Science 10Aim: Algebra, Motion Graphs, and Kinetic and Potential Energy

AgendaAlgebra, Motion Graphs, and Kinetic and Potential Energy Practice calculations

Homework: read p. 155-160Next class

Working with FormulasSometimes the variable you are looking for is mixed in with the other variables…

Example: A = 15

C = 6 Solve for B

D = 2

… so you must Rearrange the Formula so that variable is alone on one side of the equals

sign

A = BC

D

B =

Example: A = 15

C = 6 Solve for B

D = 2

Two ways to do this type of rearrangement question: Method 1:

- Rearrange the formula and then replace the symbols with their number values

Method 2:- Replace the symbols with their number values,

then rearrangeMethod 1 is a lot less messy!

A = BC

D

AN IMPORTANT RULE!!

When you Rearrange Formulas… …WHAT YOU DO TO ONE SIDE, YOU HAVE TO DO TO THE OTHER

Math Operation Opposites:

Multiply Divide

Add Subtract

Squared Square Root

Math Operation Opposites

Multiply Divide

Add Subtract

Squared Square Root

Solve for B in the Following Formulas:

A = B + C A = B - C

A = BC A = B C

A = B - CD A = B2

SOLVE FOR B… A = 15

C = 6 D = 2

A = BC

D

SOLVE FOR B… A = 15

C = 6 A = C + B2

WORK INDIVIDUALLY FIND THE ACCELERATION?

Velocity (m/s[N])

Time (s)

0 1 2 3 4 5 6 7 8

6050403020100

Graphs and Motion

Graphs and MotionGraphs can be used to show different

types of motion.

3 types of graphs that can show the same type of motion:

Distance vs. Time Velocity vs. Time Acceleration vs. Time

Type of Motion:An Object or Body at Rest

Distance vs. Time Velocity vs. Time Acceleration vs. Time

Type of Motion:An Object of Body in Uniform Motion

Distance vs. Time Velocity vs. Time Acceleration vs.

Time

Type of Motion:An Object or Body in Positive Uniform Motion

Distance vs. Time Velocity vs. Time Acceleration vs. Time

Type of Motion:An Object or Body in Negative Uniform Motion

Distance vs. Time Velocity vs. Time Acceleration vs. Time

Determine the Acceleration

Seat Work:

0 1 2 3 4 5 6 7 8

6050

40

30

20

10

0

Velocity (m/s[N

])

Time (s)

KENETIC AND POTENTIAL ENERGY

KENETIC ENERGY (KE or EK) is the energy of motion. The amount of kinetic energy depends

on the speed and mass of the object.

KE Formula…

Ek = ½ mv2 = = mv2

2

Ek = kinetic energy (J)m = mass of object (kg)v = speed of object (m/s)

Units:Ek = ½ mv2 (J) = ½ (kg)(m/s)2

Using the Formula ( Ek = ½ mv2 )1) A car with a mass of 1500 kg is moving at a speed of 14 m/s. What is the kinetic energy of the car?  

2) A hockey puck has a mass of 0.21kg. If the hockey puck has 73J of kinetic energy, what is its speed?

Work The transfer of mechanical energy from one object to another

W = Fd

Work can either add or remove kinetic energy from an object.

Positive Work (adding KE ):A pitcher does work on a ball transfers kinetic energy to the ball.

Negative work is done if you remove kinetic energy from

an object (if a force is applied opposite to the object’s motion, or the object slows down).

Example: catching the ball removes kinetic energy causing it to slow down

POTENTIAL ENERGY (PE) is stored energy.

Forms of potential energy Elastic Chemical Nuclear  Gravitational

Elastic Potential Energy An object is elastic if it always returns to its original form after its been distorted

Work done on an elastic object to distort it gives it elastic potential energy

E.g. bungee cords

Chemical Potential Energy chemicals that lose little energy when bonds are formed have the potential of releasing even more energy by undergoing chemical reactions

This chemical reaction releases thermal energy (heat)

 

Chemical Potential Energy Glucose is the principal form of chemical energy for plants and animals… the reaction that breaks down glucose and supplies the energy is called the CELLULAR RESPIRATION reaction

C6H12C6 + 6O2 6CO2 + 6H2O + Energy

Nuclear Potential Energy very large nuclei (uranium and plutonium) have the potential to split into two smaller nuclei and release large amounts of energy

Nuclear Potential Energy very large nuclei (uranium and

plutonium) have the potential to split into two smaller nuclei and release large amounts of energy

Einstein said during a nuclear reaction, some of the mass of the reactants was converted into energy (mass of products does not = mass of the reactants in nuclear reactions)

2mcE

Gravitational Potential Energy the potential energy an object has due

to its location above the Earth’s surface (a mass at a height)

Gravity… is a property of all objects with mass. any two masses attract each other with

a gravitational force this force is not noticeable unless one

of the masses is very large (moon, planet, star)

if there is no force opposing the force of gravity on an object, its motion will change

Gravity… if there were no air friction, all objects

near Earth’s surface would fall with the same acceleration, called the acceleration due to gravity (g = 9.81 m/s2)

http://www.youtube.com/watch?v=5C5_dOEyAfk

Weight is the force of gravity acting on an object

Weight ≠ Mass

Weight is the force of gravity acting on an object

Weight ≠ MassMass = Quantity of Matter in an Object

Weight

Force of gravity (weight) (N ) m = mass (kg) g = acceleration due to gravity (9.81m/s2)

mgFg

is the force of gravity acting on an object

When all of the work done on an object gives it gravitational potential energy, the work done is equal to the gravitational potential energy gained.

pEW

Ep = gravitational potential energy (J or ) m= mass (kg) g = acceleration due to gravity (9.81m/s2) h = Change in height (m)

dFW

hFW

hmgW pEW

mgFg since

since

hmgEp

GravitationalPOTENTIAL ENERGY

FORMULA!

