-Kinetic Energy-Work-Kinetic Energy

Theorem-Energy Losses due to

Friction-Power

AP Physics CMrs. Coyle

Energy and Work

• Energy is the ability to do work.

• Work is the energy transferred to or from a system by a force that acts on it.

Video Link: Kinetic Sculpture

• http://www.youtube.com/watch?v=WcR7U2tuNoY&feature=related

Energy• Symbol: E

• Scalar

• Units:– J, Joule– cal, calorie– kcal, kilocalorie (Cal)– erg– eV– pound -foot

Mechanical Energy

• Potential Energy• Kinetic Energy

Kinetic Energy, K= 1 mv2

2Energy of Motion

Question

• Can Kinetic Energy be Negative?

Derivation of K

2 21 1

2 2

f f

i i

f

i

x x

x x

v

v

f i

W F dx ma dx

W mvdv

W mv mv

Work-Energy Theorem

W=KE

W=KEf-KEi

“In the case in which work is done on a system and the only change in the system is in its speed, the work done by the net force equals the change in kinetic energy of the system.”

• The Work-Kinetic Energy Theorem can be applied to nonisolated systems

• A nonisolated system is one that is influenced by its environment (external forces act on the system)

Potential Energy, U:stored energy

• Examples:–elastic potential energy –

stored in a spring–gravitational potential energy–electrical potential energy

• Compared to a Reference Point (base level)

Conservation of Energy

• Energy can neither be created nor destroyed. It can only change from form to form.

• In a closed system energy is conserved

• Conservation of Mechanical Energy

U1+ K1 = U2 + K2

Energy can be transferred to and from the System by:• Work • Mechanical Waves• Heat transfer• Matter Transfer (across the

boundary of the system carrying energy with it)

• Electrical Current Transmission• Electromagnetic Radiation

Change in Energy of the system equals total energy

transferred

• Esystem =

– T is the energy transferred across the system boundary

– Twork = W Theat = Q

• The Work-Kinetic Energy theorem is a special case of Conservation of Energy

What happens when kinetic friction is present?

When friction is present, the work done by the frictional force

W=f·r is transferred to heat energy.

Internal Energy

• The energy associated with an object’s temperature is called its internal energy, Eint

Power

• Energy transfer per unit time

• Average power :

WP

t

Instantaneous Power

dW drP F F v

dt dt

dEP

dt

Units of Power

• SI unit of power: Watt 1 watt = 1 J/s = 1 kg . m2 / s2

• US Customary unit: horsepower– 1 hp = 746 W

kilo Watt · hour, kWh

• kWh is a units of work or energy

• 1 kWh =(1000 W)(3600 s)= =3.6 x106 J

Example 1 (#26)

A 3kg object has a velocity (6i-2j)m/s. a)What is the kinetic energy at this

time?

b)Find the total work done on the object if its velocity changes to (8i+4j) m/s .(Note: v2 = v·v)

Ans: a)60J, b)60J

Pile Driver

Example 2 (#27)• A 2,100kg pile driver is used to drive

a steel I-beam into the ground. The pile driver falls 5m before coming into contact with the top of the beam and it drives the beam 12cm farther into the ground before coming to rest. Using energy considerations, calculate the average force the beam exerts on the pile driver while the pile driver is brought to rest.Ans: 8.78 x 105 upwards

Figure for Example 3

Example 3 (#32)A 2kg block is attached to a spring of a

force constant 500N/m on a horizontal table. The block is pulled 5.00cm to the right of equilibrium and released from rest. Find the speed of the block as it passes through equilibrium if a)the horizontal surface is frictionless and b) the coefficient of friction between block and surface is 0.350.

Ans:a)0.791m/s, b) 0.531m/s

Example 4 (#40)A 650kg elevator starts from rest. It

moves upward for 3s with a constant acceleration until it reaches its cruising speed of 1.75 m/s.

a)What is the average power of the elevator motor during this period?

b)How does this power compare with the motor power when the elevator moves at its cruising speed?

Ans: a)5.91x103 W= 7.92hp b) 1.11x104 W= 14.9hp