April 1, Week 11 Today: Chapter 8, Conservation of Momentum - - PowerPoint PPT Presentation

Momentum April 1, 2013 - p. 1/9

April 1, Week 11

Today: Chapter 8, Conservation of Momentum Homework Assignment #8 - Due Monday, April 8

Mastering Physics: 8 problems from chapter 8 Written Questions: 8.101

Homework Assignment #9 - Due Friday, April 12. Exam #3 on Wednesday. Practice Exam available on

• webpage. Review session: Tuesday, April 2, 5:15-7:00 PM.

Room 114 of Regener Hall.

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Using Conservation of Momentum II

Before A − → vA1 B − → vB1 A − → vA2 B − → vB2 After MA− → vA1 + MB− → vB1 = MA− → vA2 + MB− → vB2

Momentum April 1, 2013 - p. 2/9

Using Conservation of Momentum II

Before A − → vA1 B − → vB1 A − → vA2 B − → vB2 After MA− → vA1 + MB− → vB1 = MA− → vA2 + MB− → vB2 Component Form:

Momentum April 1, 2013 - p. 2/9

Using Conservation of Momentum II

Before A − → vA1 B − → vB1 A − → vA2 B − → vB2 After MA− → vA1 + MB− → vB1 = MA− → vA2 + MB− → vB2 Component Form: MA (vA1)x + MB (vB1)x = MA (vA2)x + MB (vB2)x

Momentum April 1, 2013 - p. 2/9

Using Conservation of Momentum II

Before A − → vA1 B − → vB1 A − → vA2 B − → vB2 After MA− → vA1 + MB− → vB1 = MA− → vA2 + MB− → vB2 Component Form: MA (vA1)x + MB (vB1)x = MA (vA2)x + MB (vB2)x MA (vA2)y + MB (vB2)y = MA (vA2)y + MB (vB2)y

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Collisions

Collision - Any strong interaction that lasts a short period of time.

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Collisions

Collision - Any strong interaction that lasts a short period of time. Collisions are always assumed to conserve momentum because of the impulse hypothesis (The collision’s short duration and the large internal forces make the effect of external forces on the collision negligible.)

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Collisions

Collision - Any strong interaction that lasts a short period of time. Collisions are always assumed to conserve momentum because of the impulse hypothesis (The collision’s short duration and the large internal forces make the effect of external forces on the collision negligible.) Collisions are classified as to whether they also conserve kinetic energy.

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Collisions

Collision - Any strong interaction that lasts a short period of time. Collisions are always assumed to conserve momentum because of the impulse hypothesis (The collision’s short duration and the large internal forces make the effect of external forces on the collision negligible.) Collisions are classified as to whether they also conserve kinetic energy. Elastic Collision - Conserves Momentum and Kinetic Energy.

Momentum April 1, 2013 - p. 3/9

Collisions

Collision - Any strong interaction that lasts a short period of time. Collisions are always assumed to conserve momentum because of the impulse hypothesis (The collision’s short duration and the large internal forces make the effect of external forces on the collision negligible.) Collisions are classified as to whether they also conserve kinetic energy. Elastic Collision - Conserves Momentum and Kinetic Energy. Inelastic Collision - Conserves Momentum only.

Momentum April 1, 2013 - p. 3/9

Collisions

Collision - Any strong interaction that lasts a short period of time. Collisions are always assumed to conserve momentum because of the impulse hypothesis (The collision’s short duration and the large internal forces make the effect of external forces on the collision negligible.) Collisions are classified as to whether they also conserve kinetic energy. Elastic Collision - Conserves Momentum and Kinetic Energy. Inelastic Collision - Conserves Momentum only. Collisions may not conserve kinetic energy because they produce heat and/or the objects change shape upon collision.

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Perfectly Inelastic Collisions

When the colliding objects stick together, the collision is called perfectly inelastic or a plastic collision.

