In this worksheet, we will practice using integration to find the work done by a variable force.

Q1:

Complete the following: If a force given by acts in the direction of the positive , then the work done by the force in moving a particle from to , where equals .

A

B

C

D

E

Q2:

True or False: If an object moves along a straight line by a varying force
, then the work done to move the
object from to
is given by .

AFalse

BTrue

Q3:

The figure shows the magnitude of a force acting on a body as it moves a distance
. Given that the force is measured in newtons and the distance is
measured in meters, determine the work done in joules by the force to move the body from
to .

Q4:

A body moves along the -axis under the action of a force,
. Given that ,
where m is the displacement from the origin,
determine the work done on the body by when the body moves from to .

Q5:

A variable force , measured in newtons, is acting on a body, where . Find the work done by this force in the interval from to .

Q6:

A body moves along the under the action of a force . Given that
,
where is
the displacement from
the origin,
determine the work done on the body by when the body moves from
to .

A J

B J

C J

D J

E3 J

Q7:

A particle moves in a straight line under the action of the force ,
where and is measured in
meters.
Calculate the work done by the force
when the particle moves from
to .

A2 J

B J

C J

D J

E J

Q8:

A block moves in a straight line under the action of a
force ,
where meters is the displacement of the body
from its initial position. The work done by the force in moving the block from
to is 34 J.
Determine the work done by in moving the block from to .

Q9:

A body moves along the under the action of a force .
Given that , where m is the displacement from the origin,
determine the work done on the body by when the body moves from to .

A J

B28 J

C J

D J

E J

Q10:

A body moves along the under the action of a force .
Given that ,
where m
is the displacement from
the origin,
determine the work done on the body by when the body moves from
to
.

Approximate your answer to the nearest decimal place.

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