chapter 6: energy, work and simple machines 6a work and power
TRANSCRIPT
Chapter 6:Energy, Work and Simple Machines
6A Work and Power
6A Objectives
Display an ability to calculate work done by a force.
Describe the relationship between work and energy.
Differentiate between work and power and correctly calculate power used.
Identify the force that does work.
Concept Development Map
Energy
Latin energia = en (in) + ergon (work) = active
Internal or Inherent Power
Energetic, energize
DefinitionsApplications
Chemical Energy
Thermal Energy
Nuclear Energy
Motion Energy (momentum)
What is it?
The property of an object that allows it to produce change in itself or its environment.
Examples
I ran out of energy. I need to re-energize.
I don’t feel very energetic.Potential Energy
Concept Development Map
Work
Middle European werk, wirk, work = to do
Exertion of Strength
The matter on which someone labors on.
DefinitionsApplications
Engines
Springs; Pulleys
Human Efforts
Torque
What is it?
The process of changing energy of a system by means of forces.
Examples
This is a work of art!
She’s a real piece of work!
I need to get to work.
WORKMOSHER’S
Work Defined
€
Work = Force × distance
Work (W): The product of the force on an object and the distance through which the object is moved.
or in Symbols:
€
W = FΔdLet’s compare this new W with I (impulse)…
Work = Force X Distance
Where is the Force and where is the distance in this picture?
Work Defined
Work Clarified
Be careful!
Only the force in the same direction as the motion counts towards the work.€
W = (F cosθ) • Δd
Work Clarified
Case 1. A man pushes against a car stuck in a snow bank while his date sits nervously behind the steering wheel trying not to make the tires spin. However, the car does not move. How much work did he do on the car? €
W = (F cosθ) • Δd
Answer: The man did no work on the car since d=0. He may have burned calories, converting chemical energy into heat, but still, the car did not move.
Work Clarified
Case 2. Sally carries a 0.5 kg textbook under her arm along a horizontal path. How much work was done on the text book?
€
W = (F cosθ) • Δd
Answer: None, since both gravity and the force Sally exerted against gravity are perpendicular to the distance the book moved. (cosø = 0 so W = 0).
Work Clarified
Case 3. An asteroid traveling at constant velocity out of reach of gravitational fields [etc.]... How much work is done on the satellite?€
W = (F cosθ) • Δd
Answer: None, since F = 0, W = 0.
Power
Power - the rate of doing work. Work per unit time. 1 Watt = 1 Joule/sec.
€
P =W
Δt=FΔd
Δt= Fv
€
PΔt =W
Compare:
€
FΔt = I
Units: Units:
€
N • m
€
N • s
James Watts
6A Conclusions
Power - energy of an object due to its motion. Units of 1 kgm2/s3 = 1 Watt=1 J/s.
Work - a force applied over a certain distance. Force times distance has units of 1 Nm = 1 Joule.
Mechanical Energy Defined
€
ME = PE +KE
Mechanical Energy (ME): Energy due to the position or the movement of something; potential energy or kinetic energy or a combination of both.
But just what is potential energy and kinetic energy?
What do these have to do with Potential?
Potential Energy Defined
€
PE = mgh
Potential Energy (PE): “Height” energy, position energy. It is usually related to the relative position of two things, such as a stone and the earth (gravitational PE), or an electron and a nucleus (Electric PE).
h – relative to reference level; hground = 0.
What does this have to do with potential Energy?
Work?
Kinetic Energy Defined
€
KE = 12 mv
2
Kinetic Energy (KE): Motion energy. Equal to half the mass multiplied by the speed (scalar!) squared.
Kinetic Energy Defined
When does potential become kinetic?
(when does HEIGHT energy becomeMOTION energy)
When does potential become kinetic?
When does potential become kinetic?
Bill Nye: Energy (0:00 to 6:00)
6B Conclusions
Potential Energy – energy due to position = height energy = mgh
Kinetic Energy - energy of an object due to its motion. Units of 1 kgm2/s2 = 1 Joule.
Energy Transfer – Potential energy can be turned into kinetic energy and visa versa. Roller coasters and pendulums are examples of this.
6C Objectives
Solve problems using the work-energy theorem.
Solve problems using the law of conservation of energy.
