July 9, Week 6 Today: Chapter 10, Elastic Potential Energy Homework - - PowerPoint PPT Presentation

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July 9, Week 6 Today: Chapter 10, Elastic Potential Energy Homework - - PowerPoint PPT Presentation

May 16, 2023 140 likes •883 views

July 9, Week 6 Today: Chapter 10, Elastic Potential Energy Homework #6 due Friday Office hours today, 1:00-5:00 Elastic Energy 9th July 2014 Hookes Law A simple example of a variable force is the force needed to stretch a spring. Elastic

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SLIDE 1

July 9, Week 6

Elastic Energy 9th July 2014

Today: Chapter 10, Elastic Potential Energy Homework #6 due Friday Office hours today, 1:00-5:00

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SLIDE 2

Hooke’s Law

Elastic Energy 9th July 2014

A simple example of a variable force is the force needed to stretch a spring.

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SLIDE 3

Hooke’s Law

Elastic Energy 9th July 2014

A simple example of a variable force is the force needed to stretch a spring.

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SLIDE 4

Hooke’s Law

Elastic Energy 9th July 2014

A simple example of a variable force is the force needed to stretch a spring. Hooke’s Law

  • The

force needed to stretch

  • r

compress a spring increases linearly with stretching distance

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SLIDE 5

Hooke’s Law

Elastic Energy 9th July 2014

A simple example of a variable force is the force needed to stretch a spring. Hooke’s Law

  • The

force needed to stretch

  • r

compress a spring increases linearly with stretching distance

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SLIDE 6

Hooke’s Law

Elastic Energy 9th July 2014

A simple example of a variable force is the force needed to stretch a spring. Hooke’s Law

  • The

force needed to stretch

  • r

compress a spring increases linearly with stretching distance

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SLIDE 7

Hooke’s Law

Elastic Energy 9th July 2014

A simple example of a variable force is the force needed to stretch a spring. s Hooke’s Law

  • The

force needed to stretch

  • r

compress a spring increases linearly with stretching distance

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SLIDE 8

Hooke’s Law

Elastic Energy 9th July 2014

A simple example of a variable force is the force needed to stretch a spring. s Hooke’s Law

  • The

force needed to stretch

  • r

compress a spring increases linearly with stretching distance Fsp = ks

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SLIDE 9

Hooke’s Law

Elastic Energy 9th July 2014

A simple example of a variable force is the force needed to stretch a spring. s Hooke’s Law

  • The

force needed to stretch

  • r

compress a spring increases linearly with stretching distance Fsp = ks k = spring constant, Unit: N/m s = stretching distance

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SLIDE 10

Hooke’s Law

Elastic Energy 9th July 2014

A simple example of a variable force is the force needed to stretch a spring. s lo Hooke’s Law

  • The

force needed to stretch

  • r

compress a spring increases linearly with stretching distance Fsp = ks k = spring constant, Unit: N/m s = stretching distance

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SLIDE 11

Hooke’s Law

Elastic Energy 9th July 2014

A simple example of a variable force is the force needed to stretch a spring. s lo l Hooke’s Law

  • The

force needed to stretch

  • r

compress a spring increases linearly with stretching distance Fsp = ks k = spring constant, Unit: N/m s = stretching distance

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SLIDE 12

Hooke’s Law

Elastic Energy 9th July 2014

A simple example of a variable force is the force needed to stretch a spring. s lo l s = l − lo Hooke’s Law

  • The

force needed to stretch

  • r

compress a spring increases linearly with stretching distance Fsp = ks k = spring constant, Unit: N/m s = stretching distance

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SLIDE 13

Spring Exercise

Elastic Energy 9th July 2014

Fsp = ks A horizontal 50-N force is applied to a 100 N/m spring whose unstretched length is 0.5 m. What is the spring’s length after the force has been applied? 50 N

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SLIDE 14

Spring Exercise

Elastic Energy 9th July 2014

Fsp = ks A horizontal 50-N force is applied to a 100 N/m spring whose unstretched length is 0.5 m. What is the spring’s length after the force has been applied? 50 N (a) 0 m

