Energy [J] is defined as the ability to do work. Or Work is the Energy supplied to on object to make it move

Work and Energy • Work (W) is done on an object by an force when the object moves through a distance (displacement). Since Force and displacement are ...
Author: Marian Jordan
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Work and Energy • Work (W) is done on an object by an force when the object moves through a distance (displacement). Since Force and displacement are vectors, work has to be a scalar. We use the r scalar product:

r W = F s = Fs cos θ [Joule J = Nm]

Energy [J] is defined as the ability to do work. Or “Work is the Energy supplied to on object to make it move”. Work is an energy transfer by the application of a force. For work to be done there must be a nonzero displacement.

How much work is 1 Joule? – Let’s compare Annual U.S. energy use

8 x 1019

Mt. St. Helens eruption

1018

Burning one gallon of gas

108

Human food intake/day Melting an ice cube

107 104

Lighting a 100-W bulb for 1 6000 minute Heartbeat

0.5

Turning page of a book

10–3

Hop of a flea

10–7

Breaking a bond in DNA

10–20

The Law of Conservation of Energy The total energy of the Universe is unchanged by any physical process. The three kinds of energy are: kinetic energy, potential energy, and rest energy. Energy may be converted from one form to another or transferred between bodies.

Work done by a force – an example Consider you are pushing a box, then:

ÆMore work is required to exert a greater force for a finite distance

Æ More work is required to exert a finite force over a greater distance

ÆTherefore: “Work equals force times displacement” rr W = F s = Fs cos θ [Joule J = Nm]

θ = 0 ; cos0 = 1 (angle between the two vectors) ⇒W = F s

Work W can be………….

+W

0

-W

Example 1: A person pulls a suitcase If the person would pull horizontal little force would be necessary to do the same work!!!

Example 2: Work done by gravity Force needed to lift up the box F1 = mg, W1=Fs=(mg)h =mgh cos(0)=mgh Work done by gravity Wg= mgh cos(180)= -mgh

It is only the force in the direction of the displacement that does work. Free Body Diagram for the box F θ

Δrx

y

Δrx

N θ

w

x

F

WF = Fx Δrx = (F cos θ )Δx The work done by the force N is:

WN = 0

The normal force is perpendicular to the displacement. The work done by gravity (w) is: Wg = 0 The force of gravity is perpendicular to the displacement.

Wnet = WF + WN + Wg

= (F cos θ )Δx + 0 + 0 = (F cos θ )Δx

Example: A ball is tossed straight up. What is the work done by the force of gravity on the ball as it rises? y

Δr

FBD for rising ball:

x

w

r r Wg = WΔy cos 180° = − mgΔy

Conceptual Checkpoint Which way is more work?

Total Work?? When more then a force acts on an object the total work……………….

Force F1 (e.g. Friction) does work W1, Force F2 does work W2, etc. Wtotal = W1 + W2 + W3 + ...... = ∑ W i

OR Calculate the net force (or total force)

r r W = Ftotal s = Ftotal s cos θ

Example: A box of mass m is towed up a frictionless incline at constant speed. The applied force F is parallel to the incline. What is the net work done on the box? y F N

F x

θ

θ

w Apply Newton’s 2nd Law: Fx = F − w sin θ = 0

∑ ∑F

y

= N − w cos θ = 0

The magnitude of F is:

F = mgsinθ

If the box travels along the ramp a distance of Δx the work by the force F is

WF = FΔx cos0° = mgΔx sinθ

The work by gravity is

Wg = wΔx cos(θ + 90°) = − mgΔx sin θ

Example continued:

The work by the normal force is:

WN = NΔx cos 90° = 0

The net work done on the box is:

Wnet = WF + Wg + WN = mgΔx sin θ − mgΔx sin θ + 0 =0

Graphical Representation of Work Plot force vs position and the area under the curve represents the Work W= F d (The area of a rectangle with length a and with b: Area = ab)

What if Force isn´t constant? Split the curve in several intervals/ rectangles and add them up OR with calculus

Are work and speed are related? Of course: When the total work done on a object is: Positive, its speed increases (W >0, vf>vi) Negative, ist speed decreases (W

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