Energy A central concept underlying all sciences

However, concept of energy is very difficult to define

Concept of energy is unknown to Isaac Newton. Its existence was still debated in the 1850s

A quantity that is often understood as the capacity to do work on a physical system

Energy We observe only the effects of energy when

something is happening

When energy is being transferred from one place to another

When energy is being transformed from one form to another

Forms of Energy Thermal energy

Chemical energy

Electrical energy

Radiant energy

Nuclear energy

Magnetic energy

Elastic energy

Sound Energy

Mechanical energy

Luminous energy

Work The amount of energy transferred by a force acting

through a distance

Work = net force x distance

W = Fnet x d Unit of work: newton-meter (Nm) = joule

(J)

Work A scalar quantity

Independent of time

Unit of work: newton-meter (Nm) = joule (J)

1 J = 1 N x 1 m = 1 kgm2/s2

1 KJ = 1,000 J

1 MJ = 1,000,000 J

Work

Work

WorkTwo ways to do work

Force acts to change motion

Force acts against another force

Work Example An 80 N force has been applied to a block and move

it 20 m along the direction of the force. How much work has been done to the block?

Work Example An 80 N force has been applied to a block and move

it 20 m along the direction of the force. How much work has been done to the block?

W = F d

= 80 N x 20 m

= 1600 J

Work Exercise Calculate the work done when a 20-N force pushes a

cart 3.5 m ?

Work Exercise How much work is required to lift a 360 kilogram

piano to a window whose height is 10 meters from the ground?

Work Exercise A box rests on a horizontal, frictionless surface. A girl

pushes on the box with a force of 18 N to the right and a boy pushes on the box with a force of 12 N to the left. The box moves 4.0 m to the right. Find the work done by (a) the girl, (b) the boy, and (c) the net force.

Work vs. Impulse impulse = net force x time J = F t

impulse changes the momentum of a system

unit of impulse: newton-second (Ns)

work = net force x distance W = F d

work changes the energy of a system

unit of work: newton-meter (Nm) = joule (J)

Work and Force with an Angle

W = F cos θ d

d

Work Exercise If 100 N force has 30o angle pulling on 15 kg block for

5 m. What’s the work?

Work Exercise If 100 N force has 30o angle pulling on 15 kg block for

5 m. What’s the work?

W = F d cos W = 100 N (5 m) cos 30o = 433 J

Positive or Negative Work Man does positive work

lifting box Man does negative work

lowering box

Gravity does positive work when box lowers

Gravity does negative work when box is raised

Power Power – The rate at which work is done Power = (Work Done) / (Time Interval)

P = W/t Unit of power: joule per second , or

Watt (W) 1 watt (W) = 1 J / 1 second

1 kilowatt (kW) = 1,000 watts

1 megawatt (MW) = 1,000,000 watts

Power When W is in the equation, W means work; when W

is in the unit, W means Watt

In metric system of units, automobiles are rated in kilowatts; in the US, we rate engines in units of horsepower (hp).

1 hp = 0.75 kW or 134 hp = 100 kW

Power Example Calculate the power expended when a 500 N barbell

is lifted 2.2 m in 2 s

Power Example Calculate the power expended when a 500 N barbell

is lifted 2.2 m in 2 s

W = Fd/t = 500 N x 2.2 m / 2 s

= 1,100 J / 2 s

= 550 watts

Power Exercise An escalator is used to move 20 passengers every

minute from the first floor of a department store to the second. The second floor is located 5-meters above the first floor. The average passenger's mass is 60 kg. Determine the power requirement of the escalator in order to move this number of passengers in this amount of time

Power Power = Force x Average Velocity

P = W/t = Fd/t = Fv

Power Example A 500N force is applied to an object. If the object

travels with a constant velocity of 20 meters per second, calculate the power expended on the object

Power Example A 500N force is applied to an object. If the object

travels with a constant velocity of 20 meters per second, calculate the power expended on the object

P = Fv

= (500N)(20m/s)

= 10,000 W

= 10 kW

Power Exercise An elevator must lift 1000 kg a distance of 100 m at a

velocity of 4 m/s. What is the average power the elevator exerts during this trip?