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SLIDE 15

Spring Exercise

Elastic Energy 9th July 2014

Fsp = ks A horizontal 50-N force is applied to a 100 N/m spring whose unstretched length is 0.5 m. What is the spring’s length after the force has been applied? 50 N (a) 0 m (b) 0.5 m

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SLIDE 16

Spring Exercise

Elastic Energy 9th July 2014

Fsp = ks A horizontal 50-N force is applied to a 100 N/m spring whose unstretched length is 0.5 m. What is the spring’s length after the force has been applied? 50 N (a) 0 m (b) 0.5 m (c) 1 m

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SLIDE 17

Spring Exercise

Elastic Energy 9th July 2014

Fsp = ks A horizontal 50-N force is applied to a 100 N/m spring whose unstretched length is 0.5 m. What is the spring’s length after the force has been applied? 50 N (a) 0 m (b) 0.5 m (c) 1 m (d) 1.5 m

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SLIDE 18

Spring Exercise

Elastic Energy 9th July 2014

Fsp = ks A horizontal 50-N force is applied to a 100 N/m spring whose unstretched length is 0.5 m. What is the spring’s length after the force has been applied? 50 N (a) 0 m (b) 0.5 m (c) 1 m (d) 1.5 m (e) 2 m

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SLIDE 19

Spring Exercise

Elastic Energy 9th July 2014

Fsp = ks A horizontal 50-N force is applied to a 100 N/m spring whose unstretched length is 0.5 m. What is the spring’s length after the force has been applied? 50 N (a) 0 m (b) 0.5 m (c) 1 m (d) 1.5 m (e) 2 m

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SLIDE 20

Spring Exercise

Elastic Energy 9th July 2014

Fsp = ks A horizontal 50-N force is applied to a 100 N/m spring whose unstretched length is 0.5 m. What is the spring’s length after the force has been applied? 50 N l0 = 0.5 m s = 0.5 m l (c) 1 m s = 50 N 100 N/m = 0.5 m

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SLIDE 21

Spring Exercise II

Elastic Energy 9th July 2014

Fsp = ks A 5-kg mass is attached, as shown, to a 100 N/m spring whose unstretched length is 0.5 m. If the mass is pushed 0.3 m to the left, what is the magnitude and direction of the force exerted by the spring on the mass? 0.3 m

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SLIDE 22

Spring Exercise II

Elastic Energy 9th July 2014

Fsp = ks A 5-kg mass is attached, as shown, to a 100 N/m spring whose unstretched length is 0.5 m. If the mass is pushed 0.3 m to the left, what is the magnitude and direction of the force exerted by the spring on the mass? 0.3 m (a) 30 N, Left

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SLIDE 23

Spring Exercise II

Elastic Energy 9th July 2014

Fsp = ks A 5-kg mass is attached, as shown, to a 100 N/m spring whose unstretched length is 0.5 m. If the mass is pushed 0.3 m to the left, what is the magnitude and direction of the force exerted by the spring on the mass? 0.3 m (a) 30 N, Left (b) 30 N, Right

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SLIDE 24

Spring Exercise II

Elastic Energy 9th July 2014

Fsp = ks A 5-kg mass is attached, as shown, to a 100 N/m spring whose unstretched length is 0.5 m. If the mass is pushed 0.3 m to the left, what is the magnitude and direction of the force exerted by the spring on the mass? 0.3 m (a) 30 N, Left (b) 30 N, Right (c) 20 N, Left

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SLIDE 25

Spring Exercise II

Elastic Energy 9th July 2014

Fsp = ks A 5-kg mass is attached, as shown, to a 100 N/m spring whose unstretched length is 0.5 m. If the mass is pushed 0.3 m to the left, what is the magnitude and direction of the force exerted by the spring on the mass? 0.3 m (a) 30 N, Left (b) 30 N, Right (c) 20 N, Left (d) 20 N, Right

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SLIDE 26

Spring Exercise II

Elastic Energy 9th July 2014

Fsp = ks A 5-kg mass is attached, as shown, to a 100 N/m spring whose unstretched length is 0.5 m. If the mass is pushed 0.3 m to the left, what is the magnitude and direction of the force exerted by the spring on the mass? 0.3 m (a) 30 N, Left (b) 30 N, Right (c) 20 N, Left (d) 20 N, Right (e) 50 N, Right

