Elastic Potential Energy:More Practice

Elastic Potential Energy:More Practice

Conservation of Mechanical Energy: Learning GoalThe student will

investigate a simple energy transformation, explain the energy input and output, and calculate the efficiency. (E2.5)

Conservation of Mechanical Energy

SPH4C

Starting with Gravitational Potential

An object of mass 3.0 kg is suspended at a height of 12 m above the ground. Calculate its gravitational potential energy.

Starting with Gravitational Potential

An object of mass 3.0 kg is suspended at a height of 12 m above the ground. Calculate its gravitational potential energy.

?

:

12

8.9

0.3

:

2

g

sm

E

Unknown

mh

g

kgm

Givens

Starting with Gravitational Potential

An object of mass 3.0 kg is suspended at a height of 12 m above the ground. Calculate its gravitational potential energy.

?

:

12

8.9

0.3

:

2

g

sm

E

Unknown

mh

g

kgm

Givens

Starting with Gravitational Potential

An object of mass 3.0 kg is suspended at a height of 12 m above the ground. Calculate its gravitational potential energy.

?

:

12

8.9

0.3

:

2

g

sm

E

Unknown

mh

g

kgm

Givens

JE

mkgESolve

mghESelect

g

sm

g

g

350

)12)(8.9)(0.3(:

:

2

Starting with Gravitational Potential

An object of mass 3.0 kg is suspended at a height of 12 m above the ground. Calculate its kinetic energy.

Starting with Gravitational Potential

An object of mass 3.0 kg is suspended at a height of 12 m above the ground. Calculate its kinetic energy.

v = 0 so Ek = 0

The Object is Released

The object is released and hits the ground at a speed of 15.3 m/s. What is its kinetic energy when it hits the ground?

The Object is Released

The object is released and hits the ground at a speed of 15.3 m/s. What is its kinetic energy when it hits the ground?

?

:

3.15

0.3

:

k

sm

E

Unknown

v

kgm

Givens

The Object is Released

The object is released and hits the ground at a speed of 15.3 m/s. What is its kinetic energy when it hits the ground?

?

:

3.15

0.3

:

k

sm

E

Unknown

v

kgm

Givens

The Object is Released

The object is released and hits the ground at a speed of 15.3 m/s. What is its kinetic energy when it hits the ground?

?

:

3.15

0.3

:

k

sm

E

Unknown

v

kgm

Givens

JE

kgESolve

mvESelect

k

sm

k

k

350

)3.15)(0.3(:

:2

21

221

And Now We Have Kinetic EnergyCalculate the gravitational potential energy of the

object when it hits the ground.

And Now We Have Kinetic EnergyCalculate the gravitational potential energy of the

object when it hits the ground.

h = 0 so Eg = 0

And Now We Have Kinetic EnergyOur energy has been entirely transformed from

gravitational potential energy to kinetic energy.

And Now We Have Kinetic EnergyOur energy has been entirely transformed from

gravitational potential energy to kinetic energy.

But the total mechanical energy of the object (potential energy + kinetic energy) has not changed.

Conservational of Mechanical Energy

In general, if no work is being done on an object by an outside force, the total mechanical energy of the system will remain constant:

2211 kgkg EEEE

In Real Life

Note that in real life, energy is never transformed with 100% efficiency: a ball dropped from a given height will never bounce back up to that same height.

Some energy is always “lost” as heat energy or sound energy because of friction. However, just as we often neglect friction, we will often neglect these losses.

Efficiency

Efficiency is the ratio of useful energy or work output to the total energy or work input:

Efficiency

Efficiency is the ratio of useful energy or work output to the total energy or work input (written as a percent):

%100energyinputtotal

energyoutputusefulEfficiency

Efficiency Example 1

A model rocket engine contains explosives storing 3500 J of chemical potential energy. Calculate how efficiently the rocket transforms stored chemical energy into gravitational potential energy if the 0.50 kg rocket is propelled to a height of 1.0 x 102 m.

Efficiency Example 1

A model rocket engine contains explosives storing 3500 J of chemical potential energy. Calculate how efficiently the rocket transforms stored chemical energy into gravitational potential energy if the 0.50 kg rocket is propelled to a height of 1.0 x 102 m.

Efficiency Example 1

A model rocket engine contains explosives storing 3500 J of chemical potential energy. Calculate how efficiently the rocket transforms stored chemical energy into gravitational potential energy if the 0.50 kg rocket is propelled to a height of 1.0 x 102 m.

JmkgmghEE

JE

sm

goutput

input

490100.18.950.0

35002

2

Efficiency Example 1

A model rocket engine contains explosives storing 3500 J of chemical potential energy. Calculate how efficiently the rocket transforms stored chemical energy into gravitational potential energy if the 0.50 kg rocket is propelled to a height of 1.0 x 102 m.

JmkgmghEE

JE

sm

goutput

input

490100.18.950.0

35002

2

Efficiency Example 1

A model rocket engine contains explosives storing 3500 J of chemical potential energy. Calculate how efficiently the rocket transforms stored chemical energy into gravitational potential energy if the 0.50 kg rocket is propelled to a height of 1.0 x 102 m.

JmkgmghEE

JE

sm

goutput

input

490100.18.950.0

35002

2

%1414.03500

490or

J

J

E

EEfficiency

input

output

Efficiency, alternately

Efficiency is also the ratio of useful power output to the power input:

in

out

tEt

E

in

out

P

P

E

EEfficiency

in

out

Efficiency Example 2

A 120-W motor accelerates a 5.0-kg mass from rest to a speed of 4.0 m/s in 2.0 s. Calculate the motor’s efficiency.

Efficiency Example 2

A 120-W motor accelerates a 5.0-kg mass from rest to a speed of 4.0 m/s in 2.0 s. Calculate the motor’s efficiency.

Efficiency Example 2

A 120-W motor accelerates a 5.0-kg mass from rest to a speed of 4.0 m/s in 2.0 s. Calculate the motor’s efficiency.

W

s

kg

t

mv

t

EP

WP

sm

outputoutput

input

200.2

0.40.5

120

212

21

Efficiency Example 2

A 120-W motor accelerates a 5.0-kg mass from rest to a speed of 4.0 m/s in 2.0 s. Calculate the motor’s efficiency.

W

s

kg

t

mv

t

EP

WP

sm

outputoutput

input

200.2

0.40.5

120

212

21

Efficiency Example 2

A 120-W motor accelerates a 5.0-kg mass from rest to a speed of 4.0 m/s in 2.0 s. Calculate the motor’s efficiency.

W

s

kg

t

mv

t

EP

WP

sm

outputoutput

input

200.2

0.40.5

120

212

21

%1717.0120

20or

W

W

P

PEfficiency

input

output

More Practice

Conservation of Energy Lab Activity

For Wednesday: Roller Coaster Construction!