Work versus Impulse
€
I = FΔt = mΔv = mv2 −mv1
Starting with the Impulse-Momentum Theorem:
Multiplying both sides by d/t:
€
FΔt •Δd
Δt= mΔv •
Δd
Δt
Work versus Impulse (cont’d)
€
FΔd = mΔv •Δd
Δt
This simplifies to:
Substitution of vavg = d/t = (v2+v1)/2:
€
FΔd = mΔv •1
2(v2 + v1) =
1
2m(v2 − v1)(v2 + v1)
Work - Energy Theorem
This simplifies to:
This is the Work-Energy Theorem:
€
Work = FΔd =1
2mΔv 2 = ΔK =Kinetic Energy Change€
FΔd =1
2m(v2 − v1)(v2 + v1) =
1
2m(v2
2 − v1v2 + v1v2 − v12) =
1
2m(v2
2 − v12)
Work - Impulse Comparison
Let’s compare the two theorems:
Work-Energy Theorem:
€
FΔd =1
2mΔv 2 =
1
2mv2
2 −1
2mv1
2€
FΔt = mΔv = mv2 −mv1
Impulse-Momentum Theorem:
Kinetic Energy vs. Momentum
Another conclusion:
€
d(K.E .)
dt=d( 1
2 mv2)
dt= mv
Kinetic Energy is the derivative of Momentum
Work - Impulse Comparison
Let’s compare the two graphs:
Work (Force versus Distance)Impulse (Force versus Time)
Force
Time
Conservation of Mechanical Energy
Mechanical Energy is the sum of kinetic energy and gravitational energy. It cannot change in an ideal system.
€
ME = 0 = ΔKE + ΔPE = 12 mΔv 2 + mgΔh
The decrease in potential energy is equal to the increase in kinetic energy.
The decrease in kinetic energy is equal to the increase in potential energy.
Conservation in a Pendulum
Simple Harmonic Motion conserves energy on each swing.
€
ME = 0 = ΔKE + ΔPE = 12 mΔv 2 + mgΔh
The decrease in potential energy is equal to the increase in kinetic energy.
The decrease in kinetic energy is equal to the increase in potential energy.
Momentum and Kinetic Energy Conservation
Hew35: Bowling Ball Conservation Of Energy
Hew36: Math Example Conservation Of Energy
Bill Nye: Energy (6:00 to 12:56)
6D Machines
6D Objectives
Communicate an understanding of mechanical advantage in ideal and real machines.
Demonstrate Knowledge of why simple machines are useful.
Calculate efficiencies for simple and compound machines.
Analyze compound machines and describe them in terms of simple machines.
6D Vocabulary
Simple Machine - A lever, pulley, gear, wheel and axle, inclined plane, wedge, or screw.
Machine - A device that changes the magnitude or the direction of the force needed to do work, making the task easier to accomplish.
Compound Machine - A device that consists of two or more simple machines linked so that the resistance force of one machine becomes the effort force of the second machine.
Japanese Rube Goldberg Machines
Rube Goldberg Machines #1
Rube Goldberg Machines #2
Mechanical Advantage - Pulleys
Mechanical Advantage - Pulleys
Mechanical Advantage
€
MA =Fr
Fe
Mechanical Advantage - The ratio of the resistance (r) force to the effort (e) force.
Ideal Mechanical Advantage - The ratio of the resistance distance to the effort distance.
€
IMA =dedr
Torque Balance - The resistance torque equals the effort torque.
€
Frdr = Fede
€
MA =Fr
Fe
=dedr
= IMA
Efficiency
€
% Efficiency =Wout
W in
×100%
Percent Efficiency - The ratio of the output work to the input work times 100%.
€
(FΔd)out(FΔd)in
=FrdrFede
=MA
IMA
Baseball-Basketball Bounce
Demo:
Place a baseball on top of a basketball. Drop both at the same time on the floor and see what happens. What do you think will happen? Why?
Baseball-Basketball Bounce
What does all this have to do with baseball or sports in general?
When you bounce a baseball off a basketball, you are transferring energy from the deformation of the basketball to the baseball. When you bounce a baseball off a bat, you are transferring energy from the bat to the baseball. How well a ball bounces off the basketball has to do with timing. When the basketball hits the floor, it squashes the bottom a bit. When it springs back to its original shape, it pushes off the floor -- it bounces. The baseball indents into the basketball on the top. When the basketball returns to its round shape all the energy is transferred to the baseball. The effect is similar to a man on a trampoline.
Conservation of Mechanical Energy
The Amazing Oscillating Spring Thing
€
ME = 0 = ΔKE + ΔPE + ΔUe
= 12 mΔv 2 + mgΔh + ΔUe
Efficiency
€
(% Efficiency)IDEAL =100%
Ideal Machines:
Real Machines:
€
(% Efficiency)REAL <100%
Bill Nye: Energy (12:56 to END)