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SLIDE 27

Spring Exercise II

Elastic Energy 9th July 2014

Fsp = ks A 5-kg mass is attached, as shown, to a 100 N/m spring whose unstretched length is 0.5 m. If the mass is pushed 0.3 m to the left, what is the magnitude and direction of the force exerted by the spring on the mass? 0.3 m (a) 30 N, Left (b) 30 N, Right (c) 20 N, Left (d) 20 N, Right (e) 50 N, Right

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SLIDE 28

Spring Exercise II

Elastic Energy 9th July 2014

Fsp = ks A 5-kg mass is attached, as shown, to a 100 N/m spring whose unstretched length is 0.5 m. If the mass is pushed 0.3 m to the left, what is the magnitude and direction of the force exerted by the spring on the mass? s = 0.3 m Fsp = (100 N/m) (0.3 m) (b) 30 N, Right Springs pull when stretched and push when compressed

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SLIDE 29

Work to Stretch a Spring

Elastic Energy 9th July 2014

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SLIDE 30

Work to Stretch a Spring

Elastic Energy 9th July 2014

si

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SLIDE 31

Work to Stretch a Spring

Elastic Energy 9th July 2014

si

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SLIDE 32

Work to Stretch a Spring

Elastic Energy 9th July 2014

si sf

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SLIDE 33

Work to Stretch a Spring

Elastic Energy 9th July 2014

si sf s F

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SLIDE 34

Work to Stretch a Spring

Elastic Energy 9th July 2014

si sf s F Fsp = ks

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SLIDE 35

Work to Stretch a Spring

Elastic Energy 9th July 2014

si sf s F Fsp = ks

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SLIDE 36

Work to Stretch a Spring

Elastic Energy 9th July 2014

si sf s F Fsp = ks sf si

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SLIDE 37

Work to Stretch a Spring

Elastic Energy 9th July 2014

si sf s F Fsp = ks sf si

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SLIDE 38

Work to Stretch a Spring

Elastic Energy 9th July 2014

si sf s F Fsp = ks sf si Fi Ff W = 1

2(sf)(Ff) − 1 2(si)(Fi)

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SLIDE 39

Work to Stretch a Spring

Elastic Energy 9th July 2014

si sf s F Fsp = ks sf si Fi Ff W = 1

2(sf)(Ff) − 1 2(si)(Fi)

W = 1

2(sf)(ksf) − 1 2(si)(ksi)

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SLIDE 40

Work to Stretch a Spring

Elastic Energy 9th July 2014

si sf s F Fsp = ks sf si Fi Ff W = 1

2(sf)(Ff) − 1 2(si)(Fi)

W = 1

2(sf)(ksf) − 1 2(si)(ksi)

W = 1

2ks2 f − 1 2ks2 i

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SLIDE 41

Elastic Potential Energy

Elastic Energy 9th July 2014

Elastic Potential energy - Potential energy due to a spring.

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SLIDE 42

Elastic Potential Energy

Elastic Energy 9th July 2014

Elastic Potential energy - Potential energy due to a spring.

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SLIDE 43

Elastic Potential Energy

Elastic Energy 9th July 2014

Elastic Potential energy - Potential energy due to a spring.

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SLIDE 44

Elastic Potential Energy

Elastic Energy 9th July 2014

Elastic Potential energy - Potential energy due to a spring.

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SLIDE 45

Elastic Potential Energy

Elastic Energy 9th July 2014

Elastic Potential energy - Potential energy due to a spring. si

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SLIDE 46

Elastic Potential Energy

Elastic Energy 9th July 2014

Elastic Potential energy - Potential energy due to a spring. si sf

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SLIDE 47

Elastic Potential Energy

Elastic Energy 9th July 2014

Elastic Potential energy - Potential energy due to a spring. si − → Fel Fel = −ks sf

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SLIDE 48

Elastic Potential Energy

Elastic Energy 9th July 2014

Elastic Potential energy - Potential energy due to a spring. si − → Fel Fel = −ks sf Wel = − 1

