Newtons Laws of Motion

1
Chapter 5 (Continued) Work and Energy

• Question
• Does the earth do work on the moon? The moon
  revolves
• around the earth in circular orbit, kept there by
  the
• gravitational force exerted by the earth.
• positive work
• negative work
• no work at all on the moon?

2
Example A 50 kg crate is pulled 40 m along a
horizontal floor by a constant force exerted by a
person, Fp100 N, which acts at an angle q370.
The coefficient of kinetic friction between the
crate and the floor is mk0.1. Determine the
total (net) work done on the crate.
3
Is the net work done on the Hammer positive or
negative?
Initial KE1gt0
Final KE20
From work-energy theorem Wnetlt0
4
Example At an accident scene on a level road,
investigators measure a cars skid mark to be 88
m long. It was a rainy day and the coefficient of
friction was estimated to be 0.42. Use these data
to determine the speed of the car when the
driver locked the brakes.
5
5.4 Potential Energy
Kinetic energy (KE) was energy as a result of
motion (½ mv2)
An object can have potential energy (PE)
associated with its position or shape.
Examples Gravitational PE PE of compressed
spring.
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Gravitational potential energy
How much work is done on an object of mass m by
lifting it to an elevation h? Assume the lifting
is done very slowly so KE 0.
External force must cancel the blocks weight,
Fext FG, work is
7
The gravitational potential energy depends on the
height of an object over some reference level.
You can chose reference level freely. but you
have to be consistent!
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5.5 Conservative and Non-conservative Forces
Conservative force is one for which the work done
does not depend on the path.
Gravitational force mechanical work against it
depends just on difference in elevation not how
an object is lifted.
Elastic force work against spring only depends
on length change.
9
For non-conservative force work done does depend
on the chosen path.
We learned Wfr -Ffr d ? longer path requires
more work. Coefficient of friction may be
different.
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Power
P W / Dt (work per unit time)
Since W F d, P F d / Dt F v
Example A man pushes a car with F200N at 1
m/s. (In English, 50 lb at 2 mi/hr) What is
power? Answer P F v 200 N 1 m/s 200 j/s
200 watts.
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5.6 Mechanical Energy and its Conservation
The change in total mechanical energy is the work
done by non-conservative forces. In case there
arent any (no friction, etc.)
The total mechanical energy doesnt change. It
is conserved in the absence of non-conservative
forces.
12
Example If the original height of the stone is
3.0 m calculate the stones speed when it has
fallen to 1.5 m above the ground.
13
Example In the high jump, kinetic energy of an
athlete is transformed into gravitational
potential energy without the aid of a pole. With
what minimal speed must the athlete leave the
ground in order to lift his center of mass 2.10 m
and across the bar with a speed of 0.7 m/s?
14
Potential energy stored in a spring
It is empirical observation that force F required
to compress a spring is proportional to the
amount, x, of the compression (compared to
un-stretched length for x not too extreme)
Spring un-stretched called the equilibrium
position.
15
What mechanical work, W, required to compress
spring? Determine work done by your hand on the
spring.
Here the force is not constant!
Remember the more general definition of work as
area under F-x curve (triangle)
16
Release spring suddenly what final velocity v2
will the ball (mass m) achieve when it leaves the
spring? No gravity
d
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• Problem solving
• Draw a picture
• Determine the system for which energy will be
  conserved the object or objects and
• the forces acting.
• Ask yourself what quantity you are looking for,
  and decide what are the initial point
• (1) and final (2) point locations.
• If the body under investigation changes its
  height during the problem, then choose
• a y 0 level for gravitational potential
  energy. This may be chosen for convenience.
• The lowest point is often a good choice.
• If springs are involved, choose the un-stretched
  spring position to be x (or y) 0.
• If no friction or other non-conservative forces
  act, then apply conservation of
• mechanical energy KE1 PE1 KE2 PE2
• Solve for the unknown quantity algebraically.

18
Example A 180 g wood block is firmly attached
to a very light horizontal spring. The block can
slide along a table where the coefficient of
friction is 0.3. A force of 20 N compresses the
spring 18 cm. If the spring is released from its
position, how far beyond its equilibrium position
will it stretch on its first swing?