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 ...
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