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Perfectly Inelastic Collisions

When the colliding objects stick together, the collision is called perfectly inelastic or a plastic collision. Before A − → vA1 B − → vB1

Momentum April 1, 2013 - p. 4/9

Perfectly Inelastic Collisions

When the colliding objects stick together, the collision is called perfectly inelastic or a plastic collision. Before A − → vA1 B − → vB1 MA− → vA1 + MB− → vB1

Momentum April 1, 2013 - p. 4/9

Perfectly Inelastic Collisions

When the colliding objects stick together, the collision is called perfectly inelastic or a plastic collision. Before A − → vA1 B − → vB1 MA− → vA1 + MB− → vB1 After

Momentum April 1, 2013 - p. 4/9

Perfectly Inelastic Collisions

When the colliding objects stick together, the collision is called perfectly inelastic or a plastic collision. Before A − → vA1 B − → vB1 MA− → vA1 + MB− → vB1 A B After

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Perfectly Inelastic Collisions

When the colliding objects stick together, the collision is called perfectly inelastic or a plastic collision. Before A − → vA1 B − → vB1 MA− → vA1 + MB− → vB1 A B − → v2 After

Momentum April 1, 2013 - p. 4/9

Perfectly Inelastic Collisions

When the colliding objects stick together, the collision is called perfectly inelastic or a plastic collision. Before A − → vA1 B − → vB1 MA− → vA1 + MB− → vB1 A B − → v2 After (MA + MB) − → v2

Momentum April 1, 2013 - p. 4/9

Perfectly Inelastic Collisions

When the colliding objects stick together, the collision is called perfectly inelastic or a plastic collision. Before A − → vA1 B − → vB1 MA− → vA1 + MB− → vB1 A B − → v2 After = (MA + MB) − → v2

Momentum April 1, 2013 - p. 4/9

Perfectly Inelastic Collisions

When the colliding objects stick together, the collision is called perfectly inelastic or a plastic collision. Before A − → vA1 B − → vB1 MA− → vA1 + MB− → vB1 A B − → v2 After = (MA + MB) − → v2 Components: MA (vA1)x + MB (vB1)x = (MA + MB) (v2)x MA (vA1)y + MB (vB1)y = (MA + MB) (v2)y

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2D Conservation Exercise

A 6 kg box-shaped firecracker explodes into two unequal

• pieces. If the first piece of mass 2 kg has velocity 20 m/s at

45◦, what speed and direction must the other piece have? BEFORE 6 kg

Momentum April 1, 2013 - p. 5/9

2D Conservation Exercise

A 6 kg box-shaped firecracker explodes into two unequal

• pieces. If the first piece of mass 2 kg has velocity 20 m/s at

45◦, what speed and direction must the other piece have? BEFORE 6 kg AFTER 2 kg 45◦ 20 m/s

Momentum April 1, 2013 - p. 5/9

2D Conservation Exercise

A 6 kg box-shaped firecracker explodes into two unequal

• pieces. If the first piece of mass 2 kg has velocity 20 m/s at

45◦, what speed and direction must the other piece have? BEFORE 6 kg AFTER 2 kg 45◦ 20 m/s (a) 10 m/s at 225◦

Momentum April 1, 2013 - p. 5/9

2D Conservation Exercise

A 6 kg box-shaped firecracker explodes into two unequal

• pieces. If the first piece of mass 2 kg has velocity 20 m/s at

45◦, what speed and direction must the other piece have? BEFORE 6 kg AFTER 2 kg 45◦ 20 m/s (a) 10 m/s at 225◦ (b) 20 m/s at 225◦

Momentum April 1, 2013 - p. 5/9

2D Conservation Exercise

A 6 kg box-shaped firecracker explodes into two unequal

• pieces. If the first piece of mass 2 kg has velocity 20 m/s at

45◦, what speed and direction must the other piece have? BEFORE 6 kg AFTER 2 kg 45◦ 20 m/s (a) 10 m/s at 225◦ (b) 20 m/s at 225◦ (c) 40 m/s at 225◦

