Download PAP Work and Energy Notes

Pre AP Physics
Work and Energy
“Work” has a variety of meanings (taking out the trash is hard work; the toaster doesn’t work;
Mom goes to work)
In physics, “work” has a specific meaning  work is what is accomplished when a force acts on
an object and the object moves through a distance
W = component of force parallel to the distance object moved x magnitude of distance
I.e. push a cart with a horizontal force
F
d
W = Fd
F = magnitude of constant force
d = distance object moves
Work is a scalar quantity – has only magnitude and no direction
Work is measured in N•m or Joules
[examples #1 together, #2 on own #3-5 HW]
i.e. if pull a wagon at an angle
F
Θ
d
If force is exerted at an angle, it becomes W = (Fcos Θ)d
Θ = angle between force and distance moved
(is cos Θ because need component of force parallel to the displacement)
[examples # 6 together, #7 on own, #8-9 HW]
Demo:
a) Pick up stool vertically, supporting so force is also vertical “did I do work on the stool?” YES!
b) Carry the stool across the room with constant velocity, still supporting vertically. “Am I doing
work on the stool?” NO! because the force is perpendicular to the displacement
c) Hold the stool still in front of you “Am I doing work on the stool?” No because there is no
displacement
(there is work being done on your muscles because they are undergoing many displacements
and that’s why they get tired, but there is no work done on the stool)
What about waiters carrying the tray at the restaurant? No work done!
When looking at work – need to specify whether the work is done BY the object or done ON the
object
Also specify if work is done due to one particular force or due to net force
Sign convention:
+ work  if force is in same direction as distance (force is trying to speed object up)
- work  if force is in opposite direction as distance, ex. Friction (force is trying to slow object
down)
[examples #10a,b together, c,d,e on own)
Energy is a very important concept in science
The 6 main types of energy:
Mechanical energy – energy of moving objects
Radiant energy – travels in waves – light, sound
Chemical energy – stored in food and fuels
Heat energy – thermal
Electrical energy –
Nuclear energy – from nucleus of atom – fission and fusion
General definition of energy = the ability to do work – though doesn’t describe all types of
energy
We are going to focus on mechanical energy in the forms of kinetic energy and potential energy
A moving object can do work on another object that it strikes  a cannonball does work on a
brick wall it knocks down, a hammer does work on a nail it drives into wood
In both cases, a moving object exerts a force on a 2nd object which moves a distance
An object in motion has the ability to do work and therefore has energy  kinetic energy – the
energy of motion
(skip derivation of W = change of KE)
KE = ½ mv2
Measured in Joules
Scalar quantity
Depends on mass and velocity
Relationships
KE directly related to mass  if m x2 KE x2
KE directly related to square of velocity  if v x2 KE x4
Work-energy principle:
Wnet = ΔKE = KE2 – KE1 = ½ mvf2 – ½ mvo2
The net work done on an object is equal to the change in the object’s kinetic energy
This principle is only valid if work is the net work (total work) done on the object
If + W net done on an object  object’s KE increased (velocity increased)
If – W net done on an object  object’s KE decreased (velocity decreased)
A net force exerted on an object opposite to the object’s direction of motion decreases
its speed and its KE
Ex. Moving hammer striking a nail
When hammering a nail, hammer does work on the nail (applies a force to the nail that causes
the nail to move a certain distance) The hammer has a change in its KE (it decreases – moving
to come to a stop on impact) and that change in KE equals the work done on the nail [workenergy principle]
[examples #11 together, #12 on own, #13-17 HW]
[examples #18 together, #19 on own, #20-22 HW]
FIRST DAY GOAL!