Mechanical Energy A compression of atoms in the material of an object,

a physical separation of attracting bodies, or a rearrangement of electric charges in the molecules of a substance

Energy enables an object to do work

Unit of energy: energy is measured in joules

Mechanical Energy Two most common forms of mechanical energy:

potential energy (PE) and kinetic energy (KE)

Mechanical energy can be in the form of either one, or the sum of the two

Potential energy— the energy due to the position of something, or

Kinetic energy— the energy due to the movement of something

Potential Energy Definition: An object may store energy by virtue of its

position

The energy that is held in readiness is called potential energy (PE), because in the stored state it has the potential for doing work

Potential Energy Examples of potential energy:

A stretched/compressed spring

A drawn bow

A stretched rubber band

The chemical energy in fuels (at submicroscopic level)

Any substance that can do work through chemical action possesses potential energy (such as fossil fuels, electric batteries and food)

Gravitational Potential Energy Work is required to elevate objects against Earth’s

gravity

The potential energy due to elevated positions is called gravitational potential energy (GPE)

The amount of gravitational potential energy possessed by an elevated object is equal to the work done against gravity in lifting it

Gravitational Potential Energy The upward force required while moving at constant

velocity is equal to the weight (mg) of the object

Gravitational Potential Energy = Weight x Height

GPE = Fgh = mgh or PE = mgh

The gravitation potential energy depends only on mg and h, does not depend on the path

Unit of gravitational potential energy: kg m2/s2 =

joule (J)

Potential Energy Example The floor of the basement of a house is 3.0 m below

ground level, and the floor of the attic is 5.0 m above ground level. What is the change in potential energy if an 2.0 kg object in the attic is brought to the basement?

Potential Energy Example The floor of the basement of a house is 3.0 m below

ground level, and the floor of the attic is 5.0 m above ground level. What is the change in potential energy if an 2.0 kg object in the attic is brought to the basement?

PE = mgh

= (2.0 kg)(9.8 m/s2)(5.0 m + 3.0 m)

= 156.8 J

Potential Energy Exercise A box has a mass of 5.8kg. The box is lifted from the

garage floor and placed on a shelf. If the box gains 145J of Potential Energy (Ep), how high is the shelf?

Potential Energy Exercise A man climbs on to a wall that is 3.6m high and gains

2268J of potential energy. What is the mass of the man?

Spring Force Hooke’s Law: Hooke's Law says that the spring

restoration force (FS) due to a spring is proportional to the length that the spring is stretched or compressed, and acts in the opposite direction

FS = kx

k is spring constant, and x change in spring length from the equilibrium position

Unit of spring force: newton (N)

Hooke’s Law The more force that was put on materials the

more they extended

With some materials they also extended in a regular way e.g. if the force was doubled so did the extension

This was true as long as their elastic limit was not exceeded

Hooke’s Law

Elastic limit The material no longer shows elastic behavior

(i.e. does not return to original size when stretching force is removed)

The material is permanently deformed i.e., is larger or longer than originally

Spring Constant k is called the spring constant and is a measure of the

stiffness of the spring or material

Unit of of k: N/m (newtons per meter)

The higher the k the stiffer the spring, it needs a large force to for a given extension

Spring Force Example A linear spring has a constant of 377.16 N/m. How

much force is necessary to stretch it 0.39 m?

Spring Force Example A linear spring has a constant of 377.16 N/m. How

much force is necessary to stretch it 0.39 m?

Fs = kx

= (377.16 N/m)(0.39 m)

= 147.09 N

Spring Force Exercise It requires a force of 594.55 N to stretch a certain

linear spring 0.15 m. What is the constant for this spring?

Spring Potential Energy Spring Potential Energy: A spring may store energy

due to compression or stretching and is called spring potential energy (PES)

The potential energy stored in spring is equal to the work done to the spring:

PES = FSx = (1/2FS)x = (1/2kx)x = 1/2kx2

PES = 1/2kx2 Unit of Spring Potential Energy: N m = joule (J)

Spring Potential Energy Example Vincent's mountain bike has a spring with a constant

of 64 N/m in the front-wheel suspension, and it compressed 0.17m when she hit a bump. How much energy does the front spring now store?

