Name
Period
Date
Energy: Worksheet 6
Work Done by a Variable Force
1. A 5.0 kg object moves in a straight line on a horizontal frictionless surface under the
influence of a force that varies with position as in the diagram below. How much
work is done by the force in moving the box


from the origin to x  8.0 m ?
F N 
10
5

x m
0
2
4
6
8
-5
-10
2. A 10 kg mass moves horizontally. Its acceleration as a function of position is shown

below. What is the net work performed on the mass as it is moved from x  0 m to

x  8.0 m .
20
 s

am
2
15
10
5
0
2
4
6

x m
8
 9.0 Nm 2
3. How much work is done on an object by a force given by F 
in moving an
2
x

object from 1.0 m  x  3.0 m ?
Energy: Worksheet 6
page 2


4. The force exerted on an object is F  Fo  x  1 . Find the work done in moving the
 xo 


object from x  0 to x  2 xo .
 
a. By plotting F  x  and finding the area under the curve.

F
Fo

x
xo
2 xo
 Fo
b. By evaluating the integral analytically.

5. What work is done by a force F   2 x kg 2 iˆ  3 N  ˆj where x is in meters that is
s 


exerted on a particle while it moves from a position of ri  2 miˆ  3 m ˆj to a position

of r f   4 miˆ  3 m ˆj ?