Momentum April 1, 2013 - p. 5/9

2D Conservation Exercise

A 6 kg box-shaped firecracker explodes into two unequal

• pieces. If the first piece of mass 2 kg has velocity 20 m/s at

45◦, what speed and direction must the other piece have? BEFORE 6 kg AFTER 2 kg 45◦ 20 m/s (a) 10 m/s at 225◦ (b) 20 m/s at 225◦ (c) 40 m/s at 225◦ (d) 10 m/s at 135◦

Momentum April 1, 2013 - p. 5/9

2D Conservation Exercise

A 6 kg box-shaped firecracker explodes into two unequal

• pieces. If the first piece of mass 2 kg has velocity 20 m/s at

45◦, what speed and direction must the other piece have? BEFORE 6 kg AFTER 2 kg 45◦ 20 m/s (a) 10 m/s at 225◦ (b) 20 m/s at 225◦ (c) 40 m/s at 225◦ (d) 10 m/s at 135◦ (e) 40 m/s at 135◦

Momentum April 1, 2013 - p. 5/9

2D Conservation Exercise

A 6 kg box-shaped firecracker explodes into two unequal

• pieces. If the first piece of mass 2 kg has velocity 20 m/s at

45◦, what speed and direction must the other piece have? BEFORE 6 kg AFTER 2 kg 45◦ 20 m/s (a) 10 m/s at 225◦ (b) 20 m/s at 225◦ (c) 40 m/s at 225◦ (d) 10 m/s at 135◦ (e) 40 m/s at 135◦ 0 = MA− → vA2 + MB− → vB2 ⇒ − → vB2 = − MA MB

• −

→ vA2 = − 2 4

• −

→ vAf

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2D Exercise II

A block with MA = 1 kg and velocity 3 m/s to the right has a perfectly inelastic collision with MB = 2 kg that has velocity 3 m/s up. How fast must the masses be going the instant after their collision? 1 kg 3 m/s 2 kg 3 m/s

Momentum April 1, 2013 - p. 6/9

2D Exercise II

A block with MA = 1 kg and velocity 3 m/s to the right has a perfectly inelastic collision with MB = 2 kg that has velocity 3 m/s up. How fast must the masses be going the instant after their collision? 1 kg 3 m/s 2 kg 3 m/s (a) 9 m/s

Momentum April 1, 2013 - p. 6/9

2D Exercise II

A block with MA = 1 kg and velocity 3 m/s to the right has a perfectly inelastic collision with MB = 2 kg that has velocity 3 m/s up. How fast must the masses be going the instant after their collision? 1 kg 3 m/s 2 kg 3 m/s (a) 9 m/s (b) √ 45 m/s = 6.7 m/s

Momentum April 1, 2013 - p. 6/9

2D Exercise II

A block with MA = 1 kg and velocity 3 m/s to the right has a perfectly inelastic collision with MB = 2 kg that has velocity 3 m/s up. How fast must the masses be going the instant after their collision? 1 kg 3 m/s 2 kg 3 m/s (a) 9 m/s (b) √ 45 m/s = 6.7 m/s (c) 3 m/s

Momentum April 1, 2013 - p. 6/9

2D Exercise II

A block with MA = 1 kg and velocity 3 m/s to the right has a perfectly inelastic collision with MB = 2 kg that has velocity 3 m/s up. How fast must the masses be going the instant after their collision? 1 kg 3 m/s 2 kg 3 m/s (a) 9 m/s (b) √ 45 m/s = 6.7 m/s (c) 3 m/s (d) √ 5 m/s = 2.236 m/s

Momentum April 1, 2013 - p. 6/9

2D Exercise II

A block with MA = 1 kg and velocity 3 m/s to the right has a perfectly inelastic collision with MB = 2 kg that has velocity 3 m/s up. How fast must the masses be going the instant after their collision? 1 kg 3 m/s 2 kg 3 m/s (a) 9 m/s (b) √ 45 m/s = 6.7 m/s (c) 3 m/s (d) √ 5 m/s = 2.236 m/s (e) 1 m/s