Spring Potential Energy Example Vincent's mountain bike has a spring with a constant

of 64 N/m in the front-wheel suspension, and it compressed 0.17m when she hit a bump. How much energy does the front spring now store?

PEs = (1/2) kx2

= (1/2)(64 N/m)(0.17 m)2    

= 0.92 J

Spring Potential Energy Exercise A spring has a potential energy of 22.14 J and a

constant of 676.96 N/m. How far has it been stretched?

Kinetic Energy If an object is moving, then it is capable of doing

work. It has energy of motion, or kinetic energy (KE)

The kinetic energy of a moving object is equal to the work required to bring it to that speed from the rest, or the work the object can do while being brought to rest

The kinetic energy of an object depends on the mass and speed of the object

Kinetic Energy Work = Net Force x Distance = Kinetic Energy

KE = W = Fd = mad = m(v2/(2d))d = 1/2mv2

KE = 1/2mv2

Unit of kinetic energy: kg m2/s2 = joule (J)

Kinetic Energy Example A 3 kg ball is rolling 2 m/s. How much

kinetic energy does it have?

Kinetic Energy Example A 3 kg ball is rolling 2 m/s. How much

kinetic energy does it have?

KE = ½ mv2

= ½ (3 kg) (2 m/s)2

= 6 J

Kinetic Energy Exercise Determine the kinetic energy of a 500-kg roller

coaster car that is moving with a speed of 20 m/s

If the roller coaster car were moving with twice the speed, then what would be its new kinetic energy?

Kinetic Energy Exercise Missy Diwater, the former platform diver for the

Ringling Brother's Circus, had a kinetic energy of 12000 J just prior to hitting the bucket of water. If Missy's mass is 40 kg, then what is her speed?

Kinetic Energy If the speed of an object is doubled (the speed is

squared), its kinetic energy is quadrupled It takes four times the work to double the speed It takes four times of work to stop a double-speed

object Work-Energy Theorem: Work changes energy. If no

change in energy occurs, then no work is done.

W= E

A skater of mass 60 kg has an initial velocity of 12 m/s. He slides on ice where the frictional force is 36 N. How far will the skater slide before he stops?

A skater of mass 60 kg has an initial velocity of 12 m/s. He slides on ice where the frictional force is 36 N. How far will the skater slide before he stops?

W = E = KE

Fnet d = 1/2mv2

36 N x d = ½ (60 kg)(12 m/s)2

d = 120 m

Work Exercise When a small brass ball is dropped into soft clay, it

makes a dent. If the ball hits with twice the speed, the dent of the clay is

a) more or less the same depth.

b) twice as deep.

c) three times as deep

d) four times as deep.

Conservation of Energy Law of conservation of energy: Energy cannot be created

or destroyed. It can be transformed from one form into another, but the total amount of energy never changes

Total Energy at point A = Total Energy at point B

PEA + KEA = PEB + KEB

PE = mgh

KE = 1/2mv2

Conservation of Energy Example A diver of mass m drops from

a board 10.0 m above the water surface. Find his speed 5.00 m above the water surface

Conservation of Energy Example A diver of mass m drops from

a board 10.0 m above the water surface. Find his speed 5.00 m above the water surface

PE = KE

mgh = ½ mv2

m(9.81 m/s)(10 m – 5m) = ½ m v2

v = 9.9 m/s

Conservation of Energy Exercise A diver of mass m drops from

a board 10.0 m above the water surface. Find his speed right above the water surface

Conservation of Energy ExerciseA skier slides down the frictionless slope as shown. What is the skier’s speed at the bottom?

H=40 m

L=250 m

start

finish

Conservation of Energy ExerciseThree identical balls are thrown from the top of a building with the same initial speed. Initially, Ball 1 moves horizontally. Ball 2 moves upward. Ball 3 moves downward.Neglecting air resistance, which ball has the fastest speed when it hits the ground?

A) Ball 1B) Ball 2C) Ball 3D) All the same

Conservation of Energy ExerciseTarzan swings from a vine whose length is 12 m. If Tarzan starts at an angle of 30 degrees with respect to the vertical and has no initial speed, what is his speed at the bottom of the arc?