|
Work - Constant Force
Introduction
If a constant force is applied, Work is the magnitude of displacement
times the component of the force parallel to the displacement.
In the diagram above, W = Fd Cos
Be very careful in analysis of the force. If a different angle is
measured, it could be the sin instead of the cosine.
I Joule = 1 Newton . meter
In the diagram to the left, is
90o and the cosine of 90o is 0.
There is no work performed in this situation.
No force is applied in the direction parallel to the
displacement.
No work is performed if a person attempts to lift a dump truck.
Although a force is applied, there is no displacement.
 There is no
acceleration in the diagram to the left.
Fparallel = FwCos
W = Fd Cos
h = dCos thus
W = mgh
Observe that the work is only dependent on height in this situation and
not the angle.
If had been measured at
the bottom,
we would have used the sine instead of the cosine.
BE CAREFUL!!!
Table of Contents
Problems
| 1. |
Sam is pulling a 500. kg sled with a
kinetic coefficient of friction of 0.25 on a level floor at a constant
velocity. How much work is performed when the sled is pulled 40.0 m?
|
| 2. |
Paula is pulling with a force of 600. N at
an inclination of 30.0o on a rope attached to a sled. How
much work is performed when the sled is pulled 50.0 m on a level surface?
|
| 3. |
Andrew is pulling a 400. kg sled with a
kinetic coefficient of friction of 0.15 at a constant velocity up an
inclined plane with an inclination of 25.0o. If the
inclined plane is 60.0 m long, how much work does it take to move the sled
to the top of the incline? How much work is done if a 30.0 m incline
reaches the same height?
|
| 4. |
Jessica, mass of 55.0 kg, carries a 45.0 kg
package up three floors using a spiral staircase. The staircase has
an incline of 45.0o. If there is 3.00 m difference in
height between each floor, how much work does Jessica perform? |
Table of Contents
Answers
| 1. |
Sam is pulling a 500. kg sled with a
kinetic coefficient of friction of 0.25 on a level floor at a constant
velocity. How much work is performed when the sled is pulled 40.0 m?
|
|
Ffr is the force parallel to the displacement.
W = Ffr d =  FN
d = 0.25 x 500. kg x 9.80 m s -2 x 40.0 m = 1230 J
|
|
|
| 2. |
Paula is pulling with a force of 600. N at
an inclination of 30.0o on a rope attached to a sled. How
much work is performed when the sled is pulled 50.0 m on a level surface?
|
|
The Fparallel = FropeCos
30.0o
W = Fparalleld = FropeCos
30.0od = 600. N x Cos 30.0o x 50.0 m = 2.60 x 10
4 J
|
|
|
| 3. |
Andrew is pulling a 400. kg sled with a
kinetic coefficient of friction of 0.15 at a constant velocity up an
inclined plane with an inclination of 25.0o. If the
inclined plane is 60.0 m long, how much work does it take to move the sled
to the top of the incline? How much work is done if a 30.0 m incline
reaches the same height?
|
|
Fparallel to displacement = Fp
+ Ffr = Fw Sin 25.0o +
Fw Cos 25.0o
= 400. kg x 9.80 m s -2 x Sin 25.0o + 0.15 x 400. kg
x 9.80 m s -2 x Cos 25.0o
= 2190 N
Work = F parallel d = 2190 N x 60.0
m = 131,000 J
h = 60.0 m x Sin 25.0o = 25.4 m
If the same height of 25.4 m is obtained using
a 30.0 m incline
25.4 m
 = Sin
-1 ( ----------- ) = 57.9o
30.0 m
Fparallel to displacement = Fp
+ Ffr = Fw Sin 57.9o +
Fw Cos 57.9o
= 400. kg x 9.80 m s -2 x Sin 57.9o + 0.15 x 400. kg
x 9.80 m s -2 x Cos 57.9o
= 3630 N
Work = F parallel d = 3630 N x 30.0
m = 109,000 J
Observe that there is more friction and thus more work with a smaller
angle. If the surface is frictionless, the amount of work will not
change.
|
|
|
| 4. |
Jessica, mass of 55.0 kg, carries a 45.0 kg
package up three floors using a spiral staircase. The staircase has
an incline of 45.0o. If there is 3.00 m difference in
height between each floor, how much work does Jessica perform?
|
|
Since Jessica is carrying the package up the stairs instead of sliding it
up the stairs, only the height is important. Remember to include
Jessica's mass since it is also going up the stairs.
W = mgh = (55.0 kg + 45.0 kg) x 9.80 m s
-2 x 9.00 m = 8820 J
|
Table of Contents
|
