Chapter 12: Work & Energy Section 1 – Work & Power

Imagine that you need to change a flat tire. The car has to be lifted off the ground. If you tried to do this yourself, you could use a great amount of force and the car would not budge!

Did you do any work while trying to lift the car? NO, you didn’t! In order to understand why no work was done, lets look at the definition of WORK.

Definition: work – the use of force to cause an object to accelerate in the direction of the force.  Work = force x distance (W=F * d)  Work is the amount of energy needed to move an object.

 Work is only done when a force causes an object to accelerate (move).  Even though you put a lot of force into the car, it did not move. So, the work done on the car was 0. Work is measured in units called Joules (J).

To put it in perspective: You do about 1 J of work when you lift an apple from your waist to the top of your head. That’s about 1 meter.

Lets look at an example…  Raymond pushes a crate 10 meters. He used 60 Newtons of force to move the crate.  How much work did he do? W = (60 N) x (10 m) = 600 J Raymond did 600 Joules of work. Work?

Lets look at an example…  Ed exerts 250 Joules of work to lift a box 1 meter off the ground.  How much did the box weigh? Remember that weight is a force! W = F x d ; so, F = W/d F = 250 J / 1 m = 250 N The box weighed 250 N ( 56 lbs ) Work?

What if we wanted to measure how much work is done over a certain period of time? Then, we would measure the POWER used! Definition: power – the rate at which work is done over a period of time. P = W/t Power is measured in Watts (W)

 The quicker work is done, the more power it takes.  Work done at a slower speed takes less power.  Example: You do 200 J of work. If you do it over 2 seconds, you would use 100 W of power. P = 200 J / 2 s = 100 W If you do it over 10 seconds, you would use 20 W of power. P = 200J / 10 s = 20 W

Think about an electric mixer…  On a slow speed, the mixer does not move very fast.  It will take a long time to mix something. Power & Time Connections

If you want to decrease the amount of time it takes to mix something…  Then you increase the power level.  The mixer does the same amount of work, but in much less time! Power & Time Connections

Chapter 12: Work & Energy Section 2 – Machines

Machines make work easier to do.  They do not decrease the amount of work done! Machines

Machines are all around us!

Definition: simple machine – one of the six basic machines.  All complex machines are made from simple machines joined together.  Example: The wheel is a simple machine… A car is a complex machine made of wheels, levers, and other types of simple machines.

The 6 Simple Machines: Lever Definition: lever – a machine composed of an arm and fulcrum.  The fulcrum is the pivot point of the lever.  Levers are often used to lift objects.

Real Examples of Levers

The 6 Simple Machines: Pulleys Definition: pulley – a rotating wheel used to lift or pull objects.

The 6 Simple Machines: Wheel & Axle Definition: wheel & axle – a simple machine that consists of two circular objects of different sizes.  The wheel is the larger object.

The 6 Simple Machines: Inclined Planes Definition: inclined plane – a flat surface with endpoints at different heights.  There are three types of inclined planes:  Ramps – IP’s that make it easier to lift objects to different heights.

The 6 Simple Machines: Inclined Planes  Definition: wedge – an IP that is forced between two objects.

The 6 Simple Machines: SCREWS Definition: screw – an IP that is wrapped around a cylinder.

Machines… Definition: compound machine – a machine composed of 2 or more simple machines.

Some machines work better than others, obviously…  Definition: mechanical advantage – the advantage created by a machine that allows work to be done easier. Choose the right machine for the job to get the biggest advantage! Machines

Mechanical Advantage Tells how much a machine multipies force or increases distance The ratio between the output force and the input force Mechanical Advantage= output force input force or Mechanical Advantage = input distance output distance

Mechanical Advantage Machines with a MA greater than 1 multiplies the input force. Machines with a MA of less than 1 does not multiply force, but increases distance and speed.

Mechanical Advantage Problem Calculate the mechanical advantage of a ramp that is 5.0 m long and 1.5 m high.  Given: input distance = 5.0 m Output distance = 1.5 m  Unknown: mechanical advantage=?  MA= input force output force MA= 5.0 m / 1.5 m MA = 3.3

Mechanical Advantage Problem A bus driver applies a force of 55.0 N to the steering wheel, which in turn applies 132 N of force on the steering column. What is the mechanical advantage of the steering wheel? MA = output force/input force MA = 132 N / 55 N MA = 2.4

 When using machines, some of the energy we put into the machine is lost.  The more energy that a machine can keep… The more efficient that machine is.  Definition: efficiency – a measure of how much useful work a machine can do. Friction often causes a machine to lose efficiency.

Efficiency A measure of how much useful work a machine can do The ratio of useful work output to total work input Efficiency = useful work output work input Usually expressed as a percentage To change an answer found using the efficiency equation to a percentage, multiply the answer by 100 and add the % sign.