Momentum April 1, 2013 - p. 6/9

2D Exercise II

A block with MA = 1 kg and velocity 3 m/s to the right has a perfectly inelastic collision with MB = 2 kg that has velocity 3 m/s up. How fast must the masses be going the instant after their collision? 1 kg 3 m/s 2 kg 3 m/s (a) 9 m/s (b) √ 45 m/s = 6.7 m/s (c) 3 m/s (d) √ 5 m/s = 2.236 m/s (e) 1 m/s

Momentum April 1, 2013 - p. 6/9

2D Exercise II

A block with MA = 1 kg and velocity 3 m/s to the right has a perfectly inelastic collision with MB = 2 kg that has velocity 3 m/s up. How fast must the masses be going the instant after their collision? 1 kg 3 m/s 2 kg 3 m/s (d) √ 5 m/s = 2.236 m/s

MA (vA1)x + MB (vB1)x = (MA + MB) (v2)x (1 kg)(3 m/s) = (3 kg)(v2)x ⇒ (v2)x = 1 m/s MA (vA1)y + MB (vB1)y = (MA + MB) (v2)y (2 kg)(3 m/s) = (3 kg)(v2)y ⇒ (v2)y = 2 m/s v2 =

• (v2)2

x + (v2)2 y

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Rotation

Rotational Motion - Spinning or rolling of rigid bodies.

b b

Momentum April 1, 2013 - p. 7/9

Rotation

Rotational Motion - Spinning or rolling of rigid bodies. Circular Objects:

b b

Momentum April 1, 2013 - p. 7/9

Rotation

Rotational Motion - Spinning or rolling of rigid bodies. Circular Objects: A

b b

B Follow two points, A and B

b b

Momentum April 1, 2013 - p. 7/9

Rotation

Rotational Motion - Spinning or rolling of rigid bodies. Circular Objects: A

b b

B Follow two points, A and B

b b

Momentum April 1, 2013 - p. 7/9

Rotation

Rotational Motion - Spinning or rolling of rigid bodies. Circular Objects: A

b b

B Follow two points, A and B

b b

Momentum April 1, 2013 - p. 7/9

Rotation

Rotational Motion - Spinning or rolling of rigid bodies. Circular Objects: A

b b

B Follow two points, A and B

b b

Momentum April 1, 2013 - p. 7/9

Rotation

Rotational Motion - Spinning or rolling of rigid bodies. Circular Objects: A

b b

B Follow two points, A and B

b b

Momentum April 1, 2013 - p. 7/9

Rotation

Rotational Motion - Spinning or rolling of rigid bodies. Circular Objects: A

b b

B Follow two points, A and B

b b

Momentum April 1, 2013 - p. 7/9

Rotation

Rotational Motion - Spinning or rolling of rigid bodies. Circular Objects: A

b b

B Follow two points, A and B

b b

Momentum April 1, 2013 - p. 7/9

Rotation

Rotational Motion - Spinning or rolling of rigid bodies. Circular Objects: A

b b

B Follow two points, A and B

b b

Momentum April 1, 2013 - p. 7/9

Rotation

Rotational Motion - Spinning or rolling of rigid bodies. Circular Objects: A

b b

B Follow two points, A and B

b b

Momentum April 1, 2013 - p. 7/9

Rotation

Rotational Motion - Spinning or rolling of rigid bodies. Circular Objects: A

b b

B Follow two points, A and B

b b

Momentum April 1, 2013 - p. 7/9

Rotation

Rotational Motion - Spinning or rolling of rigid bodies. Circular Objects: A

b b

B Follow two points, A and B Distance traveled during one revolution:

b b

Momentum April 1, 2013 - p. 7/9

Rotation

Rotational Motion - Spinning or rolling of rigid bodies. Circular Objects: A

b b

B Follow two points, A and B Distance traveled during one revolution: A : 2πrA

b b

Momentum April 1, 2013 - p. 7/9

Rotation

Rotational Motion - Spinning or rolling of rigid bodies. Circular Objects: A

b b

B Follow two points, A and B Distance traveled during one revolution: A : 2πrA rA