E.g. The shelf in your locker is 1.8 m above the floor. If your science book has a mass of 1.2 kg, what is its gravitational potential energy relative to the floor if it is sitting on the shelf?

 

E.g. If you did 565 J of work on a 12 kg box by carrying it up a flight of stairs, how high is the flight of stairs?

The second law of thermodynamics says:

No process can be 100% efficient. Some energy will always remain in

the form of thermal energy.

During any process, some energy is always transformed into a form that is not useful. This energy is often said to be wasted.

Efficiency

USEFUL ENERGY: Energy that performs a task

WASTE ENERGY: Energy converted during process into a form that is not useful, such as heat

Example: Light Bulb useful energy = light

wasted energy = heat

Efficiency

is a ratio of the useful energy output to the total energy input. In other words, the percentage of the energy we put in to a system that is converted into the type of energy we want.

%100energyinputtotalenergyoutputusefulefficiency

To use the equation, you must be able to identify the useful energy output and the total energy

input.

Example: You climb up the steps of a slide at the waterpark. The top of theslide is 100 m above the pool below. Your mass is 55.0 kg and you are traveling at a speed of 4.30 m/s at the bottom of the slide.Calculate the efficiency of the transformation of gravitational potential energy into kinetic energy.

mghEp msmkg 100/81.90.55 2

1) Energy Input → Gravitational potential energy

= 53 955 J

Example: (Continued)

2

21 mvEk

2/30.40.5521 smkg

2) Energy Output → Kinetic Energy

= 508.475J

Example: (Continued)

%100energyinputtotalenergyoutputusefulefficiency

%10053955475.508

JJ

3) Calculate Efficiency

= 0.942%

Simple Systems A simple pendulum is a simple example of

energy transformations

Chemical Potential of Gasoline

Ignition (reaction) of Internal Combustion Engine

Mechanical Energy of Motor and Movement of Wheels

+

+

+

Heat and Noise

Gravitational Potential Energy of Child on Slide

Physical Propulsion

Kinetic Energy of Sliding Down

Heat (from friction) and some Noise

Chemical Potential of Food (Ex. Glucose)

Breakdown of Glucose (Chemical Reaction)

Muscle Movement, Digestions, Respiration, etc

Heat

Mechanical Energy From a Turbine

A Generators Magnetic Field and Spinning Motion

Current = Electrical Energy

+ Heat and Noise

Energy TransformationsInput Energy Converter Useful Output +Waste Energy

EXAMPLES

Calculating Efficiency Class Practice Problem You use the chemical energy obtained from your

food to pedal your bicycle up a steep hill, thus gaining gravitational potential energy. You then coasted down the hill, transforming the gravitational potential energy into kinetic energy. Suppose the you pedalled up a hill and gained a vertical distance of 25 m. You turned around and coasted down the hill. At the bottom of the hill, you were coasting at a speed of 13 m/s. If the combined mass of yourself and your bicycle is 68 kg, what was the efficiency of the transformation of your gravitational potential energy into kinetic energy?

Practice ProblemsDo practice problems page 227 # 1-9

(odd)

Efficiency Formula:

What do we care about efficiency?

A Simple Answer....One way to reduce pollution caused by machines is to stop using them.

Problems with this idea:1. We rely on machines to improve our

standard of living 2. Food shortage across the globe would

occur 3. Production of goods could not meet

demand (economic impact)

Efficiency of the Internal Combustion Engine

On average, cars are only about 20% efficient.

Where does the other 80% of the energy go?

Efficiency of the Internal Combustion Engine

Where does the other 80% of the energy go?

36% - lost to the coolant

38% - Heat in the exhaust gases

6% - Frictions between the moving parts

Electrical Devices What percentage of energy in an incandescent light bulb is converted into light energy?

Electrical Devices What percentage of energy in an incandescent light bulb is converted into light energy?

5%

The remaining 95% is converted into heat

Electrical Devices

Compact Fluorescent bulbs are 20% efficient.

Electrical Devices

Almost half of all the electrical energy generated in North America is used to

drive electric motors.

Efficiency of Energy Transformations in Living Plants

Plant cells use solar energy to help facilitate a chemical reaction called photosynthesis, in which glucose is formed.

Efficiency of Energy Transformations in Living Plants

Glucose = a molecule that can then be broken down to release useable energy to the plant for growth, reproduction, etc.

In general, plants have relatively low efficiency….approximately 1%!

However, nearly all of the energy used by society originally came for the sun

and was stored in plants.

When calculating the efficiency of photosynthesis, what factors

increase the uncertainty of these measurements?

When calculating the efficiency of photosynthesis, what factors increase the

uncertainty of these measurements?

1. Amount of light reaching the leaf2. Amount of light absorbed by leaf

3. The rate at photosynthesis can occur

Cogeneration

Joffre Power Plant Red Deere

Using the ‘waste’ thermal energy from a electric power plant to heat buildings, greenhouses etc. This can increase the energy efficiency of a power plant from 40-80%!

Why Save Energy?Three benefits of saving energy:

Saves money 

Reduces environmental pollutants 

Conserves natural resources (especially non-renewables)