Unit 4, Chapter 10

CPO ScienceFoundations of Physics

Chapter 9

Unit 4: Energy and Momentum

10.1 Machines and Mechanical Advantage

10.2 Work

10.3 Energy and Conservation of Energy

Chapter 10 Work and Energy

Chapter 10 Objectives

1. Calculate the mechanical advantage for a lever or rope and pulleys.

2. Calculate the work done in joules for situations involving force and distance.

3. Give examples of energy and transformation of energy from one form to another.

4. Calculate potential and kinetic energy.

5. Apply the law of energy conservation to systems involving potential and kinetic energy.

10.1 Machines and Mechanical Advantage

Key Question:How do simple

machines work?

10.1 Machines

In physics the term “simple machine” means a machine that uses only the forces directly applied and accomplishes its task with a single motion.

10.1 Machines The best way to analyze what a machine

does is to think about the machine in terms of input and output.

10.1 Mechanical Advantage Mechanical advantage is the

ratio of output force to input force.

For a typical automotive jack the mechanical advantage is 30 or more.

A force of 100 newtons (22.5 pounds) applied to the input arm of the jack produces an output force of 3,000 newtons (675 pounds)— enough to lift one corner of an automobile.

10.1 Mechanical Advantage

Output force (N)

Input force (N)

Mechanicaladvantage

𝑴𝑨=𝑭𝒐

𝑭 𝒊

10.1 Mechanical Advantage of a Lever

Length of input arm (m)

Length of output arm(m)

Mechanicaladvantage

𝑴𝑨𝒍𝒆𝒗𝒆𝒓=𝑳𝒊

𝑳𝒐

10.1 Calculate position Where should the fulcrum of a

lever be placed so one person weighing 700 N can lift the edge of a stone block with a mass of 500 kg?

The lever is a steel bar three meters long. Assume a person can produce an input force

equal to their own weight. Assume that the output force of the lever

must equal half the weight of the block to lift one edge.

10.1 Wheels, gears, and rotating machines

Axles and wheels provide advantages. Friction occurs where the wheel and axle touch or

where the wheel touches a surface. Rolling motion creates less wearing away of material

compared with two surfaces sliding over each other.

With gears the trade-off is made between torque and rotation speed.

An output gear will turn with more torque when it rotates slower than the input gear.

10.1 Ramps and Screws

Ramps reduce input force by increasing the distance over which the input force needs to act.

A screw is a simple machine that turns rotating motion into linear motion.

A thread wraps around a screw at an angle, like the angle of a ramp.

10.2 Work

Key Question:What are the

consequences of multiplying forces in machines?

10.2 Work

In physics, work has a very specific meaning.

In physics, work represents a measurable change in the energy of a system, caused by a force.

10.2 Work

If you push a box with a force of one newton for a distance of one meter, you have done exactly one joule of work.

10.2 Work (force is parallel to distance)

W = F x dDistance (m)

Force (N)

Work (joules)

10.2 Work (force at angle to distance)

W = Fd cos (q)

Distance (m)

Force (N)

Work (joules) Angle

10.2 Work done against gravity

W = mghHeight object raised (m)

Gravity (m/sec2)

Work (joules)

Mass (g)

10.3 Why the path doesn't matter

10.3 Calculate work

A crane lifts a steel beam with a mass of 1,500 kg.

Calculate how much work is done against gravity if the beam is lifted 50 meters in the air.

How much time does it take to lift the beam if the motor of the crane can do 10,000 joules of work per second?

10.3 Energy and Conservation of Energy Energy is the ability to make things

change. A system that has energy has the

ability to do work. Energy is measured in the same units

as work because energy is transferred during the action of work.

10.3 Forms of Energy Mechanical energy is the energy

possessed by an object due to its motion or its position.

Radiant energy includes light, microwaves, radio waves, x-rays, and other forms of electromagnetic waves.

Nuclear energy is released when heavy atoms in matter are split up or light atoms are put together.

The electrical energy we use is derived from other sources of energy.

10.3 Potential Energy

Ep = mgh Height (m)

Mass (kg)

Potential Energy (joules)

Accelerationof gravity (m/sec2)

10.3 Potential Energy A cart with a mass of 102

kg is pushed up a ramp.

The top of the ramp is 4 meters higher than the bottom.

How much potential energy is gained by the cart?

If an average student can do 50 joules of work each second, how much time does it take to get up the ramp?

10.3 Kinetic Energy

Energy of motion is called kinetic energy.

The kinetic energy of a moving object depends on two things: mass and speed.

Kinetic energy is proportional to mass.

10.3 Kinetic Energy

Mathematically, kinetic energy increases as the square of speed.

If the speed of an object doubles, its kinetic energy increases four times. (mass is constant)

10.3 Kinetic Energy

Ek = ½ mv2

Speed (m/sec)

Mass (kg)

Kinetic Energy (joules)

10.3 Kinetic Energy

Kinetic energy becomes important in calculating braking distance.

10.3 Calculate Kinetic Energy A car with a mass of

1,300 kg is going straight ahead at a speed of 30 m/sec (67 mph).

The brakes can supply a force of 9,500 N.

Calculate:a) The kinetic energy

of the car.b) The distance it takes

to stop.

10.3 Law of Conservation of Energy

As energy takes different forms and changes things by doing work, nature keeps perfect track of the total.

No new energy is created and no existing energy is destroyed.

10.3 Energy and Conservation of Energy

Key Question:How is motion on a

track related to energy?

Application: Hydroelectric Power