2ks2 f − 1 2ks2 i

  • Elastic work converted to potential energy
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SLIDE 49

Elastic Potential Energy

Elastic Energy 9th July 2014

Elastic Potential energy - Potential energy due to a spring. si − → Fel Fel = −ks sf Wel = − 1

2ks2 f − 1 2ks2 i

  • Elastic work converted to potential energy

Wel = −∆Uel ⇒ Uel = 1

2ks2

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SLIDE 50

Conservation of Elastic Energy

Elastic Energy 9th July 2014

If a spring is the only force doing work on something, Ei = Ef

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SLIDE 51

Conservation of Elastic Energy

Elastic Energy 9th July 2014

If a spring is the only force doing work on something, Ei = Ef E = K + Uel = 1 2mv2 + 1 2ks2

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SLIDE 52

Conservation of Elastic Energy

Elastic Energy 9th July 2014

If a spring is the only force doing work on something, Ei = Ef E = K + Uel = 1 2mv2 + 1 2ks2 1 2mv2

i + 1

2ks2

i = 1

2mv2

f + 1

2ks2

f

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SLIDE 53

Elastic Potential Energy Exercise

Elastic Energy 9th July 2014

A 10-kg mass slides across a frictionless, horizontal floor going 5 m/s (and therefore has 125 J of kinetic energy) when it collides with the k = 500 N/m spring shown. What is the maximum compression of the spring?

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SLIDE 54

Elastic Potential Energy Exercise

Elastic Energy 9th July 2014

A 10-kg mass slides across a frictionless, horizontal floor going 5 m/s (and therefore has 125 J of kinetic energy) when it collides with the k = 500 N/m spring shown. What is the maximum compression of the spring? (a) 125 J 500 N/m = 0.25 m

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SLIDE 55

Elastic Potential Energy Exercise

Elastic Energy 9th July 2014

A 10-kg mass slides across a frictionless, horizontal floor going 5 m/s (and therefore has 125 J of kinetic energy) when it collides with the k = 500 N/m spring shown. What is the maximum compression of the spring? (a) 125 J 500 N/m = 0.25 m (b) 50 kg · m/s 500 N/m = 0.1 m

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SLIDE 56

Elastic Potential Energy Exercise

Elastic Energy 9th July 2014

A 10-kg mass slides across a frictionless, horizontal floor going 5 m/s (and therefore has 125 J of kinetic energy) when it collides with the k = 500 N/m spring shown. What is the maximum compression of the spring? (a) 125 J 500 N/m = 0.25 m (b) 50 kg · m/s 500 N/m = 0.1 m (c) 125 J 250 N/m = 0.5 m

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SLIDE 57

Elastic Potential Energy Exercise

Elastic Energy 9th July 2014

A 10-kg mass slides across a frictionless, horizontal floor going 5 m/s (and therefore has 125 J of kinetic energy) when it collides with the k = 500 N/m spring shown. What is the maximum compression of the spring? (a) 125 J 500 N/m = 0.25 m (b) 50 kg · m/s 500 N/m = 0.1 m (c) 125 J 250 N/m = 0.5 m (d)

  • 125 J

250 N/m = 0.7071 m

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SLIDE 58

Elastic Potential Energy Exercise

Elastic Energy 9th July 2014

A 10-kg mass slides across a frictionless, horizontal floor going 5 m/s (and therefore has 125 J of kinetic energy) when it collides with the k = 500 N/m spring shown. What is the maximum compression of the spring? (a) 125 J 500 N/m = 0.25 m (b) 50 kg · m/s 500 N/m = 0.1 m (c) 125 J 250 N/m = 0.5 m (d)

  • 125 J

250 N/m = 0.7071 m (e)

  • 125 J

500 N/m = 0.5 m

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SLIDE 59

Elastic Potential Energy Exercise

Elastic Energy 9th July 2014

A 10-kg mass slides across a frictionless, horizontal floor going 5 m/s (and therefore has 125 J of kinetic energy) when it collides with the k = 500 N/m spring shown. What is the maximum compression of the spring? (a) 125 J 500 N/m = 0.25 m (b) 50 kg · m/s 500 N/m = 0.1 m (c) 125 J 250 N/m = 0.5 m (d)

  • 125 J

250 N/m = 0.7071 m (e)

  • 125 J

500 N/m = 0.5 m

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SLIDE 60

Elastic Potential Energy Exercise

Elastic Energy 9th July 2014

A 10-kg mass slides across a frictionless, horizontal floor going 5 m/s (and therefore has 125 J of kinetic energy) when it collides with the k = 500 N/m spring shown. What is the maximum compression of the spring?

