WORK and ENERGY

Work

•Occurs when a force causes a change in position or motion of an object

•W = force x distance

•W = f x d

•Unit of measurement is the Joule (J)

•1 Joule = 1 Newton meter or 1 kg m2/s2

Work ● The applied force must make the

object move, or else work is zero

● The movement of the object must be parallel to the applied force

– If the force and direction of the object’s motion are in the same direction, the work is positive

– If the force and direction of the object’s motion are in opposite directions, the work is negative

Example of Work •How much work does a student do when he exerts a force of 190N to lift a box 2.0 m?

•

Energy •Energy is the ability to do work

•Work = energy!! If an object has energy, it’s because work is done on it

•Whenever work is done, energy is transformed or transferred from one system to another

•Energy can be present in objects even when nothing is happening

•Work is measured in Joules

● This is easy to understand when you think about how you feel after carrying a heavy box up a flight of stairs.

● You transferred energy from your moving muscles to the box and increased its gravitational potential energy by increasing its height

● Energy is always transferred from the object that is doing the work to the object on which the work is done

Gravitational Potential Energy Eg

•Energy of position, or stored energy

•Results from the relative positions of objects in a system

•Results from the gravitational attraction between objects

•Equals the work done by gravity

•Depends on mass (m) , height (h), and the acceleration due to gravity (g)

Gravitational Potential Energy

•Example 1. An apple at the top of a tree has more Eg than an apple of the same size on a lower branch. Why?

•Example 2. A large apple on the same branch as a small apple has more Eg. Why?

Gravitational Potential Energy (continued)

• Eg = mass x gravity x height

• Eg = m g h

m = mass (in kilograms)

h = height (in meters)

g = 9.8 m/s2

NOTE: m x g is the weight of the object in Newtons

- This is equal to the force on the object due to gravity, so like work, gravitational potential energy can be calculated by multiplying force times distance

Gravitational Potential Energy Examples

•1. What is the potential energy of a 0.15 kg apple located 6.5m from the ground?

● 2. A diver has 3400 Joules of gravitational

potential energy after climbing up onto a diving platform that is 6.0 m above the water. What is the divers mass?

● 3. A science student holds a 0.055 kg egg

out a window. Just before the student releases the egg, the egg has 8.0 J of gravitational potential energy with respect to the ground. How high is the students arm above the ground?

Kinetic Energy (Ek)

•Referred to as the energy of motion (all moving objects have kinetic energy)

•Depends on the objects mass and velocity

•Example 1. A bowling ball can do more work than a ping pong ball if they are moving at the same speed. Why?

•Example 2. An apple falling at 15 m/s can do more work than an apple falling at 1 m/s. Why?

Kinetic Energy (continued) •Ek = ½ mass x (velocity)2

•Ek = ½ m v2

m = mass

v = velocity

•Velocity is squared, so a small change in speed causes a large change in kinetic energy

•This is why car crashes are more dangerous at speeds above the speed limit!!

●Kinetic Energy Examples

1. Calculate the kinetic energy of a 1500 kg car that is moving at a speed of 11.67 m/s.

● 2. A bowling ball traveling 2.0 m/s has

16 J of kinetic energy. What is the mass of the bowling ball?

● 3. If a 44 kg cheetah has 21,142 J of

kinetic energy, at what speed is the cheetah running?

Law of Conservation of Energy ● Energy cannot be created nor destroyed,

but can change forms

● The total energy in the universe never changes.

● If energy appears to increase or decrease in a system, it is due to energy entering from an external force (work has added or subtracted energy from the system)

●Energy Transformations

● Energy readily changes from one form to another

● Energy is constantly transforming between potential and kinetic

W- Eg highest; Ek lowest X – Eg lowest; Ek highest Y – Eg increases; Ek decreases Z - Eg decreases; Ek increases

● A moving roller coaster “loses” energy

because of friction and air resistance

● The energy does not disappear

– Some increases the temperature of the track, wheels and air

– Some compresses the air causing a roaring sound

● Initial energy of the system = final energy

● Ei = Ef

● Egi + Eki + W = Egf + Ekf

The initial energy equals the initial gravitational energy plus the initial kinetic energy plus work.

The final energy equals the final gravitational energy plus the final kinetic energy.

● Whenever energy of a system decreases, it has leaked into the environment (usually in the form of heat, light, or sound)

– Ex.; a ball bouncing – the ball shifts from kinetic energy to gravitational potential energy as it bounces. Each time it bounces, it vibrates the surface (sound), transferring some energy each time.

●Examples

● 1. Starting from rest, a child zooms down a frictionless slide with an initial height of 3.0 m. What is her speed at the bottom of the slide?

● 2. A 2100kg car starts from rest at

the top of a 2.5 m high hill. If the car encounters 150N of friction over a distance of 7.2m, how fast is the car moving at the bottom of the hill?