PHY 113 C General Physics I 11 AM – 12:15 P M MWF Olin 101 Plan for Lecture 7: Chapter 7 -- The notion of work and energy Definition of work

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PHY 113 C General Physics I 11 AM – 12:15 P M MWF Olin 101 Plan for Lecture 7: Chapter 7 -- The notion of work and energy Definition of work Examples of work Kinetic energy; Work-kinetic energy theorem Potential energy and work; conservative forces. 7.3,7.15,7.31,7.34.

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PHY 113 C General Physics I

• 11 AM – 12:15 PM MWF Olin 101
• Plan for Lecture 7:
• Chapter 7 -- The notion of work and energy
• Definition of work
• Examples of work
• Kinetic energy; Work-kinetic energy theorem
• Potential energy and work; conservative forces

PHY 113 C Fall 2013 -- Lecture 7

7.3,7.15,7.31,7.34

PHY 113 C Fall 2013 -- Lecture 7

Webassign questions for Assignment 6 -- #1

52. Consider a large truck carrying a heavy load, such as steel beams. … Assume that a 10,000-kg load sits on the flatbed of a 20,000-kg truck initially moving at vi=12 m/s. Assume that the load on the truck bed has a coefficient of static friction of mS=0.5. When the truck is braked at constant force, it comes to rest in a distance d. What is the minimum stopping distance d such that the load remains stationary relative to the truck bed throughout the breaking?

m

a

vi

f

PHY 113 C Fall 2013 -- Lecture 7

Webassign questions for Assignment 6 -- #1 -- continued

• iclicker exercise --
• Do we have enough information to calculate a?
• Yes
• No

m

a

vi

f

PHY 113 C Fall 2013 -- Lecture 7

Webassign questions for Assignment 6 -- #1 -- continued

m

a

vi

f

PHY 113 C Fall 2013 -- Lecture 7

Webassign questions for Assignment 6 -- #4

A block of mass 3 kg is pushed up against a wall by a force P that makes an angle of q=50o with the horizontal. ms=0.25. Determine the possible values for the magnitude of P that allow the block to remain stationary.

f

N

f

mg

PHY 113 C Fall 2013 -- Lecture 7

f

N

f

mg

PHY 113 C Fall 2013 -- Lecture 7

Webassign questions for Assignment 6 -- #6

F

PHY 113 C Fall 2013 -- Lecture 7

Preparation for the introduction of work:

Digressionon the definition of vector “dot” product

q

PHY 113 C Fall 2013 -- Lecture 7

q

PHY 113 C Fall 2013 -- Lecture 7

Digression: definition of vector “dot” product –

component form

q

Note that the result of a vector dot product is a scalar.

PHY 113 C Fall 2013 -- Lecture 7

Definition of work:

F

dr

ri

rj

PHY 113 C Fall 2013 -- Lecture 7

Units of work:

• work = force · displacement = (N · m) = (joule)
• Only the component of force in the direction of the displacement contributes to work.
• Work is a scalar quantity.
• If the force is not constant, the integral form must be used.
• Work can be defined for a specific force or for a combination of forces

PHY 113 C Fall 2013 -- Lecture 7

iclicker question: A ball with a weight of 5 N follows the trajectory shown. What is the work done by gravity from the initial rito final displacement rf?

2.5m

rf

ri

1m

1m

10 m

(A) 0 J (B) 7.5 J (C) 12.5 J (D) 50 J

PHY 113 C Fall 2013 -- Lecture 7

Gravity does negative work:

Gravity does positive work:

ri

rf

mg

mg

ri

rf

W=-mg(rf-ri)>0

W=-mg(rf-ri)<0

PHY 113 C Fall 2013 -- Lecture 7

Work done by a variable force:

PHY 113 C Fall 2013 -- Lecture 7

Example:

PHY 113 C Fall 2013 -- Lecture 7

Example – spring force: Fx = - kx

PHY 113 C Fall 2013 -- Lecture 7

Positive work

Negative work

F

x

PHY 113 C Fall 2013 -- Lecture 7

Detail:

PHY 113 C Fall 2013 -- Lecture 7

More examples:

Suppose a rope lifts a weight of 1000N by 0.5m at a constant upward velocity of 4.9m/s. How much work is done by the rope?

