energy energy is conserved ∆ke = w

Part 2, A: THERMODYNAMICS

WORK

156

Definition (Young): Energy is the capacityto do work.

Part 2, A: THERMODYNAMICS

WORK

1656

Definition (Young): Energy is the capacityto do work.

W = Fd

W is the work done (Joules)F is the applied force (Newtons)d is the distance moved as a

result of the applied force (meters)

Part 2, A: THERMODYNAMICS

KINETIC ENERGY

Quantity of Motion

KE = ½ m v 2

109

Part 2, A: THERMODYNAMICS

KINETIC ENERGY

An object of mass 10 kg has a speed of10 m/sec. What is the kinetic energy?

11

Part 2, A: THERMODYNAMICS

KINETIC ENERGY

An object of mass 10 kg has a speed of10 m/sec. What is the kinetic energy?

KE = ½ (10 kg) (10 m/sec) (10 m/sec)500 Joules

12

Part 2, A: THERMODYNAMICS

KINETIC ENERGY

An object of mass 10 kg has a speed of10 m/sec. By how much will the kineticenergy increase if the speed is doubled?

132

Part 2, A: THERMODYNAMICS

KINETIC ENERGY

An object of mass 10 kg has a speed of10 m/sec. By how much will the kineticenergy increase if the speed is doubled?

KE = ½ m (2v) = 2 (½ m v ) = 4 (½ m v )

The kinetic energy is 4 times greater.

2 2 2 2

14

Energy

Energy is Conserved

∆KE = W

Energy

Energy is Conserved

∆KE = W

Work-Energy Theorem

15

Motion – Newton’s Laws

Special Case: Friction

Example: A force is applied to an object, causing the object to slide on a table (with friction) at a constant velocity. The speed is 2 m/sec. If the force is removed, how far will the block slide before it stops? The coefficient of kinetic friction is 0.8 and g = 10 m/s2.

16

Motion – Newton’s Laws

Special Case: Friction

Example: A force is applied to an object, causing the object to slide on a table (with friction) at a constant velocity. The speed is 2 m/sec. If the force is removed, how far will the block slide before it stops? The coefficient of kinetic friction is 0.8 and g = 10 m/s2.

NOTE: We already solved this problem in our discussions about Newton’s second Law.

John E. Erdei, SCI190 Lecture Slides – Newton’s Second Law, Slide 18, University of Dayton (Unpublished) .

17

Motion – Newton’s Laws

Special Case: Friction

Example: A force is applied to an object, causing the object to slide on a table (with friction) at a constant velocity. The speed is 2 m/sec. If the force is removed, how far will the block slide before it stops? The coefficient of kinetic friction is 0.8 and g = 10 m/s2.

ΔKE = W = F d = µk m g d

½ m v2 = µk m g d

v2 = 2 µk g d

d = v2 / ( 2 µk g) = 0.25 m

18

Motion – Newton’s Laws

Special Case: Friction

Example: A force is applied to an object, causing the object to slide on a table (with friction) at a constant velocity. The speed is 2 m/sec. If the force is removed, how far will the block slide before it stops? The coefficient of kinetic friction is 0.8 and g = 10 m/s2.

Note: This is the same result that we got using the constant acceleration equations

d = ½ a t2

Δv = a t

Energy

Potential Energy

Potential energy comes in a variety of forms.

20

Motion – Newton’s Laws

gsurface = G Mearth / R2 earth

Earth

MEarth

REarth m

r

21

Motion – Newton’s Laws

g = G Mearth / r2

Earth

MEarth

REarth m

r

Energy

Potential Energy

Gravitational Potential Energy of a mass m at a distance r from the Center of the

Earth

PEGRAV = mgr

= G Mearth m / r

Energy

Potential Energy

More commonly written

Gravitational Potential Energy of a mass m at a distance h from the Surface of the

Earth

PEGRAV = mg ( REarth + h)

Energy

Potential Energy

Change in Gravitational Potential Energy of a mass m at a distance h from the Surface of the Earth

h << Rearth

∆PEGRAV = mgh

Earth

h

Energy

Potential Energy

Gravitational Potential Energy

often written as

PEGRAV = mgh

Where h is measured from the surface of the earth

Part 2, A: THERMODYNAMICS

Power

36

Power is defined to be the rate at whichenergy is used.

P = Energy/Time

Part 2, A: THERMODYNAMICS

Power

37

P = Energy/Time

Energy measured in JoulesTime measured in SecondsPower measured in Joules/sec = Watt

Energy

Potential Energy

Football coach Jones becomes angry with a player, and in order to get the players attention, coach Jones makes the player go from playing field level up to the top row of seats in the stadium. Will the player do more work if he walks to the top row or runs to the top row? Assume the player starts from rest and stops when he reaches the top.

Energy

Potential Energy

Football coach Jones becomes angry with a player, and in order to get the players attention, coach Jones makes the player go from playing field level up to the top row of seats in the statium. Will the player do more work if he walks to the top row or runs to the top row? Assume the player starts from rest and stops when he reaches the top.

There is actually not enough information to determine the work from first principles. However, since the change in kinetic energy is 0, the work done by the player must be used to increase his potential energy (Conservation of Energy). The amount of potential energy (PE = mgh) is the same, independent of running or walking, and therefore the amount of work done by the player is the same if he runs or walks!

Energy

Potential Energy

Football coach Jones becomes angry with a player, and in order to get the players attention, coach Jones makes the player go from playing field level up to the top row of seats in the stadium. Will the player do more work if he walks to the top row or runs to the top row? Assume the player starts from rest and stops when he reaches the top.

If this is true, why do they make you run as punishment, ie, why not punish the player by making him walk at a leisurely pace to the top of the stadium????

Energy

Potential Energy

Football coach Jones becomes angry with a player, and in order to get the players attention, coach Jones makes the player go from playing field level up to the top row of seats in the stadium. Will the player do more work if he walks to the top row or runs to the top row? Assume the player starts from rest and stops when he reaches the top.

The punishment is related to Power, and not directly to work. Since

P = W / t

Walking will result in the work to be expended over a longer time period, therefore requiring less power. Running expends the work over a shorter time period, therefore requiring more power.