kinetic energy: more practice. elastic potential energy: learning goals the student will describe...
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Elastic Potential Energy:Learning GoalsThe student will describe the elastic potential energy of a
spring or similar object in qualitative and quantitative terms and will investigate the transformation of gravitational potential to elastic potential.
Hooke’s Law
The stretch or compression of an elastic device (e.g. a spring) is directly proportional to the applied force:
Hooke’s Law
The stretch or compression of an elastic device (e.g. a spring) is directly proportional to the applied force:
stre tch xF
kor F kx
x is the equ ilibrium position
xx
0
The spring constant
The constant k is called the spring constant or force constant. It has units of N/m
and is the slope of the line in a force-extension graph.
Example 1
A student stretches a spring 1.5 cm horizontally by applying a force of magnitude 0.18 N. Determine the force constant of the spring.
Example 1
A student stretches a spring 1.5 cm horizontally by applying a force of magnitude 0.18 N. Determine the force constant of the spring.
?
:
18.0
015.0
:
k
Unknown
NF
mx
Givens
Example 1
A student stretches a spring 1.5 cm horizontally by applying a force of magnitude 0.18 N. Determine the force constant of the spring.
?
:
18.0
015.0
:
k
Unknown
NF
mx
Givens
Example 1
A student stretches a spring 1.5 cm horizontally by applying a force of magnitude 0.18 N. Determine the force constant of the spring.
?
:
18.0
015.0
:
k
Unknown
NF
mx
Givens
Example 1
A student stretches a spring 1.5 cm horizontally by applying a force of magnitude 0.18 N. Determine the force constant of the spring.
?
:
18.0
015.0
:
k
Unknown
NF
mx
Givens
mN
m
NkSolve
x
FkkxFSelect
12015.0
18.0:
:
Elastic Potential Energy
The force stretching or compressing a spring is doing work on a spring, increasing its elastic potential energy. Note that this force is not constant but increases linearly from 0 to kx. The average force on the spring is ½kx.
Elastic Potential Energy
The force stretching or compressing a spring is doing work on a spring, increasing its elastic potential energy. Note that this force is not constant but increases linearly from 0 to kx. The average force on the spring is ½kx.
W F d F x kx x kx
Th is kx is the elastic po ten tia l energy E
x
e
12
12
2
12
2 , .
Example 2
An apple of mass 0.10 kg is suspended from a vertical spring with spring constant 9.6 N/m. How much elastic potential energy is stored in the spring if the apple stretches the spring 20.4 cm?
?
:
204.0
6.9
:
e
mN
E
Unknown
mx
k
Givens
Example 2
An apple of mass 0.10 kg is suspended from a vertical spring with spring constant 9.6 N/m. How much elastic potential energy is stored in the spring if the apple stretches the spring 20.4 cm?
?
:
204.0
6.9
:
e
mN
E
Unknown
mx
k
Givens
Example 2
An apple of mass 0.10 kg is suspended from a vertical spring with spring constant 9.6 N/m. How much elastic potential energy is stored in the spring if the apple stretches the spring 20.4 cm?
?
:
204.0
6.9
:
e
mN
E
Unknown
mx
k
Givens
JE
mESolve
kxESelect
e
mN
e
e
20.0
204.06.9:
:2
21
221
Example 2 Follow-Up
How much gravitational potential energy did the apple lose?
?
:
204.0
8.9
10.0
:
2
g
sm
E
Unknown
mh
g
kgm
Givens
Example 2 Follow-Up
How much gravitational potential energy did the apple lose?
?
:
204.0
8.9
10.0
:
2
g
sm
E
Unknown
mh
g
kgm
Givens
Example 2 Follow-Up
How much gravitational potential energy did the apple lose?
?
:
204.0
8.9
10.0
:
2
g
sm
E
Unknown
mh
g
kgm
Givens
JE
mkgESolve
hmgESelect
g
sm
g
g
20.0
204.08.910.0:
:
2
The ideal spring
An ideal spring is one that obeys Hooke’s Law – within compression/stretching limits. Beyond those limits the spring may deform.