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Chapter 4Work and Energy
• Section 1: Work and Machines
• Section 2: Describing Energy
• Section 3: Conservation of Energy
Section 1: Work and Machines
Work – the transfer of energy that occurs when a force makes an object move• no movement, no work• direction of the net force indicates where or on what work is
being done• calculating work:
equation for work: work = force x distance, or:
Example: How much work is done if Reggie lifts a box, m = 50-kg, 1.75 meters?Solution:
Where:W = WorkF = force (N) d = distance (m)
Units for Work:W =FdW = (N)(m) = Nm1Nm = 1 Joule (J)The unit for work is Joules (J)
m = 50.0kgd = 1.75m
Because Reggie is lifting the box he must exert a force greater than the weight of the box
Solve for work:
Section 1: Work and Machines
Machine – a device that makes doing work easier• Machines make doing work easier in three ways:
1. Increasing the force applied to the objectexample: a car jack to lift a car to change a flat tire
2. Increasing the distance over which the force is appliedexample: using a ramp to raise objects to a height
3. Changing the direction of the applied forceexample: a wedge – the vertical force is changed to a horizontal force
• Work done by machines Two forces are involved when a machine is used to do work:
1. Effort force – the force applied to the machine2. Resistance force – the force applied by the machine to
overcome resistance• Conservation of Energy
You transfer energy to a machine, the machine transfers that energy to the object
Energy is neither created nor destroyed, so the work done by the machine is never greater than the work done to the machine
Because of energy losses due to friction, the work done by the machine is always less than the work done to the machine
Section 1: Work and Machines
• Mechanical Advantage – the number of times a machine multiplies the effort force Equation for Mechanical Advantage :
Example: A claw hammer is used to pull a nail from a board. If the claw exerts a resistance force of 2500-N to the applied force of 125-N, what is the mechanical advantage of the hammer?Solution:
Notice that the force units (N) cancel; mechanical advantage has no units, it is just a number.
Where:MA = mechanical advantagefo = force out (force applied by the machine)fi = force in (force applied to the machine)
fo = 2,500.0Nfi = 125.0NMA =?
Section 1: Work and Machines
Simple machine – a machine that does work with only one movement• There are six (6) simple machines divided into two types:
Compound machine – a machine that consists of two or more simple machines used together
The lever type The inclined plane type
Includes: Lever Pulley Wheel and axle
Includes: Ramp Wedge Screw
Section 1: Work and MachinesLever – a bar that is free to pivot, or turn, about a fixed point.• There are three classes of levers:
1st class lever – the fulcrumis between the effort and the resistanceMultiplies effort force
and changes its directionExamples: crow bars, teeter-totters
2nd class lever – the resistanceforce is between the effort force and the fulcrumMultiplies force without
changing directionExamples: wheel barrows, doors
3rd class lever – the effort force is between the fulcrum and the resistance forceThe effort force is always
greater than the resistance force. MA < 1Examples: the fore-arm, fishing poles
If the 3rd class lever has no mechanical advantage, why use one?
Section 1: Work and Machines
Calculating the mechanical advantage of levers• Equation: or:
the distances are measured from the fulcrum to the point where the forces are acting
Example: If the distance of the effort force is 3-m, and the distance of the resistance arm is 1-m, what is the mechanical advantage of the lever?Solution:
Notice the distance units cancel. Remember, mechanical advantage is just a number.
de = 3.0mdr = 1.0mMA = ?
Section 1: Work and MachinesPulleys• The two sides of the pulley are the effort arm and the
resistance arm.• A fixed pulley changes the direction of the force only, it does
not increase force• A moveable pulley will increase the effort• Block-and-tackle – a system of pulleys consisting of fixed
and moveable pulleys. The block-and-tackle will multiply the effort force
Wheel-and-axle – a machine consisting of two wheels of different sizes that rotate togetherInclined plane (ramp) – a sloping surface that reduces the amount of force required to do work• The same amount of work is done by lifting a box straight up
or by sliding it up a ramp. However, the ramp reduces the amount of force required by increasing the distance Mechanical advantage of a ramp:
, or: Example: Jessica uses a ramp 5-m long to raise a box to a height of 1-m. What is the mechanical advantage of the ramp?Solution
Length =5.0mHeight = 1.0mMA = ?