(A) 500 J (B) 750 J (C) 4900 J (D) None of these

Suppose a rope lifts a weight of 1000N by 0.5m at a constant upward acceleration of 4.9m/s2. How much work is done by the rope?

(A) 500 J (B) 750 J (C) 4900 J (D) None of these

PHY 113 C Fall 2013 -- Lecture 7

Another example

FP

n

q

fk

mg

xi

xf

Assume FP sinq<<mg

Work of gravity?

0

FPcosq (xf-xi)

Work of FP?

-mkn(xf-xi)=-mk(mg- FP sin q) (xf-xi)

Work of fk?

PHY 113 C Fall 2013 -- Lecture 7

iclicker exercise:

• Why should we define work?
• Because professor like to torture students.
• Because it is always good to do work
• Because it will help us understand motion.
• Because it will help us solve the energy crisis.

 Work-Kinetic energy theorem.

PHY 113 C Fall 2013 -- Lecture 7

Back to work:

F

dr

ri

rj

PHY 113 C Fall 2013 -- Lecture 7

Why is work a useful concept?

Consider Newton’s second law:

Ftotal = m a  Ftotal · dr= m a ·dr

Wtotal = ½ m vf2 -½ m vi2

Kinetic energy (joules)

PHY 113 C Fall 2013 -- Lecture 7

Introduction of the notion of Kinetic energy

Some more details:

Consider Newton’s second law:

Ftotal = m a  Ftotal · dr= m a ·dr

Wtotal = ½ m vf2 -½ m vi2

Kinetic energy (joules)

PHY 113 C Fall 2013 -- Lecture 7

Kinetic energy: K = ½ m v2

units: (kg) (m/s)2 = (kg m/s2) m

N m = joules

Work – kinetic energy relation:

Wtotal = Kf – Ki

PHY 113 C Fall 2013 -- Lecture 7

Kinetic Energy-Work theorem

• iclicker exercise:
• Does this remind you of something you’ve seen recently?
• Yes
• No

PHY 113 C Fall 2013 -- Lecture 7

Kinetic Energy-Work theorem

PHY 113 C Fall 2013 -- Lecture 7

Kinetic Energy-Work theorem

Example: A ball of mass 10 kg, initially at rest falls a height of 5m. What is its final velocity?

i

0

h

f

PHY 113 C Fall 2013 -- Lecture 7

A block, initially at rest at a height h, slides down a frictionless incline. What is its final velocity?

Example

h=0.5m

h

0

PHY 113 C Fall 2013 -- Lecture 7

Example

• A block of mass m slides on a horizontal surface with initial velocity vi, coming to rest in a distance d.

vi

vf=0

d

Determine the work done during this process.

Analyze the work in terms of the kinetic friction force.

PHY 113 C Fall 2013 -- Lecture 7

Example -- continued

f

vi

vf=0

d

PHY 113 C Fall 2013 -- Lecture 7

Example

A mass m initially at rest and attached to a spring compressed a distance x=-|xi|, slides on a frictionless surface. What is the velocity of the mass when x=0 ?

k

0

PHY 113 C Fall 2013 -- Lecture 7

Special case of “conservative” forces

conservative  non-dissipative

PHY 113 C Fall 2013 -- Lecture 7

k

PHY 113 C Fall 2013 -- Lecture 7

iclicker exercise:

• Why would you want to write the work as the difference between two “potential” energies?
• Normal people wouldn’t.
• It shows a lack of imagination.
• It shows that the work depends only on the initial and final displacements, not on the details of the path.

PHY 113 C Fall 2013 -- Lecture 7

Energy diagrams

PHY 113 C Fall 2013 -- Lecture 7

Example: Model potential energy function U(x) representing the attraction of two atoms

PHY 113 C Fall 2013 -- Lecture 7