b b

Momentum April 1, 2013 - p. 7/9

Rotation

Rotational Motion - Spinning or rolling of rigid bodies. Circular Objects: A

b b

B Follow two points, A and B Distance traveled during one revolution: A : 2πrA rA B : 2πrB

b b

Momentum April 1, 2013 - p. 7/9

Rotation

Rotational Motion - Spinning or rolling of rigid bodies. Circular Objects: A

b b

B Follow two points, A and B Distance traveled during one revolution: A : 2πrA rA B : 2πrB rB

b b

Momentum April 1, 2013 - p. 7/9

Rotation

Rotational Motion - Spinning or rolling of rigid bodies. Circular Objects: A

b b

B Follow two points, A and B Distance traveled during one revolution: A : 2πrA rA B : 2πrB rB B travels farther than A

b b

Momentum April 1, 2013 - p. 7/9

Rotation

Rotational Motion - Spinning or rolling of rigid bodies. Circular Objects: A

b b

B Follow two points, A and B Distance traveled during one revolution: A : 2πrA rA B : 2πrB rB B travels farther than A

b b

Momentum April 1, 2013 - p. 7/9

Rotation

Rotational Motion - Spinning or rolling of rigid bodies. Circular Objects: A

b b

B Follow two points, A and B Distance traveled during one revolution: A : 2πrA rA B : 2πrB rB B travels farther than A

b b

Momentum April 1, 2013 - p. 7/9

Rotation

Rotational Motion - Spinning or rolling of rigid bodies. Circular Objects: A

b b

B Follow two points, A and B Distance traveled during one revolution: A : 2πrA rA B : 2πrB rB B travels farther than A

b b

Momentum April 1, 2013 - p. 7/9

Rotation

Rotational Motion - Spinning or rolling of rigid bodies. Circular Objects: A

b b

B Follow two points, A and B Distance traveled during one revolution: A : 2πrA rA B : 2πrB rB B travels farther than A

b b

Momentum April 1, 2013 - p. 7/9

Rotation

Rotational Motion - Spinning or rolling of rigid bodies. Circular Objects: A

b b

B Follow two points, A and B Distance traveled during one revolution: A : 2πrA rA B : 2πrB rB B travels farther than A

b b

Momentum April 1, 2013 - p. 7/9

Rotation

Rotational Motion - Spinning or rolling of rigid bodies. Circular Objects: A

b b

B Follow two points, A and B Distance traveled during one revolution: A : 2πrA rA B : 2πrB rB B travels farther than A

b b

Momentum April 1, 2013 - p. 7/9

Rotation

Rotational Motion - Spinning or rolling of rigid bodies. Circular Objects: A

b b

B Follow two points, A and B Distance traveled during one revolution: A : 2πrA rA B : 2πrB rB B travels farther than A

b b

Momentum April 1, 2013 - p. 7/9

Rotation

Rotational Motion - Spinning or rolling of rigid bodies. Circular Objects: A

b b

B Follow two points, A and B Distance traveled during one revolution: A : 2πrA rA B : 2πrB rB B travels farther than A

b b

Momentum April 1, 2013 - p. 7/9

Rotation

Rotational Motion - Spinning or rolling of rigid bodies. Circular Objects: A

b b

B Follow two points, A and B Distance traveled during one revolution: A : 2πrA rA B : 2πrB rB B travels farther than A

b b

Momentum April 1, 2013 - p. 7/9

Rotation

Rotational Motion - Spinning or rolling of rigid bodies. Circular Objects: A

b b

B Follow two points, A and B Distance traveled during one revolution: A : 2πrA rA B : 2πrB rB B travels farther than A Take the same amount of time

b b

Momentum April 1, 2013 - p. 7/9

Rotation

Rotational Motion - Spinning or rolling of rigid bodies. Circular Objects: A

b b

B Follow two points, A and B Distance traveled during one revolution: A : 2πrA rA B : 2πrB rB B travels farther than A Take the same amount of time B going faster than A!

