Part II: The Answers
452
Answers
701–800
720.
1.51 J
Begin by using the equation F(x) = kx to find the value of the spring constant. Make
sure you convert the centimeters to meters so you can use the units newton-meters,
or joules.
8
9
100
800
9
N
m
N m
= ( )
⋅ =
k
k
Now compute the work, again making sure to convert the lengths into meters.
Because you’re stretching the spring from 12 centimeters beyond its natural length
to 22 centimeters beyond its natural length, the limits of integration are from
12
100 to
22
100 ; therefore, the integral to compute the work is
W
x dx
x
=
=
=
−
(
)
∫
800
9
800
18
400
9
0 22
012
12 100
22 100
2
0 12
0 22
2
2
.
.
( . ) ( . )
= = 1 51
. J
721.
6 3 1
π
−
(
) J
Use an integral to find the work:
W
x dx
x
=
( )
= −
( )

 

 
= −
( ) − ( )

∫ 2
6
2 6
6
12
3
6
1
2
1
2
sin
cos
cos
cos
π
π
π
π
π
π
 




= −
−






=
−
(
)
12 1
2
3
2
6 3 1
π
π
J
722.
25.2 J
Begin by finding the spring constant, k, using the information about the initial
work required to stretch the spring 10 centimeters, or 0.10 meters, from its
natural length: