- 1. Work, Energy and Power PHF02 Week 5
2. Tutorial questions for next wk
3. What is Energy?
- We need energy to do work
- We need energy to watch TV
- We need energy for lighting
- We need energy for cooking
- We need energy for almost everything
- IS AN IDEA, A CONCEPT THAT DEFINES THE CAPACITY TO DO WORK
4. Some Energy Considerations
- Energy can be transformed from one form to another
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- Essential to the study of physics, chemistry, biology, geology,
astronomy
- Can be used in place of Newtons laws to solve certain problems
more simply
5. Work
- Provides a link between force and energy
F 6. The work,W , done by a constant force on an object is
defined as the product of the component of the force along the
direction of displacement and the magnitude of the displacement 7.
Work, cont.
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- Fis the magnitude of the force
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- x is the magnitude of the objects displacement
8. More About Work
- The work done by a force is zero when the force is
perpendicular to the displacement
- If there are multiple forces acting on an object, the total
work done is the algebraic sum of the amount of work done by each
force
9. Work and Dissipative Forces
- Work can be done by friction
- The energy lost to friction by an object goes into heating both
the object and its environment
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- Some energy may be converted into sound
- For now, the phrase Work done by friction will denote the
effect of the friction processes on mechanical energy alone
10. Kinetic Energy
- Energy associated with the motion of an object
- Scalar quantity with the same units as work
- Work is related to kinetic energy
11. Work-Kinetic Energy Theorem
- When work is done by a net force on an object and the only
change in the object is its speed, the work done is equal to the
change in the objects kinetic energy
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- Speed will increase if work is positive
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- Speed will decrease if work is negative
12. Lets Check! 13.
- The object moves from v ito v fin a distance x; using equation
of motion we can find its acceleration.
- Also from Newton's 2 ndlaw F = ma, we can write;
14. 15. Work and Kinetic Energy
- An objects kinetic energy can also be thought of as the amount
of work the moving object could do in coming to rest
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- The moving hammer has kinetic energy and can do work on the
nail
16. Types of Forces
- There are two general kinds of forces
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- Work and energy associated with the force can be recovered
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- The forces are generally dissipative and work done against it
cannot easily be recovered
17. Conservative Forces
- A force is conservative if the work it does on an object moving
between two points is independent of the path the objects take
between the points
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- The work depends only upon the initial and final positions of
the object
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- Any conservative force can have a potential energy function
associated with it
18. More About Conservative Forces
- Examples of conservative forces include:
- Potential energy is another way of looking at the work done by
conservative forces
19. Nonconservative Forces
- A force is nonconservative if the work it does on an object
depends on the path taken by the object between its final and
starting points.
- Examples of nonconservative forces
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- kinetic friction, air drag, propulsive forces
20. Example 1
- The driver of a 1000 kg car traveling on the interstate at 35
m/s slams on his brakes to avoid hitting a second vehicle infront
of him, which had come to rest because of congestion ahead. After
the brakes are applied, a constant friction force of 8000 N acts on
the car. Ignore air resistance.
- At what minimum distance should the brakes be applied to avoid
a collision with the other vehicle?
21. 22.
- b. If the distance between the vehicles is initially only 30 m,
at what speed would the collision occur?
23. Gravitational Potential Energy
- Gravitational Potential Energy is the energy associated with
the relative position of an object in space near the Earths
surface
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- Objects interact with the earth through the gravitational
force
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- Actually the potential energy is for the earth-object
system
24. Work and Gravitational Potential Energy
- Units of Potential Energy are the same as those of Work and
Kinetic Energy
25. Work-Energy Theorem, Extended
- The work-energy theorem can be extended to include potential
energy:
- If other conservative forces are present, potential energy
functions can be developed for them and their change in that
potential energy added to the right side of the equation
26. Conservation of Mechanical Energy
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- To say a physical quantity isconservedis to say that the
numerical value of the quantity remains constant throughout any
physical process
- In Conservation of Energy, the total mechanical energy remains
constant
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- In any isolated system of objects interacting only through
conservative forces, the total mechanical energy of the system
remains constant.
27. Conservation of Energy, cont.
- Total mechanical energy is the sum of the kinetic and potential
energies in the system
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- Other types of potential energy functions can be added to
modify this equation
28. Example 2
- (T12) A projectile is launched with a speed of 40 m/s at an
angle of 60 above the horizontal. Find the maximum height reached
by the projectile during its flight by using conservation of
energy.
29. Example 3
- (T14) A 70-kg diver steps off a 10-m tower and drops, from
rest, straight down into the water. If he comes to rest 5.0 m
beneath the surface, determine the average resistive force exerted
on him by the water.
30. Potential Energy Stored in a Spring
- Involves thespring constant , k
- Hookes Law gives the force
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- F is in the opposite direction of x
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- k dependson how the spring was formed, the material it is made
from, thickness of the wire, etc.
31. Potential Energy in a Spring
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- related to the work required to compress a spring from its
equilibrium position to some final, arbitrary, position x
32. Work-Energy Theorem Including a Spring
- W nc= (KE f KE i ) + (PE gf PE gi ) + (PE sf PE si )
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- PE gis the gravitational potential energy
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- PE sis the elastic potential energy associated with a
spring
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- PE will now be used to denote the total potential energy of the
system
33. Conservation of Energy Including a Spring
- The PE of the spring is added to both sides of the conservation
of energy equation
- The same problem-solving strategies apply
34. Nonconservative Forces with Energy Considerations
- When nonconservative forces are present, the total mechanical
energy of the system isnotconstant
- The work done by all nonconservative forces acting on parts of
a system equals the change in the mechanical energy of the
system
35. Nonconservative Forces and Energy
- The energy can either cross a boundary or the energy is
transformed into a form of non-mechanical energy such as thermal
energy
36. Transferring Energy
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- Produces a displacement of the system
37. Transferring Energy
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- The process of transferring heat by collisions between
molecules
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- For example, the spoon becomes hot because some of the KE of
the molecules in the coffee is transferred to the molecules of the
spoon as internal energy
38. Transferring Energy
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- A disturbance propagates through a medium
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- Examples include sound, water, seismic
39. Transferring Energy
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- Transfer by means of electrical current
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- This is how energy enters any electrical device
40. Transferring Energy
- Electromagnetic radiation
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- Any form of electromagnetic waves
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- Light, microwaves, radio waves
41. Power
- Often also interested in therateat which the energy transfer
takes place
- Poweris defined as this rate of energy transfer
42.
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- Can define units of work or energy in terms of units of
power:
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- kilowatt hours (kWh) are often used in electric bills
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- This is a unit of energy, not power
43. Center of Mass
- The point in the body at which all the mass may be considered
to be concentrated
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- When using mechanical energy, the change in potential energy is
related to the change in height of the center of mass
44. Work Done by Varying Forces
- The work done by a variable force acting on an object that
undergoes a displacement is equal to the area under the graph of F
versus x
45. Spring Example
- Spring is slowly stretched from 0 to xmax
46. Spring Example, cont.
- The work is also equal to the area under the curve
- In this case, the curve is a triangle
47. Example 4
- (T13) A 0.250-kg block is placed on a light vertical spring (
k= 5.00 x 10 3N/m) and pushed downward, compressing the spring
0.100 m. After the block is released, it leaves the spring and
continues to travel upward. What height above the point of release
will the block reach if air resistance is negligible?
48. Example 5
- (T16) A 50.0-kg student climbs a 5.00-m-long rope and stops at
the top. (a) What must her average speed be in order to match the
power output of a 200-W light bulb? (b) How much work does she
do?
49. God bless Fiji at Hong Kong Stadium! 50. Final Question!
- An extreme skier, starting from rest, coasts down a mountain
that makes an angle 25.0 with the horizontal. The coefficient of
kinetic friction between her skis and the snow is 0.200. She coasts
for a distance of 8.0 m before coming to the edge of a cliff.
Without slowing down, she skis off the cliff and lands downhill at
a point whose vertical distance is 4.00 m below the edge. How fast
is she going just before she lands?