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332 – UNIT 6
WORK & ENERGY
Work Done by a Constant Force
The definition of work, when the force is
parallel to the displacement:
Work for Force at an Angle
If the force is at an angle to the displacement:
Only the horizontal component of the force
does any work (horizontal displacement).
Negative, Positive, Zero Work
Example:
A rope inclined upward at
45o pulls a suitcase through
the airport. The tension in
the rope is 20N.
a) How much work does the tension do, if the suitcase
is pulled 100m?
b) How much work does the normal force do on suitcase?
c) If friction between the suitcase and floor is 9.5N, how
much work is done by friction?
Net Work
The sum of all the work done
by all forces is the net work
done on an object.
If the person lifts the box with the same force
as gravity, the box will move at constant
speed. Net work is zero. Why?
Force vs Distance Graph
What is the
significance of
this type of
graph? What
information
can be gained
from this?
Find the work done on the object from 0-6.0m.
Example
A 3,000kg truck is to be loaded onto
a ship by a crane that exerts an
upward force of 31000N on the
truck. This force is applied over a
distance of 2.0 m.
a) Find the work done on the
truck by the crane.
b) Find the net work done on the
truck.
Example 2:
a) Determine the work done by gravity on a 5.0 kg block
that slides down a 5.0m long ramp of angle 30o. The
block starts from rest.
b) If a 20N frictional force acts on the block during the
entire length of the slide, determine the net work done
on the block.
Springs
Springs can exert forces on objects.
Pull on a spring, it pulls back. Push
on a spring, it pushes back.
Force exerted by spring is
given by Hooke’s Law:
Work done by spring or on
spring is given by:
Spring Example
A 1.5kg block hangs motionless
from a spring with spring
constant 250 N/m.
a) How far will is the spring stretched from its
relaxed position?
b) How much work was done in stretching the spring
to its position?
Question
Two men, Bubba and Jerry, push against a wall. Jerry
stops after 10 min, while Bubba is able to push for 5
minutes longer. Compare the work against the wall they
each do.
A) Bubba does 50% more work than Jerry.
B) Jerry does 50% more work than Bubba.
C) Bubba does 75% more work than Jerry.
D) Neither of them do any work.
ENERGY
Kinetic Energy
W-E theorem
The total work done on an object is equal to its
change in kinetic energy.
Example
You pull a sled across a frozen lake. To get started,
you pull the sled (mass 80 kg) with a force of 180 N
at 40° above the horizontal. The sled moves 5.0m,
starting from rest. Find the final speed of your sled.
Gravitational Potential Energy
Elastic Potential Energy
Power
Example
A 60kg student runs up the steps to the football
stadium. The steps are 8m high. How much power
was developed by the student if he reached the top
of the stairs in 4.5 seconds?
Example
A car moves 125m in a time of 6.7s at a constant
speed. If the force of air resistance was a steady
300N, find the power developed by the car during
this time.
Conservation of Energy
Example:
A child runs forward with her sled at 2.0m/s.
She hops onto the sled at the top of a 5.0m high
icy hill. What is her speed at the bottom?
A
C
h
B
A) A 500kg rollercoaster starts from rest
from a height of 20m above ground at point
A. How fast will it be moving after the first
drop which is 5.0m above ground at point B?
Assume no friction.
B) Assuming there is friction, how much energy
is transferred to heat from A to C which is 12m
above ground if coaster has speed of 8.5m/s
at point C?
The hills of a rollercoaster must get
smaller than the hill that preceded it
true or false
Example
A block (0.80 kg) is
given an initial velocity
of vA=1.2m/s to the
right and collides with a
spring of force constant
k = 50.0 N/m.
Determine the compression of the
spring when the block is brought to rest
assuming no friction.
example
A spring is compressed 40cm by
a 0.50kg block. The spring
constant is 30N/m. The surface
of the ground is rough after the
equilibrium point of the spring
Determine how far the block will slide after it leaves
the spring if µk = 0.25?
How much thermal energy is generated due to
friction?
Question
A small child slides down four
frictionless sliding boards. Rank the
boards in terms of which will yield the
largest speed at the bottom?