1 2mv2

i + 1

2ks2

i = 1

2mv2

f + 1

2ks2

f

vi = 5 m/s si = 0 vf = 0 sf =? ⇒ 125 J + 0 = 0 + 1 2(500 N/m)s2

f

(d)

  • 125 J

250 N/m = 0.7071 m

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SLIDE 61

General Energy Problems

Elastic Energy 9th July 2014

The most general problems (this term) involve gravity, springs, and

  • ther forces all doing work.
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SLIDE 62

General Energy Problems

Elastic Energy 9th July 2014

The most general problems (this term) involve gravity, springs, and

  • ther forces all doing work.
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SLIDE 63

General Energy Problems

Elastic Energy 9th July 2014

The most general problems (this term) involve gravity, springs, and

  • ther forces all doing work.

m− → g

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SLIDE 64

General Energy Problems

Elastic Energy 9th July 2014

The most general problems (this term) involve gravity, springs, and

  • ther forces all doing work.

m− → g − → Fel

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SLIDE 65

General Energy Problems

Elastic Energy 9th July 2014

The most general problems (this term) involve gravity, springs, and

  • ther forces all doing work.

m− → g − → Fel − → Fother ANY other force doing work

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SLIDE 66

General Energy Problems

Elastic Energy 9th July 2014

The most general problems (this term) involve gravity, springs, and

  • ther forces all doing work.

m− → g − → Fel − → Fother ANY other force doing work Wtotal = Wg + Wel + Wother

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SLIDE 67

General Energy Problems

Elastic Energy 9th July 2014

The most general problems (this term) involve gravity, springs, and

  • ther forces all doing work.

m− → g − → Fel − → Fother ANY other force doing work Wtotal = Wg + Wel + Wother ∆K

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SLIDE 68

General Energy Problems

Elastic Energy 9th July 2014

The most general problems (this term) involve gravity, springs, and

  • ther forces all doing work.

m− → g − → Fel − → Fother ANY other force doing work Wtotal = Wg + Wel + Wother ∆K −∆Ug

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SLIDE 69

General Energy Problems

Elastic Energy 9th July 2014

The most general problems (this term) involve gravity, springs, and

  • ther forces all doing work.

m− → g − → Fel − → Fother ANY other force doing work Wtotal = Wg + Wel + Wother ∆K −∆Ug −∆Uel

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SLIDE 70

General Energy Problems

Elastic Energy 9th July 2014

The most general problems (this term) involve gravity, springs, and

  • ther forces all doing work.

m− → g − → Fel − → Fother ANY other force doing work Wtotal = Wg + Wel + Wother ∆K −∆Ug −∆Uel 1 2mv2

i + mgyi + 1

2ks2

i + Wother = 1

2mv2

f + mgyf + 1

2ks2

f

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SLIDE 71

General Energy Conservation III

Elastic Energy 9th July 2014

1 2mv2

i + mgyi + 1

2ks2

i + Wother = 1

2mv2

f + mgyf + 1

2ks2

f

Example: An 80 kg man jumps onto a spring platform (k = 18000 N/m) going 9 m/s. How far does he compress the spring?

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SLIDE 72

General Energy Conservation III

Elastic Energy 9th July 2014

1 2mv2

i + mgyi + 1

2ks2

i + Wother = 1

2mv2

f + mgyf + 1

2ks2

f

Example: An 80 kg man jumps onto a spring platform (k = 18000 N/m) going 9 m/s. How far does he compress the spring? Example: An 80 kg man skydives from a plane 1600 m above the

  • ground. If he lands with a speed of 10 m/s (and was essentially at

rest when he jumped), how much work did his parachute do?