Energy, Work andSimple Machines
Chapter 10
Physics
Objectives: The student will beable to:
1. distinguish between work in the scientific sense as comparedto the colloquial sense.2. write the definition of work in terms of force and displacementand calculate the work done by a constant force when the forceand displacement vectors are at an angle.3. state and apply the relationship that work done with noopposing force equals the change in kinetic energy.
4.state and apply the relationship that work done against gravityequals the change in gravitational potential energy.
5.Define and calculate power from calculating the amount ofwork done by an object.
What is work?
In science, the word work has adifferent meaning than you may befamiliar with.
The scientific definition of work is: usinga force to move an object a distance(when both the force and the motion ofthe object are in the same direction.)
Work
Work has its own meaning in physics.
Work is done on an object when anapplied force acting on the objectmoves the object over a distance.
Work depends on two factors.
Force (F)
Displacement (d)
Work
Work = Force x Displacement
W = Fd
Unit for Work = Newton Meter (Nm)
1 Nm = 1 Joule (J) (Same as Energy)
Work is a scalar quantity (no direction)
In doing Work the Displacement has tobe in the same direction as the Force!
Work or Not?
According to the scientific definition,what is work and what is not?
A teacher lecturing to her class
A mouse pushing a piece of cheese withits nose across the floor
7
8
What’s work?What’s work?
A scientist delivers a speech to an audience of his peers.A scientist delivers a speech to an audience of his peers.
NoNo
A body builder lifts 350 pounds above his head.A body builder lifts 350 pounds above his head.
YesYes
A mother carries her baby from room to room.A mother carries her baby from room to room.
NoNo
A father pushes a baby in a carriage.A father pushes a baby in a carriage.
YesYes
A woman carries a 20 km grocery bag to her car?A woman carries a 20 km grocery bag to her car?
No No
Physicist’s definition of “work”Physicist’s definition of “work”
dist
Work = F x dist∥
A scalar
(not a vector)
dist∥
Scalar Dot Product?
A product is obviously a result of multiplying 2 numbers. A scalar is aquantity with NO DIRECTION. So basically Work is found bymultiplying the Force times the displacement and result is ENERGY,which has no direction associated with it.
A dot product is basically a CONSTRAINTon the formula. In this case it means thatF and x MUST be parallel. To ensure thatthey are parallel we add the cosine on theend.
FORCE
Displacement
Work
FORCE
Displacement
Work Done by a Constant Force
The work done by a constant force is defined as the distance movedmultiplied by the component of the force in the direction ofdisplacement:
Work
In the figure above, we see the woman applying a force at an angletheta. Only the HORIZONTAL COMPONENT actually causes thebox to move and thus imparts energy to the box. The verticalcomponent (Fsin) does NO work on the box because it is NOTparallel to the displacement.
Work
•Relates force to change in energy
•Scalar quantity
•Independent of time
Atlas holds up the Earth
But he doesn’t move,dist∥ = 0
Work= Fx dist∥ = 0
He doesn’t do any work!
Work
Work can be Zero (WNET = 0) in threeways;
d = 0 (does not move or finisheswhere it starts)
FNET = 0 (v = 0 or v = constant)
FNET is perpendicular to d (F | d)
Work
If F ll d, then W = Fd or W = -Fd
W = Fd, Force in same direction asdisplacement( = 0o: cos = 1, Positive Work)
W = -Fd, Force is in the oppositedirection as the displacement( = 180o: cos = -1, Negative Work)
Work From a Force vsDisplacement Graph
If you have a Force vs DisplacementGraph, where the Force is in Newtons(N) and the Displacement is in Meters(m), you can find the Work by findingthe Area Under the Curve!
W = Area under F vs d graph
Formula for Work
Work = Force x Distance
The unit of force is newtons
The unit of distance is meters
The unit of work is newton-meters
One newton-meter is equal to one joule
So, the unit of work is a joule
Work Done by a Constant Force
In the SI system, the units of work are joules:
As long as this person doesnot lift or lower the bag ofgroceries, he is doing no workon it. The force he exerts hasno component in the directionof motion.
SI unit = Joule
1 J = 1 Nm = 1 kgm2/s2
Work
FORCE
Displacement
Work can be positive or negativeWork can be positive or negative
•Man does positive worklifting box
•Man does negative worklowering box
•Gravity does positivework when box lowers
•Gravity does negativework when box is raised
Work performed climbingstairsWork performed climbingstairs
lWork = Fd
lForce
lSubject weight
lFrom mass, ie 65 kg
lDisplacement
lHeight of each step
lTypical 8 inches (20cm)
lWork per step
l650N x 0.2 m = 130.0 Nm
lMultiply by the number of steps
PowerPower
lThe rate of doing work
lWork = Fd
Units: Fd/s = J/s = watt
Energy
Energy is the property that describes anobject’s ability to change itself or theenvironment around it.
