Physics

Work, Energy, and Machines

• Fd = work = change in energy

• PE = potential energy = mgh

• KE = kinetic energy = 1/2 mv^2

• Energy is conserved! (always)

• PE+KE stays the same

• Power = work / time, or change in energy / time

• mechanical advantage = F(out) / F(in)

• Proportional changes in energy when you change the height, mass, velocity.

• Find velocity, given KE and mass.

Agenda

•Work/Conservation of Energy

•Kinetic and potential energy

•Formulas

•Conservation

California State Standards

Physics: Conservation of Energy and Momentum

2. The laws of conservation of energy and momentum provide a way to predict and describe the movement of objects. As a basis for understanding this concept:

California State Standards

a. Students know how to calculate kinetic energy by using the formula E = (1/2)mv2

b. Students know how to calculate changes in gravitational potential energy near Earth by using the formula (change in potential energy) = mgh (h is the change in the elevation).

California State Standards

c. Students know how to solve problems involving conservation of energy in simple systems, such as falling objects.

California State Standards

Physics: Heat & Thermodynamics

3. Energy cannot be created or destroyed, although in many processes energy is transferred to the environment as heat. As a basis for understanding this concept:

Energy and Work

• Work = force x distance = change in energy

• Units are “Joules (J)” = Newton · meters Newton · meter = kg · m2/s2

• Energy is not a vector (no direction)

Power

• Power = work / time or energy / time

• Joules/second or Watts

Kinetic Energy

• KE = 1/2 mv2

• Double the speed = 4 times the KE

• Triple the speed = ? times the KE

• Quadruple the speed = ? times the KE

Gravitational Potential Energy

• “Energy of position”

• PE = mgh (gravitational potential energy)

• m = mass

• g = acceleration of gravity (10 m/s2)

• h = height

• Twice the height = twice the PE

• Triple the height = ? times the PE

• Quadruple the height = ? times the PE

Potential Energy (Stored Energy) (Gravitational)

Potential Energy

Potential Energy

• Only depends on height

• Does not depend on the path to get there

Conservation of Energy

• If no friction, etc.:

• PE + KE = constant

Conservation of Energy

Path Doesn’t Matter

Only the change in height affects the kinetic energy Potential energy + Kinetic energy stays the same

Path Doesn’t Matter

Compute Potential Energy

• What is the PE of a 100 kg man on top of a 10 meter diving platform?

• PE = mgh

• PE = 100 kg x 10 m/s2 x 10 m = 10,000 J

• What is the PE of the man when he has fallen half the distance?

• 5,000 J

Compute Kinetic Energy

• What is the KE and velocity of the man when he is half way down?

• KE = 1/2 mv2

• KE + PE = 10,000 J

• PE = 5000 J, so

• KE = (10,000 – 5000) J = 5000 J

• KE = 5000 N·m = 1/2 mv2

• v2 = (5000 x 2) / 100 kg = 100 m2/s2

• v = 10 m/s

Sample Problems:

• How far does an object fall in “t” seconds?

• 1s: 0.5(10m/s/s)1^2= 5 m

• 2s: 0.5(10m/s/s)2^2= 20 m

• 5s: 0.5(10m/s/s)5^2= 125 m

• 6s: 0.5(10m/s/s)6^2= 180 m

Cont.

• So, if something falls from 180 m, how high is it after “t” seconds?

• 1s: 180m – 5m = 175m

• 2s: 180m – 20m = 160m

• 5s: 180m – 125m = 55 m

• 6s: 180m – 180m = 0 m

Cont.

• How much potential energy will those objects have after “t” seconds (assume 2kg mass)?

• 1s: 2kg x 10m/s/s x 175m = 3500 J

• 2s: 2kg x 10m/s/s x 160m = 3200 J

• 5s: 2kg x 10m/s/s x 55m = 1100 J

• 6s: 2kg x 10m/s/s x 0m = 0 J

What’s the velocity after “t” seconds?

• 1s: 10m/s/s x 1s = 10m/s

• 2s: 10m/s/s x 2s = 20 m/s

• 5s: 10m/s/s x 5s = 50 m/s

• 6s: 10m/s/s x 6s = 60 m/s

What is the kinetic energy after “t” seconds? (Still 2kg)

• 1s: 0.5 x 2kg x 10m/s x 10 m/s =100 J

• 2s: 0.5 x 2 kg x 20m/s x 20 m/s = 400 J

• 5s: 0.5 x 2 kg x 50m/s x 50 m/s = 2500 J

• 6s: 0.5 x 2 kg x 60m/s x 60 m/s = 3600 J

Machines

Machines

Machines

• Can change the size of the force

• Increase or decrease

• By changing the distance

• Can also change the direction of the force

• Force is a vector (direction matters)

Fd = Work = Change in Energy

This picture assumes no friction

Machines Can Multiply Force and Change Direction

Give me a lever long enough and a fulcrum on which to place it, and I shall move the world.

-Archimedes

Machines Can Multiply Force

Three Types of Levers

Three Types of Levers

The Law of See-Saws

In order to balance: F1 x D1 = F2 x D2

(your weight x your distance = their weight x their distance

F1

d1

F2

d2

Fulcrum

The Law of See-Saws