08 u8 ws 4-keyrevised

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Modeling Instruction - AMTA 2013 1 U8 Energy - ws 4 v3.1

Name

Date Pd

Energy Storage and Transfer Model Worksheet 4:

Quantitative Energy Calculations & Energy ConservationBe careful with units and unit conversions!

1. How much kinetic energy does a 2000 kg SUV traveling 70 mph have? (1 mile = 1600 meters)

70mileshr

1600m

1mi

1hr

3600s= 31.1m

s

Ek =

12mv

2=

12 2000kg( ) 31.1ms( )

2

= 967,000Jor 967kJ

2. Consider your 3 kg physics binder resting on the table in the

classroom. Determine the gravitational energy of the earth-book system if the zero reference level is chosen to be:

Eg = mgh

a) the tableBecause h = 0, Eg= 0

b) the floor, 0.68 meters below the book

Eg = 3.0kg( ) 10 Nkg( ) 0.68m( ) = 20.4J

c) the ceiling, 2.5 meters above the book

3.0 10 2.50 75Ng kgE kg m J Eg is (-) because the object is below the zero reference level.

3. A bungee cord stretches 25 meters and has a spring constant of 140 N/m. How much energy is

stored in the bungee?

221 1

2 2 140 25 43,800N

el mE k x m J

4. How fast does a 50 gram arrow need to travel to have 40 joules of kinetic energy?

Ek=

12mv2 v=

2 40J( )0.050kg

= 40ms

5. How much energy is stored when a railroad car spring is compressed 10 cm?

(The spring requires about 10,000 N to be compressed 3.0 cm.)

10,000

.030 333,000

N N

m m

k

Eel =

12k x

2=

12 333,000

N

m( )0.10m( )2

=1670J


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6. A cart moving at 5.0 m/s collides with a spring. At the instant the cart is motionless, what is the

largest amount that the spring could be compressed? Assume no friction.

a. Define the system with the energy flow diagram, then complete the energy bar graphsqualitatively.

b. Quantitative Energy Conservation Equation:

Ek= E

el

12mv

2=

12k x

2

c. Determine the maximum compression of the spring.

1

2mv2

=

1

2k x2

x=mv2

k=

8.0kg 25 m2

s2( )50 N

m

= 2.0m

7. A rock is shot straight up into the air with a slingshot that had been stretched 0.30 m.

Assume no air resistance.

a. Qualitatively complete the energy flow diagram and the energy bar graphs.

b. Quantitative Energy Conservation Equation:

Eel= E

g

12k x2 =mgh

c. Determine the greatest height the rock could reach.

12k x2 =mg h h =

k x2

2mg=

100 Nm

0.30m( )2

2 0.50kg( )10 Nkg( )=

9.0Nm

10N=0.90m

Position A

Energ

y

(J)

0

Ek Eg Eel

Position B

Energ

y

(J)

0

Ek Eg Eel EthSystem/Flow

0

A B

k = 100 N/m

x = 0.30 m

m = 500 gv = 0

Position A

Energy(J)

0

Ek Eg Eel

Position B

Energy(J)

0


A B

m = 8.0 kg

v = 5.0 m/s

k = 50 N/mv = 0

cart

spring

rock

slingshot


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8. Determine final velocity of the rollercoaster, assuming a 10% loss to friction.

Eg=E

k+ E

th E

g

1

10E

g=E

k

0.90mgh= 12mv2 2 0.90gh( )= v2

v= 1.8 10Nkg( )5.0m= 90 m

2

s2 =9.5 m

s

Position A

Energ

y

(J)

0

Ek Eg Eel

Position B

Energy

(J)

0


A

B

m = 40 kgv = 0

5.0 m

0

coaster

Earth

track

08 u8 ws 4-keyrevised

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