PHYSICAL SCIENCE PSC1121Physics in Films

© Christos Velissaris & Costas Efthimiou

LECTURE

Energy

If there is no gravity, a liquid will take the shape of

A cube

B pyramid

C cone

D sphere

E wedge

REVIEW QUESTION

Roads are made with a slope around a turn to help cars have

A more friction

B less friction

C more centripetal force

D less centripetal force

E less air resistance

REVIEW QUESTION

When a Lynx bus makes a right turn at constant speedoff of Alafaya onto University Blvd, the bus

A does not accelerate

B accelerates towards the center of the turn

C accelerates away from the center of the turn

D decelerates along Alafaya

REVIEW QUESTION

Rotating the Mir Space Station is not providing a way to create artificial gravity identical to that on Earth.This statement is

A wrong. Rotation always generates centrifugal force and therefore we can use it as artificial gravity.

B right only when we rotate the station very fast.

C right only when we rotate the station slowly.

D right since the Mir station is very long in size.

E right since the Mir station has small diameter.

REVIEW QUESTION

• Energy– definition– kinds of energy

• Some applications in movies• Conservation of energy

Energyyet another way to view the motion or the possibility to move

It is hard to give a general definition of energy. Usually, we define energy by looking at special cases.

Such special cases are:

• kinetic energy

• potential energy

due to gravity

due to elastic forces

• chemical energy

International System of Units

Length meter mQuantity unit symbol

Force Newton NEnergy Joule J

Remember that

kJ = 1,000 Joules

MJ = 1,000,000 Joules

For food we use:

1 calorie = 4.2 J

1 Calorie = 1000 calories = 4200 J

For atomic and nuclear weapons we use:

1 ton of TNT = 4.2 x 109 J

1 megaton of TNT = 4.2 x 1015 J

Hiroshima bomb = 0.012 megatons of TNT = 5 x 1013 J

When an object moves we say that it has kinetic energy.

E = 1/2 m v 2

An F-1 racing car is speeding on a racetrack. If the car triplesits speed, then its kinetic energy

A remains the same.

B doubles.

C becomes 3 times the original.

D becomes 4 times the original.

E becomes 9 times the original.

E = 1/2 m v 2

When an object does not move but it has the `tendency’ to move, we say that it has potential energy. There are several kinds of potential energy.

When the `tendency’ to move is due to gravity, we call the energy gravitational potential energy.

Another example of gravitational potential energy.

If you know the height h then you can compute the potential energy due to gravity:

energy = m g h

About how much more potential energy does ball B have than ball A?

1m

4m

2kg

1kg

ball B:

energy = 1kg 10m/s2 4m

= 40 J

ball A:

energy = 2kg 10m/s2 1m

= 20 J

If you double the height of an object, then its potential energy

A remains the same.

B doubles.

C becomes 3 times the original.

D becomes 4 times the original.

E becomes 9 times the original.

m g h

The bow stores potential energy due to elastic forces.

Other objects that store energy due to elastic forces are springs, rubber bands, and in general everything that can be bent, suppressed, or extended.

Chemical energy is the energy that is stored in the atoms and molecules.

Such energy is used by the engine of the car.

All available energy on Earth is the result of:

A the Sun

B the animals (including humans)

C the plants

D coal, oil, gas, waterfalls, and other similar energy-giving items

E a source not in the above list

Where did the available energy on Earth come from?

You throw an object up. During the time the object is in flight it has

A gravitational potential energy only.

B kinetic energy only.

C kinetic and gravitational potential energy.

D no energy.

REVIEW QUESTION

Which of the following is not of energy?

A gravitational potential

B kinetic

C heat

D friction

E elastic potential

REVIEW QUESTION

Chapter 54: Time for a hero

play clip

What is the mass of each of the spaceships above the cities?

diameter of base = 15 mi = 24 Km

volume = base x height = 4.4 x 1011 m3

assume density same as water(!) = 1 g/cm3 = 1000 Kg/ m3

Mass = volume x density = 4.4 x 1013 kg

radius of base = 12 Km = 12,000 m

area of base = R2 = 4.4 x 108 m2

assume height = 1 Km = 1000 m

Assume that only one-tenth of volume is material = 4.4 x 1010 m3

Recall: If you know the height h then you can compute the potential energy due to gravity:

potential energy = m g h

assume spaceship location above ground = 2 Km = 2000 m

stored potential energy = 8.8 x 1017 J

Hiroshima bomb = 5 x 1013 J

Therefore the stored potential energy equals

17,600 Hiroshima bombs

This energy was released when the spaceship was brought down! Is this a victory to celebrate about?

Elastic Potential Energy (due to springs).

If the distance a spring is stretched from its equilibriumposition is halved the potential energy of the spring ismultiplied by

A) 4B) 2C) 0.5D) 0.25

Conservation of Energy

In physics, the phrase `conservation of energy’ does not have the meaning that it has in everyday life, I.e `avoiding to waste energy’.

The conservation of energy law states that, in the absence of frictional forces, the sum of energy in all of its forms (I.e. the total energy) is always the same no matter what the system does.

If frictional forces are present, they waste energy into heat. However, if we count heat too, then energy is always conserved.

B

A

C

D

The object has kinetic, elastic potential and gravitational potential Energy.

The net energy is constant in the absence of friction.

A mass moving under the influence of a spring moves with the greatest velocity

A) at the end points of its motionB) at the equilibrium position C) midway between the end point of its motion and the equilibrium position

For which quantity in the following list there is not a conservation law?