Potential Energy – energy associated with object’s position relative to its surroundings
We will look at two types
1. gravitational potential energy (GPE)
2. elastic potential energy (EPE)
Most common PE is gravitational PE  has PE because of object’s position relative to the Earth
Ex. Heavy brick held high in the air or balanced boulder on top of a cliff
A raised brick has the ability to do work – if it is released, it will fall to the ground due to the
gravitational force and can do work on a stake, driving it into the ground
GPE = mgh
mg = object’s weight (N)
h = height above some reference level
The higher an object is above the reference level, the more PE it has
The work done by external forces (W ext) is equal to change in PE
W ext = ΔPE
Changes in PE only depend on change in vertical height and not on path taken, so if lift
something up 4 m or push up an incline a vertical distance of 4 m, PE is still the same due to
change in vertical height
[examples #23 together, #24 on own, #25-26 HW]
Elastic potential energy – potential energy a spring has when compressed (or stretched)
When it is released, it can do work on a second object
(pin ball)
A spring has a natural (unstretched) length, if you want to change the spring’s length, it requires
a force, Fp = kx
k = spring stiffness constant  a measure of the stiffness of the particular spring, remains the
same for a particular spring, but is not the same for ALL springs
x = distance the spring is stretched or compressed
The stretched/compressed spring exerts an equal and opposite force, Fs = -kx  known as
Hooke’s law or spring equation
Fs is the “restoring force” the spring exerts trying to return the spring to its original position
(natural length)
As you stretch a spring, Fp is not constant, it varies over the distance it is stretched  the
further you stretch, the more force it requires
EPE = ½ kx2
k = spring constant (N/m)
x = distance spring is stretched or compressed from its natural length
In all cases looked at – PE is stored energy that can be used later
[examples #27 together, #28 on own, #29 HW]
Mechanical Energy = KE + PE
Energy is conserved – Law of Conservation of Energy – total energy before a process equals
total energy after the process
Therefore, total Mechanical energy (E) remains constant as long as there are no external forces
acting on the system (i.e. friction, air resistance)
KE + PE at time 1 = KE + PE at later time 2
KE and PE are inversely related
Examples: a. Pendulum:
All PE
Incr KE
Decr PE
All KE
b. Rock falling due to gravity from a height, h
All PE, if rock is dropped from rest
As falls, PE decreases (h decreases) and KE increases (gain in velocity)
All KE, just before hits ground
At any point along the path, E = KE + PE = ½ mv2 + mgh
Mechanical energy is conserved if ignore air resistance, so can pick any 2 points along the path
and E1 = E2
[example – show with numbers]
c. Rollercoaster: All PE at hills, all KE in valleys, changing KE/PE going up and down
hills [draw example of rollercoaster – make sure hills and valleys are same heights]
d. Toy dart gun – elastic PE and KE
We mentioned other forms of energy before – with atomic theory, these other forms of energy
can be considered KE or PE at the atomic or molecular level
i.e. thermal energy = KE (particles moving faster when heated)
chemical energy = PE (stored in food and fuels)
Energy can be transformed from one form to another
i.e. rock falling: PE  KE
water at top of dam, falls to bottom of dam, caused turbine to move, forms electricity: PE  KE
 electrical energy
transfer of energy is accompanied by the performance of work (work is done when energy is
transferred from one object to another)
Law of Conservation of Energy: total energy is not increased nor decreased in any process (it is
not created nor destroyed)
Energy can be transformed from one form to another and transferred from one object to
another, but total amount remains constant
[examples #30,31 together, #32 on own, #33-35 HW]
Power: the rate at which work is done, the rate at which energy is transformed
P = W/t = energy transformed/time
Measured in J/s = Watts (W)
The English unit is horsepower (1 hp = 746 W)
Ex. Power rating of an engine – how much chemical or electrical energy can be transformed into
mechanical energy per unit of time
Electrical devices (i.e. light bulb) – rate at which light bulb changes electrical energy into light or
rate at which heater changes electrical energy into thermal energy
Work vs. Power:
If climb stair while walking, can climb for long time, but if run up stairs, run out of energy much
faster – you are limited by power
Car engines do work to overcome the force of friction, to climb hills and to accelerate – a car is
limited by the rate at which it can do work  why cars are rated in hp (increased hp means
more power to climb hills and accelerate)
Oftentimes, convenient to look at power in terms of force and velocity
P = W/t = Fd/t = Fv
[examples #36 together, #37 on own, #38 – 42 HW] GIVE HINT for #39 W = ΔKE