Energy can be found in many forms.
Kinetic Energy (KE) – energy of motion.
Potential Energy (PE) – energy gainedby a change in position or structure
Kinetic Energy (KE)
Moving objects possess Kinetic Energy.
KE = ½ mv2
Energy is a scalar quantity and has theunit of Joule (J) (1 J = 1 Nm)
Work done against gravity
W = mgh
Height object raised (m)
Gravity (m/sec2)
Work(joules)
Mass (g)
The formula for kinetic energy
A force (F) is applied to mass (m) and
creates acceleration (a).
After a distance (d), the ball has reached speed (v),therefore the work done is its mass times acceleration timedistance:
–W= fd = (ma) x d = mad
–Also: d = ½ at2
Replace d in the equation for work, combine similar terms:
–W= ma (½ at2) = ½ ma2t2
–Also: v = at, so v2 = a2t2
Replace a2t2 by v2 shows that the resulting work is theformula for kinetic energy:
–W = ½ mv2
Period 3starts here
Work-kinetic Energy Theorem:
•Net work done on a particle equals thechange in its kinetic energy (KE)
W = ΔKE
Practice Questions
Explain who is doing more work andwhy:
A bricklayer carrying bricks and placingthem on the wall of a building beingconstructed
Or a project supervisor observing andrecording the progress of the workers froman observation booth.
Practice Question
Explain who is doing more work and why:
A bricklayer carrying bricks and placing them on the wall of abuilding being constructed
Or a project supervisor observing and recording the progressof the workers from an observation booth.
Work is defined as a force applied to an object, moving thatobject a distance in the direction of the applied force. Thebricklayer is doing more work.
Practice Question
How much work is done in pushing an object 7.0 macross a floor with a force of 50 N and then pushing itback to its original position? How much power isused if this work is done in 20 seconds?
Practice Question
How much work is done in pushing an object 7.0 macross a floor with a force of 50 N and then pushing itback to its original position? How much power isused if this work is done in 20 seconds?
Work = 7.0m x 50N x 2 = 700 Nm or 700 J
Power = 700J / 20s = 35 W
Practice Question
How much power will it take to move a 10 kg mass atan acceleration of 2 m/s2 a distance of 10 meters in 5seconds? This problem requires you to use theformulas for force, work, and power all in the correctorder.
Practice Question
How much power will it take to move a 10 kg mass atan acceleration of 2 m/s2 a distance of 10 meters in 5seconds? This problem requires you to use theformulas for force, work, and power all in the correctorder.
F = ma
F = 10 kg x 2 m/s = 20 N
W = Fd
W = 20 N x 10 m = 200 J
P = W/t
P = 200 J / 5 s = 40 watts
Calculate work done against gravity
A crane lifts a steel beam with a massof 1,500 kg. Calculate how muchwork is done against gravity if thebeam is lifted 50 meters in the air.
How much time does it take to lift thebeam if the motor of the crane can do10,000 joules of work per second?
Practice Question
You are asked for the work and time it takes to dowork.
You are given mass, height, and work done persecond.
Use: W = mgh.
Solve: W = (1,500 kg) ( 9.8 N/kg) (50 m) = 735,000 J
At a rate of 10,000 J/s, it takes 73.5 s to lift the beam.
Calculate work done against gravity
A crane lifts a steel beam with a mass of 1,500 kg.Calculate how much work is done against gravity ifthe beam is lifted 50 meters in the air.
How much time does it take to lift the beam if themotor of the crane can do 10,000 joules of work persecond?
Practice Question
Calculating kinetic energy
A car with a mass of 1,300 kg is going straight ahead at a speed of30 m/s (67 mph). The brakes can supply a force of 9,500 N.
Calculate:
a) The kinetic energy of the car.
b) The distance it takes to stop.
Practice Question
You are asked for kinetic energy and stoppingdistance
You are given mass, speed and force of brakes.
Use Ek = 1/2mv2 and W= fd
Solve for Ek = ½ (1,300 kg) ( 30 m/s)2 = 585,000 J
–To stop the car, work done by brakes = Ek of car, so W = Ek
–Solve for distance = W ÷ f = 585,000J ÷ 9,500 N = 62 m
Calculating kinetic energy
A car with a mass of 1,300 kg is going straight ahead at a speed of30 m/s (67 mph). The brakes can supply a force of 9,500 N.
Calculate:
a) The kinetic energy of the car.
b) The distance it takes to stop.
Practice Question
Elaboration
Force, Distance, and Work – Trans 10
Work and Energy Internet Activity
P. 261 #s1, 2, 3
P. 262 #s 4, 5, 6, 7, 8
P. 264 # 10 and 12
Questions and Problems
Work and Power
Stair Climbing and Power lab
Section Review #s 15-21
Closure
Kahoot 10.1 Work and Energy