Efficiency Problem A sailor uses a rope and an old, squeaky pulley to raise a sail that weighs 140 N. He finds that he must do 180 J of work on the rope in order to raise the sail by 1 m (doing 140 J of work on the sail). What is the efficiency of the pulley? Express your answer as a percent.  Given: work input = 180 J, useful work output = 140 J  Unknown: efficiency = ? %  Efficiency = useful work output/work input  Efficiency = 140 J / 180 J  Efficiency = 0.78  Efficiency = 0.78 x 100 = 78%

Efficiency Problem Alice and Jim calculate that they must do 1800 J of work to push a piano up a ramp. However, because they must also overcome friction, they actually must do 2400 J of work. What is the efficiency of the ramp?  Efficiency = useful work output/work input  Useful work output = 1800 J  Work input = 2400 J  Efficiency = 1800 J / 2400 J  Efficiency = 0.75  Efficiency = 0.75 x 100 = 75%

Efficiency Problem It takes 1200 J of work to lift the car high enough to change a tire. How much work must be done by the person operating the jack if the jack is 25% efficient?  Efficiency = useful work output/ work input  0.25 = 1200/work input  Work input = 1200/0.25  Work input = 4800 J

Chapter 12: Work & Energy Section 3 – What is energy ?

Energy comes in many forms that we are familiar with. Definition: energy – a measure of the ability to do work. Energy is measured in Joules (J) Hey… Work has the same unit as energy! Light Heat Sound

Light Energy Sound Energy Thermal & Light Energy

Energy comes in many forms…  Definition: mechanical energy – energy that can be used to do physical work. Examples:  Sound Waves  Objects in Motion (kinetic)  Definition: chemical energy – energy stored in the bonds of atoms. Examples:  Burning Gasoline  Batteries  Food Energy

 Definition: electrical energy – energy resulting from the flow of electrons. Examples:  Electricity  Lightning  Definition: radiant energy – energy travelling as electromagnetic waves. Examples:  Sunlight  Heat Energy

Energy is very closely related to work. In fact… Energy must be transferred to do work! It takes energy to do pretty much anything. Energy is constantly flowing through the universe.

 When you pull a rubber band back, you are doing work on the rubber band.  By doing that work, you are transferring some of your energy into the rubber band. You used energy to do the work that stretched the rubber band! Now, the rubber band has the energy you used!

Mechanical Energy comes in 2 Great-Tasting Flavors! KINETIC Potential

When you stretched the rubber band, the energy you transferred to it was held as “potential energy”… Definition: potential energy – the stored energy that results from an object’s position or condition. Potential Energy

 When an object is stretched or compressed, it has “elastic” potential energy. Potential Energy

 When an object is above the ground, it has “gravitational” potential energy. We will focus on GPE. Potential Energy

 GPE depends on mass and height of an object.  The GPE equation: PE = mgh  m = mass (kg)  g = gravitational acceleration (9.8 m/s 2 )  h = height (m) Gravitational Potential Energy

Gravitational Potential Energy Problem A 65 kg rock climber ascends a cliff. What is the climber’s GPE at a point 35 m above the base of the cliff?  Given: mass (m) = 65 kg Height (h) = 35 m free-fall acceleration (g) = 9.8 m/s 2  Unknown: PE = ? J  PE = mgh  PE = (65 kg)(9.8 m/s 2 )(35 m)  PE = 22,000 J

Gravitational Potential Energy Problem Calculate the GPE of a car with a mass of 1200 kg at the top of a 42 m hill.  Given: m = 1200 kg; h = 42 m; g = 9.8 m/s 2  Unknown: PE = ? J  PE = mgh  PE = (42)(9.8)(1200)  PE = 490,000 J

GPE at Work

In the example with the rubber band…after you released the rubber band… It had kinetic energy as it snapped back into place. Definition: kinetic energy – the energy an object has because of its motion. Only MOVING objects have kinetic energy! What would happen to a bottle cap if the rubber band hit it?

Kinetic Energy OMG!!! Kinetic Energy!

 The kinetic energy equation: KE = ½ mv 2 m = mass (kg) v = velocity (m/s)  Higher velocity gives increases your KE more than a higher mass. This is because velocity is squared!

Kinetic Energy Problem What is the kinetic energy of a 44 kg cheetah running at 31 m/s?  Given: mass (m) = 44 kg; speed (v) = 31 m/s  Unknown: KE = ? J  KE = ½ mv 2  KE = ½ (44)(31) 2  KE = (22)(961)  KE = 21,142 J (2.1 x 10 4 J)

Kinetic Energy Problem What is the kinetic energy in joules of a 1500 kg car moving at 18 m/s ?  Given: m = 1500 kg; v = 18 m/s  Unknown: KE = ? J  KE = ½ mv 2  KE = ½ (1500)(18) 2  KE = (750)(324)  KE = 243, 000 J (2.43 x 10 5 J)

Kinetic Energy Problem A 35 kg child has 190 J of kinetic energy after sledding down a hill. What is the child’s speed in meters per second at the bottom of the hill?  Given: m = 35 kg; KE = 190 J  Unknown: V = ? m/s  KE = ½ mv 2  190 = ½ (35)v 2  380 = 35 v 2  V 2 = 10.9  V= 3.3 m/s

When you hit a baseball, what happens to the energy that you transferred to the bat? Did the energy disappear, or did it just change into other forms…? What happens to energy??

When you hit the baseball, the kinetic energy of the swinging bat is transferred to the baseball. The baseball flies away! What happens to energy??

Energy is also used to produce the cracking sound.. And some energy is used to heat up the bat and the baseball! What happens to energy??

What happened with the baseball is an example of a very important law… The Law of Conservation of Energy. What happens to energy??

The Law of Conservation of Energy states: ENERGY CAN NEVER BE CREATED OR DESTROYED. It is always transferred.

Energy can change forms!

What point has the most PE? What about the most KE?