Work
Work
• Work is done when a force causes an object to move.
• Power is the rate at which work is done.
Recognize the component of a
force that does the work.
• W = Fd
W – work (Joules)
F – magnitude of the force parallel to the direction of
motion (Newtons)
d – distance (m)
Work is a scalar quantity.
• Therefore, work is only done if the object moves.
• Holding a 50 N bag of groceries is not doing
work even though you get tired. A force is
exerted but the distance (displacement) is zero.
Cont’d
• Carrying the same 50 N bag of groceries a
distance of 10 m is not doing work either
because there is no component of the weight
vector that is parallel to the direction of motion.
There is some work being done (not the carrying
of the groceries) but it is the work being done to
overcome friction between your shoes and the
floor.
Cont’d
• When an object is
being pulled across the
floor by a rope held at
an angle, the
component of the
force that is parallel to
the direction of motion
is Fcos.
F
θ
Fcosθ
Cont’d
• Therefore, in this case,
W=Fdcos.
F
θ
Fcosθ
Positive vs Negative work
• 1 of 2 ways to look at it
• 1) If the force is opposite the direction of motion, it is negative
• Gravity doing work as an elevator moves upward
• 2) The angle between the force and movement will be 180°,
and cos(180°) = -1
• Same gravity & elevator example, but the Fdcos will come out to a negative answer
Example
• Steve lifts a 50 N box from the floor to a shelf in his closet 1.6 m high.
(assume a constant velocity)
• How much work does Steve do on the box?
• How much work does gravity do on the box?
Another
• An 80 kg barbell is lifted 1 m. How much work does the weightlifter
do on the barbell? (again, assume a constant velocity)
Sample Problem
•
A man pulls a 50-kg stone a distance of 4 m at a constant velocity
along a rough road by applying a 250-N force along a rope that
makes an angle of 60 with the horizontal. He then stoops down
and lifts the stone vertically to a height of 1 m and carries it at a
constant velocity a distance of 5 m. How much work does he do to
the stone?
•
How much work does he do pulling the stone?
•
How much work does he do lifting the stone?
•
How much work does he do carrying the stone?
Cont’d
• The man is doing work as he pulls the stone along the ground and
again when he lifts the stone but no work is done when he is just
carrying the stone.
• To find the total work done in this problem you need to find the work
done in each part then add them together.