6.4 Work by SGLee - HSKim - JHLee
1. Find the work done in pushing a car a distance of 10
while exerting a constant force of 
.
Since 
, 
. (in Joules)
Calculus-Sec-6-4-Solution
6.4 Work by SGLee - HSKim - JHLee
1. Find the work done in pushing a car a distance of 10 while exerting a constant force of .
Since , . (in Joules)
2. How much work is done by a weightlifter in raising a 
barbell from the floor to a height of 
meter?
Since 
, 
. (in Newtons)
So 
. (in Joules)
3. A particle is moved along the 
-axis by a force that measures 
pounds at a point 
feet from the origin.
Find the work done in moving the particle from the origin to a distance of 
.
http://matrix.skku.ac.kr/cal-lab/cal-6-4-3.html
. Use a change of variable 
, so 
. Then
. (
)
4. Shown is the graph of a force function (in Newtons) that increases to its maximum value and then remains constant.
How much work is done by the force in moving an object a distance of 
?
. (in Joules)
5. A force of 
is required to hold a spring stretched 
beyond its natural length.
How much work is done in stretching it from its natural length to 
beyond its natural length?
Since 
and 
, 
.
By Hooke's Law, 
.
So 
.
6. A spring has a natural length of 
. If a 
force is required to keep it stretched to a length of 
,
how much work is required to stretch it from 
to 
?
By Hooke's Law, 
, so 
.
. (in Joules)
7. Suppose that 
of work is needed to stretch a spring from its natural length of 
to a length 
,
how much work is needed to stretch it from 
to 
.
. That is 
.
Hence 
. (in Joules)
8-14. Find the work done.
8. A heavy rope, 
long, weighs 
and hangs over the edge of a building 
high.
How much work is done in pulling the rope to the top of the building?
. (in Joules)
9. A chain lying on the ground is 
long and its mass is 
.
How much work is required to raise one end of the chain to a height of 
?
, 
.
So, 
. (in Joules)
10. A cable that weight 
is used to lift 
of coal up a mine shaft 
deep.
Find the work done.
Since the cable weight is 
, the length of cable is 
.
So 
. (in Joules)
11. A bucket that weighs 
and a rope of negligible weight are used to draw water from a well that is 
deep.
The bucket is filled with 
of water and is pulled up at a rate of 
, but water leaks out of a hole in the bucket at a rate of 
.
Find the work done in pulling the bucket to the top of the well.
Since 
,
. (in Joules)
12. A 
chain weighs 
and hangs from a ceiling.
Find the work done in lifting the lower end of the chain to the ceiling so that it is level with the upper end.
, 
.
So 
. (in Joules)
13. An aquarium 
long, 
side and 
deep is full of water.
Find the work needed to pump half of the water out of the aquarium.
. (in Joules)
14. A circular swimming pool has a diameter of 
, the sides are 
high and the depth of the water is 
.
How much work is required to pump all of the water out over the side?
. (in Joules)
15. Newton's Law of Gravitation states that two bodies with masses 
and 
attract each other with a force 
where 
is the distance between the bodies and 
is the gravitational constant.
If one of the bodies is fixed, find the work needed to move the other from 
to 
.
(in Joules)
16. Use Newton's Law of Gravitation to compute the work required to launch a 
satellite vertically to center.
Take the radius of Earth to be 
and 
.
Use the result of problem 15, then 
. (in Joules)
