Download Work and Energy

WORK AND ENERGY
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Work
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 Work as you know it means to do something that
takes physical or mental effort
 But in physics is has a very different meaning
 Think about the following:
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
A heavy chair held at arms length for several minutes
A student carries a bucket of water carried along a horizontal
path at a constant velocity
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 In both cases no work was done on the chair of the
bucket even though both required effort
 What conclusions can you draw from the two
examples about how work is defined in physics?
Equation for work
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 When a constant force is applied to an object:
 Work is equal to the magnitude of the applied force
times the magnitude of the displacement of the
object
 W=Fd
 Work is not done unless the object is moved with
the action of a force, parallel to the direction of the
force.
 Since the heavy chair doesn’t not move vertically
no work is done on the chair
Example
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 How much work is done when a box is pushed with a
force of 8 N over a distance of 4 meters?
 32 N•m
 Or, 32 Joules (32 J)
Two types of work
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 1) work done against another force (ex: gravity,
shooting a bow, friction)
 2) work done to change the speed of an object (ex:
speeding up or slowing down in a car)
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 Do we always push or pull objects directly
horizontal?
 Components of the forces will have to be found
 If the force applied is at an angle to the horizontal,
the component that is parallel to the movement will
do work on the object
 No work is done on the bucket being carried because
all the force being applied to the bucket is
perpendicular to the displacement.
The sign of work is important
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 Work is a scalar quantity (no direction)
 It can be positive of negative
 It is positive when the direction of displacement is in
the same direction as the force
 It is negative when the direction of the displacement
is in the opposite direction of the force (i.e. a car
slowing down)
 Work done by friction would be negative!
Net Work
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 Many forces can be acting on an object making it
move
 In this case each individual force can be doing work
on the object
 And together the forces can produce a net work:
 Wnet = Fnetd
ENERGY
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Kinetic Energy
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 If an object is moving, it is capable of doing work
 This is called energy of motion, or Kinetic Energy
 If you do work on an object and get it moving, it can
then do work on other objects
Kinetic Energy Equation
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 Kinetic energy = work required to bring an object up
to speed from rest, or to bring to rest from a certain
speed….therefore
 KE=W=Fd
where KE is Kinetic Energy
 Using Newton’s 2nd law, this equation can be derived
into it’s final form Fd=1/2mv2 or KE =1/2mv2
Work-Kinetic Energy Theorem
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 The net work on an object is equal to the change in
the kinetic energy of the object.
 Wnet=ΔKE=KEf-KEi
 Or, Wnet=1/2mvf2-1/2mvi2
Example
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 On a frozen pond, a person kicks a 10.0 kg sled,
giving it an initial speed of 2.2 m/s. How far does
the sled move if the coefficient of kinetic friction
between the sled and the ice is 0.10?
 Given: m=10.0 kg
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vi= 2.2 m/s
vf= 0 m/s
µk= 0.10
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 Equations: Wnet=Fnetd, Wnet=ΔKE=1/2mvf2-1/2mvi2
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Ff=µkFN
What forces are acting on the sled as it slows down?
Only friction so:
Fnet = Ff=0.10·10.0kg·9.81m/s2
= 9.8 N
Since vf = 0, Wnet=-1/2mvi2
=-1/2· 10.0kg·(2.2m/s)2
=-24 J
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 So finally, since Wnet = Fnetd
 -24J=9.8N·d
 d=2.4 m
 TA DA!
Potential Energy
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Potential Energy
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 Consider an arrow loaded on a bow.
 Once the arrow is released it will have kinetic energy
 Because of the arrows position (pulled back on the
bow) it has potential to move, it has potential energy
Gravitational Potential Energy
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 The energy associated with an object due to the
object’s position relative to the gravitational source is
called gravitational potential energy
 Given by this equation
 PEg=mgh
Elastic Potential Energy
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 Most common objects that have elastic potential
energy are springs
 When springs are compressed or stretched they have
elastic potential energy stored
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When the force holding the spring in position is removed the
spring will return to its equilibrium position
 Length of spring with no external forces is called
relaxed length
 The amount of energy depends on distance
compressed or stretched from its relaxed length
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 Elastic Potential can be found using the following
equation
 PEelastic=1/2kx2
 Where – k is the spring constant, of force constant
 Spring constants have units of N/m
Example
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 When a 2.00 kg mass is attached to a vertical spring,
the spring is stretched 10.0 cm such that the mass is
50.0 cm above the table. The spring constant of the
spring is 400.0 N/m. What is the total potential
energy of this system?
 Given: m=2.00 kg
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k=400.0 N/m
h= 50.0 cm = 0.500 m
x= 10.0 cm = 0.100 m
g=9.81 m/s2
Solution
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 PEtot= PEg+PEelastic
 PEg=mgh
 PEelastic=1/2kx2
 PEg=2.00kg·9.81 m/s2·0.500m
 = 9.81 J
 PEelastic=1/2·400.0 N/m·(0.100 m)2
 = 2.00 J
 9.81 J + 2.00 J = 11.81 J
Conservation of Energy
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Energy is Conserved
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 Something is conserved
when it remains constant
 Like matter, energy
cannot be created or
destroyed
 Energy gets transferred
or transformed in to
other types of energy
Mechanical Energy
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 Many objects have both
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mechanical and potential
energy
For example a swinging
pendulum
At the highest point of its
swing it has all gravitational
potential energy
At the bottom of the
pendulum it has all kinetic
energy.
Everywhere in between it has
both
PEg + KE=Total Energy
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 As the pendulum falls
from its highest point it
gains speed, therefore it
is gaining KE
 As it falls it is also
decreasing its height,
therefore PEg is
decreasing
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 Mechanical energy is the sum of the potential energy
and the kinetic energy associated with an object
 ME = KE + ΣPE
(Σ = sum)
 Conservation of Mechanical Energy:
 In the absence of friction, the total mechanical
energy remains the same
 MEi=Mef
POWER
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Power
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 Rate at which work is done
 Rate of energy transfer
 Equation:
 P=W/t
 Or, P=Fv (this one is less commonly used, but just in
case…)
 The unit for power is the Watt