Transcript Work and Energy

Chapter 6
W  ( F cos )s
The equation for work tells us the following:
• In order for work to be done, a force must
cause displacement
• Only the component of force in the direction
of motion will cause work to be done.
(SOHCAHTOA comes into play here)
• The derived unit of force is the Newton meter.
One Newton meter is referred to as one joule
(J).
 Work is a scalar quantity
 If the displacement is zero, the work done is also zero,
even if a force is applied!
 In the equation, θ is the angle between the force and
the displacement.
 When force points in the same direction as the
displacement, θ = 0⁰ and the equation becomes W=Fs
 The force component perpendicular to the
displacement does no work!
 Work can be (+) or (-), depending on whether a
component of the force points in the same direction as
the displacement or in the opposite direction.
Supersize
Who?
Newton’s
2nd Law
F = ma
Work
Kinematics
W = Fs
v 2f  v02  2as
WorkEnergy
Theorem
Use the above equations to come up with
an expression relating work (Fs) to
kinetic energy (1/2 mv2).
1
2
KE  mv
2
Kinetic Energy is…
• mechanical energy
• energy of motion
• like work and all forms of
energy, measured in joules
1
1
2
W  KE f  KE0  mv f  mv02
2
2
The Work-Energy Theorem tells us…
1. When a net external force does work on an object, the KE
of the object changes.
2. The difference in KE will equal the work done and vice
versa.
3. If work done by the net force is positive, the KE increases.
4. If the word done is negative, the KE decreases.
5. If the work done is zero, the KE remains the same.
 We all know that gravity is a force that can cause
objects to move toward the Earth or the slow down
when moving away from the center of the Earth.
 In examples where gravity is the force causing work to
be done, we use (h) as the symbol for displacement.
Yes… h stands for height!
Wgravity  (mg cos 0)(h0  h f )  mg(h0  h f )
 The last given equation is valid for any path taken
between initial and final heights (remember
displacement!)
 Vertical distances do not need to be measured with
respect to the surface of the earth.
PE =mgh
Gravitational Potential Energy is..
1. A “conservative force.”
2. The potential an object has to do work by virtue of the fact that is
has moved further from the surface of the earth.
3. Greater as an object moves further from the center of the earth.
4. PE = mgh
5. A scalar quantity
Conservative
Nonconservative
 The work it does on a moving
 Work done by these forces on
object is independent of the
path between the object’s initial
and final position.
 A force does no net work on an
object moving around a closed
path when starting position =
ending position.
 Gravitational, elastic spring
force, electric force
objects depends on the path of
the motion between the points.
 Static and kinetic friction, air
resistance, tension, normal
force, propulsion force of a
rocket.
Wnc =∆KE + ∆PE
This equation applies if gravity is the only
conservative force acting on the object.
 The total mechanical energy acting on a system includes

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both kinetic and gravitational potential energy.
ET = KE + PE
When an object is in motion, the total mechanical
energy remains constant all along the path between
the initial and final points.
This law holds true if the net work done by external
nonconservative forces is zero.
In situations where height varies and gravity is the driving
force of motion, PE is converted into KE and vice versa.
 In the “real world” objects are affected by
nonconservative forces such as friction.
 The work Wnc done by these combined forces is not
equal to zero.
 Therefore, the difference between the final and initial
total mechanical energies is equal to Wnc = Ef – E0
 Check out Example problems 11 and 12 for great
illustrations of how to use this equation when
nonconservative forces are present and do work!
Ehh…
Watts Up
Doc?
 For many of us, the amount of time work is done in
can be very important.
 While two objects can experience the same amount of
work, the one accomplishing the work faster is more
powerful.
W
P
t
SI unit of power: joule/s = watt (W)
Scalar quantity
1 horsepower = 550 foot pounds/ second = 745.7 watts
P  Fv
 The amount of work done on an object is equal to a change
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in KE or PE
The total mechanical energy of a system will equal KE + PE
at any given point.
Energy can neither be created nor destroyed, but can only
be converted from one form to another.
Energy can neither be created nor destroyed, but can only
be converted from one form to another.
Energy can neither be created nor destroyed, but can only
be converted from one form to another.
I am the most powerful because I finished my notes before
you did! More work done in less time 