b b

Momentum April 1, 2013 - p. 7/9

Rotation

Rotational Motion - Spinning or rolling of rigid bodies. Circular Objects: A

b b

B Follow two points, A and B Distance traveled during one revolution: A : 2πrA rA B : 2πrB rB B travels farther than A Take the same amount of time B going faster than A! A spinning object has infinitely many speeds

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Angular Motion

While A and B travel different distances, they are always at the same angle.

b b b

Momentum April 1, 2013 - p. 8/9

Angular Motion

While A and B travel different distances, they are always at the same angle. A

b b

B θ

b b b

Momentum April 1, 2013 - p. 8/9

Angular Motion

While A and B travel different distances, they are always at the same angle. A

b b

B θ All points rotate through the same angle

b b b

Momentum April 1, 2013 - p. 8/9

Angular Motion

While A and B travel different distances, they are always at the same angle. A

b

B

b

C

b

All points rotate through the same angle

b b b

Momentum April 1, 2013 - p. 8/9

Angular Motion

While A and B travel different distances, they are always at the same angle. A

b

B

b

C

b

All points rotate through the same angle

b b b

Momentum April 1, 2013 - p. 8/9

Angular Motion

While A and B travel different distances, they are always at the same angle. A

b

B

b

∆θ

C

b

All points rotate through the same angle

b b b

Momentum April 1, 2013 - p. 8/9

Angular Motion

While A and B travel different distances, they are always at the same angle. A

b

B

b

∆θ

C

b

All points rotate through the same angle

∆θ

b b b

Momentum April 1, 2013 - p. 8/9

Angular Motion

While A and B travel different distances, they are always at the same angle. A

b

B

b

∆θ

C

b

All points rotate through the same angle

∆θ ∆θ

b b b

Momentum April 1, 2013 - p. 8/9

Angular Motion

While A and B travel different distances, they are always at the same angle. A

b

B

b

∆θ

C

b

All points rotate through the same angle

∆θ ∆θ

We must distinguish linear motion = distance/time from angular motion = angle/time

b b b

Momentum April 1, 2013 - p. 8/9

Angular Motion

While A and B travel different distances, they are always at the same angle. A

b

B

b

∆θ

C

b

All points rotate through the same angle

∆θ ∆θ

We must distinguish linear motion = distance/time from angular motion = angle/time A rotating object has infinitely many linear speeds but only one angular speed

Momentum April 1, 2013 - p. 9/9

Angle

In this chapter, we’ll find it necessary to use radians instead of degrees to measure angles.

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Angle

In this chapter, we’ll find it necessary to use radians instead of degrees to measure angles. r θ

Momentum April 1, 2013 - p. 9/9

Angle

In this chapter, we’ll find it necessary to use radians instead of degrees to measure angles. r θ

Momentum April 1, 2013 - p. 9/9

Angle

In this chapter, we’ll find it necessary to use radians instead of degrees to measure angles. r θ s = arclength

Momentum April 1, 2013 - p. 9/9

Angle

In this chapter, we’ll find it necessary to use radians instead of degrees to measure angles. r θ s = arclength When θ is in radians, s = rθ

Momentum April 1, 2013 - p. 9/9

Angle

In this chapter, we’ll find it necessary to use radians instead of degrees to measure angles. r θ s = arclength When θ is in radians, s = rθ 2π rad = 360◦ = 1 rev

Momentum April 1, 2013 - p. 9/9

Angle

In this chapter, we’ll find it necessary to use radians instead of degrees to measure angles. r θ s = arclength When θ is in radians, s = rθ 2π rad = 360◦ = 1 rev Units: θ = s

r ⇒ m m = 1 ← No Unit!

Momentum April 1, 2013 - p. 9/9

Angle

In this chapter, we’ll find it necessary to use radians instead of degrees to measure angles. r θ s = arclength When θ is in radians, s = rθ 2π rad = 360◦ = 1 rev Units: θ = s

r ⇒ m m = 1 ← No Unit!

“rad" is a way specify an angular quantity