A momentum

B force

C angular momentum

D energy

E none of the above

Work done by a Force

The “Work” done by the force F (push by the worker) is defined as:

Work done by Force = Force x distance the force is acting

The force whose work I am calculating must have the same line of action (parallel or antiparallel) with the direction of motion. If a force acts perpendicular to the direction of motion it produces 0 work. If a force acts at an arbitrary angle we must split it into the part (component) of the force which acts normal to the direction of motion and the part which acts along the line of motion.

Only the 30N part (component) of the force produces work since itlies along the direction of motion. The 40N component of the forceproduces no work since it acts perpendicular to the direction of motion.

If the distance the crate moves is 2 meters, the work of the pullingforce is:Work of F = 30N x 2m = 60Nm(NOT 100Nm)

A crate is being pushed with a constant horizontal force, F. Four forces can be identified: 1) F, 2) the gravitational force, 3) the normal force, and 4) the frictional force. Which forces do NO work on the crate?

A) the gravitational and the frictional forceB) the gravitational and the normal forceC) the gravitational, the normal & the frictional forceD) F, the gravitational and the normal force

Sign convention for Work done by Forces

If a force is opposing the motion (acts at the opposite direction the object moves) the work done by that force is negative.

If a force aids the motion (acts at the same direction the object moves)the work done by that force is positive.

Friction always produces negative work since it always opposes motion.

Units of Work

Units of Work = Units of Force x Units of distance =Newtons x meters = Joules

1 Joule = 1 Nm

Units of Work and Units of Energy are the same !!!!!!!!

Work is of the same nature as Energy !!!!!!!!

Work and Kinetic Energy Theorem(or how work and energy are related).

• Suppose an object is moving under the influence of a number of forces. Some forces are aiding the motion and produce positive work and other forces are opposing the motion and produce negative work.

• The net work done on the object is the (algebraic) sum of all works done by the forces. (Can be positive or negative). That net work is equal to the change of the object’s kinetic energy. This is the Work Kinetic Energy Theorem.

• The change of the kinetic energy (kinetic energy at the final point minus kinetic energy at the initial point) can be positive (the object gains kinetic energy) or negative (the object looses kinetic energy).

• Forces that aid the motion produce positive work and give kinetic energy to the object. Forces that oppose the motion produce negative work and consume kinetic energy from the object. E.g. Friction consumes kinetic energy and transforms it into heat.

Work and Total Energy Theorem.• In the case where Potential Energies are involved together with the kinetic the

Work Kinetic Theorem can be modified as the Work Total Energy theorem.

• The change of the Total Energy (kinetic energy + all potential energies at the final point minus kinetic + all potential energies at the initial point) is equal to the (algebraic) sum of all works done on the object by all the forces that do not produce any Potential Energy. Once more the total work can be positive (the object gains Total Energy) or negative (the object looses Total Energy). This is the Work Total (or Mechanical) Energy Theorem.

• For example assume that I push a sledge uphill starting from rest for a distance of 1mile (1610m). Assume also that there is friction. The energy budget tells me. That the work of my push (positive) + the work of friction (negative) =final total energy (kinetic + gravitational) – initial total energy (0 kinetic +0 gravitational). I do not need to worry about the work of the weight of the sledge since its has already been accounted via its gravitational potential energy. In other words the work of my push which comes from energy stored in foods I have consumed becomes kinetic and potential energy stored in the object plus heat dissipated by friction.

Can the total mechanical energy Kinetic + Potential ever be negative ?

A) Yes, always.

B) Yes, because KE can be negative.

C) Yes, because PE can be negative.

D) No.

Your car has mass 2000kg and its speed is 50mph. Suddenly you step on the brake and under the influence of a 15,000N friction your car comes to a stop. What is the stopping distance? { SI Units conversion: 50mph = 50 x (1610m /3600s) = 22.36m/s }

Notice that there are more forces acting on the crate (weight and normal force). The normal force produces 0 work and the weight (gravitational force) has been taken care with the inclusion of the gravitational potential energy.

Your car pulls a crate up a hill for a distance of d = 500 meters with a pulling force of P = 300N. The friction is f =250N. When you reach your destination the crate if h = 40 m above the bottom of the hill. If the crate has mass M = 50kg how much energy has your car spent pulling the crate? How much energy has been dissipated as heat on your way up? What is the gravitational potential energy, what is the kinetic energy and what is the speed of the crate at its final destination?

Notice that there are more forces acting on the crate (weight and normal force). The normal force produces 0 work and the weight (gravitational force) has been taken care with the inclusion of the gravitational potential energy.

Kinetic Energy

GravitationalPotential Energy (GPE)

Elastic Potential Energy (EPE)

Elastic Forces (conservative)Springs, rubber bands etc

Gravitational Forces (conservative)

Heat

Chemical EnergyFood, Fuel

Non Conservative Forces Friction, Pulls, Pushes

Final Total Energy (kinetic+all potential)-Initial Total Energy= Work of all non conservative forces

ENERGY BUDGET

Fermi Calculation:How many Calories is a 220lb (100kg) person spending per mile (1610m) jogging? (assume he maintains constant speed)

When we run, walk or jog we are propelling ourselves by friction, which overcomes all resistances that tend to slow us down.

Friction is between 50% and 100% of our weight. Assume it is 70%.

For our jogger friction = 0.7 * 100 * 9.81 N = 687 N

The Energy we spend is the work of friction which is friction * distance

Energy = 687 N * 1610 m = 1,106,070 Joules. Since 1 food calorie is 4,200J the energy is:

Energy = (1,106,070/4,200) Calories = 263 Calories per mile.

Power is the rate of Energy (work) production.

If an equivalent amount of work is done in a shorter period of time

A) more power is requiredB) the same amount of power is requiredC) less power is required