work, power, energy and motion
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Work, Power, Energy and Motion. nuclear forces. chemical forces. moving electrons. moving train cars. gravitational force. Electrical force. Work and Force Go Together Too. Let work be defined as work = force × displacement. Work Done by a Constant Force. - PowerPoint PPT PresentationTRANSCRIPT
Work, Power, Energy and Motion Work, Power, Energy and Motion
moving train cars moving electrons
nuclear forces
chemical forces
gravitational force
Electrical force
Work and Force Go Together Too
Let work be defined as
work = force × displacement
Work Done by a Constant Force
In the SI system, the units of work are joules:
A complication: As long as this person does not lift or lower the bag of groceries, he is doing no work on it. The force he exerts has no component in the direction of motion.
Work Done by a Constant Force
The work done by a constant force is defined as the distance moved multiplied by the component of the force in the direction of displacement:
W = Fx cos θ
Hooke’s Law Lab
Work on a spring
Work can also be done on a spring when it is compressed or stretched; the figure below shows work yielding kinetic energy.
Work on a spring
The force required to compress or stretch a spring is:
where k is called the spring constant, and needs to be measured for each spring.
W = ½ kx2
Concept Question 1
Is it possible to do work on an object that remains at rest?
1) yes
2) no
Concept Question 1
If there is no displacement, there is no work done.If there is no displacement, there is no work done.
Work requires that there be a force acting over a
distance.
Is it possible to do work on an object that remains at rest?
1) yes
2) no
Concept Question 2
A box is being pulled A box is being pulled
across a rough floor across a rough floor
at a constant speed. at a constant speed.
What can you say What can you say
about the work done about the work done
by friction?by friction?
1) Friction does nowork at all
2) Friction doesnegative work
3) Friction does positive work
4) Work is not defined for friction as friction acts on the floor and the box
Concept Question 2
A box is being pulled A box is being pulled
across a rough floor across a rough floor
at a constant speed. at a constant speed.
What can you say What can you say
about the work done about the work done
by friction?by friction?
1) Friction does nowork at all
2) Friction doesnegative work
3) Friction does positive work
4) Work is not defined for friction as friction acts on the floor and the box
Work is defined for all forces. The friction acts opposite to the direction of displacement and is therefore negative here.
f
N
mg
displacement
Pull
Concept Question 3
Can friction ever do Can friction ever do
positive work?positive work?
1) yes
2) no
Concept Question 3
Can friction ever do Can friction ever do
positive work?positive work?
1) yes
2) no
Consider the book on your car seat. If you accelerate slowly the book does not slide on the seat but stays stationary with respect to the car. Friction is causing the book to move along with the car and hence force and displacement are in the same direction. Work is positive.
Concept Question
A box is being pulled
up a rough incline by a
rope connected to a
pulley. How many
forces are doing work
on the box?
1) one force
2) two forces
3) three forces
4) four forces
5) No forces are doing any work
Concept Question
A box is being pulled
up a rough incline by a
rope connected to a
pulley. How many
forces are doing work
on the box?
1) one force
2) two forces
3) three forces
4) four forces
5) No forces are doing any work
Any force not perpendicular to the
motion will do work: N does no workno work,
T does positivepositive workwork, f does negative negative
workwork, mg does negative worknegative work
Power
Power is the rate at which work is done. It can be thought of as work per second.
Power = Work / sec.
Power = Work / time
P = W / t
Question: Can you name 2 units for power?
Power
Power has the same trade-offs as work. A motor produces the same amount of power.
So, you can make a robot that’s fast, but weak.
Or you can make a robot that’s slow, but strong.
P = Fv
The total power in must equal the total power out (with an exception)...
Work / Power Worksheet
Kinetic Energy and the Work-Energy Principle
Because work and kinetic energy can be equated, they must have the same units: kinetic energy is measured in joules.
Kinetic Energy, and the Work-Energy Principle
Energy is defined as the ability to do work.
Mechanical energy is the energy associated with motion, i.e. masses which move. Sometimes the motion is ongoing (non-zero velocity) and sometimes it just involves a change of position (motion occurred between time t0 and t1).
Kinetic Energy
Defined:
Let work be defined as work = force × displacementKinetic energy must = work.
How’s my deriving?
Kinetic Energy, and the Work-Energy Principle
If we write the acceleration in terms of the velocity and the distance, we define that the work done here is
We define the kinetic energy:
(6-2)
(6-3)
The work-energy principleThe work-energy principle
Kinetic Energy, and the Work-Energy Principle
We define the work done to be equal to the change in the kinetic energy:
• If the net work is positive, the kinetic energy increases.
• If the net work is negative, the kinetic energy decreases.
CHAPTER 11 # 5, 17, 36, 38 & 41
Here’s why work and kinetic energy go together:
Concept Question
Two stones, one twice the Two stones, one twice the
mass of the other, are mass of the other, are
dropped from a cliff. Just dropped from a cliff. Just
before hitting the ground, before hitting the ground,
what is the kinetic energy what is the kinetic energy
of the heavy stone of the heavy stone
compared to the light one?compared to the light one?
1) quarter as much
2) half as much
3) they are equal
4) twice as much
5) four times as much
Concept Question
Two stones, one twice the Two stones, one twice the
mass of the other, are mass of the other, are
dropped from a cliff. Just dropped from a cliff. Just
before hitting the ground, before hitting the ground,
what is the kinetic energy what is the kinetic energy
of the heavy stone of the heavy stone
compared to the light one?compared to the light one?
1) quarter as much
2) half as much
3) they are equal
4) twice as much
5) four times as much
Consider the work done by gravity to make the stone fall distance d:
DKE = Wnet = F d cosθ
DKE = mg d
Thus, the stone with the greater massgreater mass has the greater KEgreater KE, which is
twicetwice as big for the heavy stone.
Concept Question
Is it possible for the kinetic
energy of an object to be
negative?
1) No.
2) Yes.
3) Maybe.
Concept Question
Is it possible for the kinetic
energy of an object to be
negative?
1) No.
2) Yes.
3) Maybe.
In Newtonian mechanics, the answer is no. The kinetic energy is always positive since the velocity squared and the mass are always positive.
Curiously, in quantum mechanics and relativity there are no such constraints. We believe it to still be true, but we are open to the possibility that it may not.