Kinetic Energy: More Practice

Kinetic Energy: More Practice

Kinetic Energy: More Practice

Kinetic Energy: More Practice

Kinetic Energy: More Practice

Kinetic Energy: More Practice

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.

Elastic Potential Energy

4C Physics

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?

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.

The ideal spring

An ideal spring is one that obeys Hooke’s Law – within compression/stretching limits. Beyond those limits the spring may deform.

Be gentle with my springs!