

½ m1v12 + ½ m2v2

2 = ½ m1v12 + ½ m2v2

2

…and solve for the unknown.


1

2

3 4


Begin Impulse/

Momentum

Practice For Thursday: Read for understanding: Section 9-7 (p. 264 – 269) Review: Sections 9-5 and 9-6 (pp. 253 - 263)** Conceptual questions: N/A Conceptual exercises: N/A Problems: 16, 17, 23, 31

Goal time: 45 minutes **do not spend a lot of time on 2D collisions just yet.


10 Dec 15

Warm Up

Δp related to impulse (FΔt), we can rank on F since the time is the same for all cases.

A = D > B = C

Center of Mass CM: the point where a system can be balanced in a uniform gravitational field.

Center of Mass

Center of Mass

The center of mass need not be within the object.

Center of Mass

Center of Mass

http://phet.colorado.edu/en/simulation/my-solar-system

Practice

Using a meter stick and a 200g and 100g mass, create a system where your system is balanced at the center point of the meter stick






– + 0


– + 0


event:


1

2

3 4


Begin Impulse/

Momentum

Practice For Friday: Read for understanding: Section 9-8 (p. 269 – 270) Conceptual questions: N/A Conceptual exercises: N/A Problems: 40 (p. 277)



11 Dec 15

Warm Up

Δp related to impulse (FΔt), we can rank on F since the time is the same for all cases.

A = D > B = C

Problem #40 from yesterday

Center of Mass

Practice

Using a meter stick and a 200g and 100g mass, create a system where your system is balanced at the center point of the meter stick






– + 0


– + 0


event:

Saturday Morning Physics is on for

Tomorrow!

10am – 12pm Student entrance will be open


1

2

3 4


Begin Impulse/

Momentum

Practice For Friday: Read for understanding: Section 9-8 (p. 269 – 270) Conceptual questions: N/A Conceptual exercises: N/A Problems: 40 (p. 277)



13 Dec 15

“Yesterday is gone. Tomorrow has not yet come.

We have only today. Let us begin.”

- Blessed Mother Teresa

Warm Up

Δp is same, but Wtotal = ΔK; ΔK greater for Bertha’s car

less than

Systems with Changing Mass

Rocket Propulsion At liftoff, an advanced rocket has a total mass (rocket and fuel) of 1.8 x 105 kg. The rocket burns fuel at a rate of 3000 kg/s with an exhaust velocity of 4500 m/s. Determine the rocket’s acceleration 12 seconds after liftoff.

https://www.youtube.com/watch?v=7C3NAj4jCb0






– + 0


– + 0


event:

CoM Practice #5 5. A 2.0 kg melon is balanced on a circus performer's head. An archer shoots a 50.0 g arrow at the

melon with a speed of 30 m/s. The arrow passes through the melon and emerges with a speed of

18 m/s.

a. Draw a momentum conservation diagram for the stunt.


c. Find the speed of the melon as it flies off the performer's head.

– + 0


– + 0


event:

Center of Mass

Triple Sunset: Planet Discovered in 3-Star System

“The triple-star system, HD 188753, is located 149 light-years away in the constellation Cygnus. The primary star is like our Sun, weighing 1.06 solar masses. The other two stars form a tightly bound pair, which is separated from the primary by approximately the Sun-Saturn distance.”

http://www.space.com/1311-triple-sunset-planet-discovered-3-star-system.html

Mass of primary star: 2.11 x 1030 kg Mass of other two stars (combined): 3.22 x 1030

Distance between cm of primary stars and other two stars: 5.88 x 108 km

Find the center of mass of this star system (assume a circular orbit)

The end of the semester

1 2

1 –Impulse/Momentum assessment #1; 2 – Work-Energy reassessment; 3 – Impulse/Momentum end of unit assessment; 4 – End of 2d quarter reassessment A, B, C – 2d, 5th, 6th Hr mid-term exams Saturday Morning Physics

3

A B C 4

Practice For Tuesday: Read for understanding: N/A Conceptual questions: N/A Conceptual exercises: N/A Problems: 25, 31 – you will present your solution in class tomorrow.



15 Dec 15

“Yesterday is gone. Tomorrow has not yet come.

We have only today. Let us begin.”

- Blessed Mother Teresa

Warm Up

The momenta of the two carts are equal and opposite before the collision; total initial momentum is zero; total final momentum must be zero as well.

√

Problem 25

Two 78-kg hockey players skating at 5.25 m/s collide and stick together. If the angle between their initial directions was 115O , what is their speed after the collision?

P1: 78 kg x 5.25 m/s

P2: 78 kg x 5.25 m/s 1150

x-direction: (78 kg) (5.25 m/s) - (78 kg) (5.25 m/s) (cos 650) = + 235.94 kg m/s 𝑥 + 235.94 kg m/s = 2 (78 kg) vf => vf = +1.5 m/s 𝑥 y-direction: 0 + (78 kg) (5.25 m/s) (sin 650) = + 371.13 kg m/s ŷ + 371.13 kg m/s = 2 (78 kg) vf => vf = +2.37 m/s ŷ Use Pythagorean theorem to find final velocity of 2.82 m/s @ 57.70

These dang “hat” things took me 20 minutes to

figure out

Problem 31

A 722-kg car stopped at an intersection is rear-ended by a 1620-kg truck moving at a speed of 14.5 m/s. If that car was in neutral and its brakes were off, so that the collision is approximately elastic, find the final speed of both vehicles after the collision. Need to solve for two unknowns using: v1,f = (m1 – m2/m1 + m2)v0 and v1,f = (2m1 / m1 + m2)v0

Triple Sunset: Planet Discovered in 3-Star System

“The triple-star system, HD 188753, is located 149 light-years away in the constellation Cygnus. The primary star is like our Sun, weighing 1.06 solar masses. The other two stars form a tightly bound pair, which is separated from the primary by approximately the Sun-Saturn distance.”

http://www.space.com/1311-triple-sunset-planet-discovered-3-star-system.html

Mass of primary star: 2.11 x 1030 kg Mass of other two stars (combined): 3.22 x 1030

Distance between cm of primary stars and other two stars: 5.88 x 108 km

Find the center of mass of this star system (assume a circular orbit)

MTM 01: I can use the relationship between the force applied to an object (or system)

and the time duration of the force to calculate the impulse delivered to that object (or

system) to determine the momentum, change in momentum, or new velocity of an object.

MTM 02: I can illustrate the mathematical connection between a collision force diagram

and the impulse-momentum theorem, to include applying data from graphs.

MTM 03: I can draw and analyze momentum bar charts for 1D interactions.

MTM 04: I can use the impulse momentum theorem to solve elastic and inelastic

collision problems.

MTM 05: I can quantitatively determine whether or not a collision is elastic or perfectly

inelastic (combine fundamental principles of conservation of momentum and

conservation of energy).

MTM 06: I can determine the center of mass of a system in 1D and 2D

MTM 07: I can use the conservation of momentum to solve 2-D problems.

Standards for Tomorrow’s Fiesta!

Practice For Wednesday: Read for understanding: N/A Conceptual questions: N/A Conceptual exercises: N/A Problems: N/A

The prudent student will review their notes and ensure they understand the fundamentals of momentum. The prudent student

will also make up problems for themselves and try to solve. Goal time: 1 – 2 hours

The end of the semester

1 2

1 –Impulse/Momentum assessment #1; 2 – Work-Energy reassessment; 3 – Impulse/Momentum end of unit assessment; 4 – End of 2d quarter reassessment A, B, C – 2d, 5th, 6th Hr mid-term exams Saturday Morning Physics

3

A B C 4

app1 unit 5: linear momentum and collisions...

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