Section 1: Work and Machines
Screw – an inclined plane wrapped around a cylinderWedge – an inclined plane with one or two sloping sides
Mechanical Efficiency (ME)• Recall that the amount of work done by the machine (work
output) is always less than the work done on the machine (work input)• Mechanical Efficiency is the measure of how much of the work
put into a machine is changed into useful output work by the machine Because of friction no machine is 100% efficient. ME will
always be less than 100% Equation: , or:
Example: John is changing a flat tire on his truck. He does 2,500J of work on the jack, while the jack does 2,100J of work on the car. How efficient is the jack?Solution
wi = 2,500Jwo = 2,100JME = ?
Section 2: Describing Energy
Energy – the ability to cause change• Energy comes in different forms chemical, electrical,
thermal, etc. We will be looking at three (3) types of energy: kinetic,
potential, and mechanical.
• Kinetic Energy (KE) KE is energy in a moving object Anything that moves has kinetic energy Kinetic energy depends of two things:
1. the mass of the moving object2. the velocity of at which the object is moving
Equation for kinetic energy:
Unit for energy:
Where:KE = kinetic energyM = mass (kg)V = velocity (m/s)
Section 2: Describing Energy
Example: A ball, m = 1.5-kg, is rolling across the floor towards the door at 2 m/s. What is the KE of the rolling ball?Solution
Important: Always square the velocity before you do any multiplication
• Potential Energy Potential energy – energy stored due to an object’s
position Three types of potential energy:
Elastic – PE stored by things that stretch or compressEx.: rubber bands, springs, pole vault poles
Chemical – PE stored in chemicals bondsEx.: nuclear weapons and fuels
Gravitational – PE stored by things that are elevatedEx.: fruit on trees, bouncing balls
m = 1.5-kgv = 2.0-m/sKE = ?
Section 2: Describing Energy
• The amount of potential energy can be determined mathematically. We will focus on gravitational PE Equation for gravitational PE:
Example: An apple, mass = 0.5-kg, is hanging from a branch 4.0-m above the ground. What is its gravitational PE?Solution
PE = Potential Energy (J)M = mass (kg)g = 9.8 m/s2
H = height (m)
m = 0.5 kgh = 4.0 mPE = ?
Section 3: Conservation of Energy
• Mechanical Energy – the total amount of potential and kinetic energy in a system Equation: mechanical energy = potential energy + kinetic energy,
or:
Example: An object held in the air has a gravitational PE of 480.0J. What is its kinetic energy if it has fallen two-thirds of the way to the ground?
• Law of Conservation of Energy: Energy is neither created nor destroyed On a large scale: total energy in the universe is constant Consequence: energy can change form:
potential kinetickinetic thermalchemical mechanical
ME = PE + KE
Solution a)Before the object started falling ME = PE, so ME = 480.0J.
b)As the object is falling PE is being converted to KE.
c)At anytime during the fall ME = PE + KE. d)When the object is two-thirds of the way down
ME = 1/3PE + 2/3KE. e)So: KE = 2/3(480.0 J), or KE = 320.0J
Section 3: Conservation of Energy
• Power – the amount of work done in a certain amount of time Power is a rate Equation for calculating power:
Units for Power: the Watt (W)1 watt is about equal to the power required to lift a glass of water from a table to your mouth
Example 1: It took 20 seconds to move a refrigerator, You did 3,150 J of work in the process. How much power was required to move the refrigerator? Solution
Example 2: It took you 1.5 s to lift a 10-kg box of the floor to a height of 1.0-m. How much work did you do on the box, and how much power was required to do this?Solution
work Wpower = ,or : P =
time t
2
3
J kg m1W = 1 = 1
s s
WP =
t3,150J
P = 20s
JP = 157.5 = 157.5 W
s
t = 1.5s
m = 10.0kg
d = 1.0m
W = ?
P = ?
2
2
F = W(eight) = mg
mF = 10kg(9.8 )
skg m
F = 98 = 98Ns
W = Fxd
W = 98N(1.0m)
W = 98N m = 98J
WP =
t98J
P = 1.5s
JP = 65.33 = 65.33W
s
