TAKS Review - Formulas

transcript

Integrated Physics and Chemistry (4) Science Concepts.The student knows concepts of force and motion evident in

everyday life. The student is expected to:(A) calculate speed, momentum, acceleration, work, and

power in systems such as in the human body, moving toys, and machines;

Common measurements and symbols

Measurement Symbol Typical Units on TAKS

speed or velocity v m/s

momentum p kg.m/s

acceleration a m/s2

Work W J

Power p W

Force F N

Time t s

Mass m kg

Energy E, KE or PE J

Using the formula chart

1. Circle what you are asked to find

2. Underline given facts with numbers and units and write the symbol above it.

3. Identify the formula(s) you will use from the formula chart

4. Rearrange the formula for what you’re asked to find.

5. Put in numbers for symbols and solve.

6. Check that you answered the question asked.

Rearranging formulas

When a formula is not solved for the variable you are trying to find, then you need to rearrange it until your variable is alone on one side of the equation.

Example, the speed formula is:

If you are given speed and time and want to find distance, what would the formula be?

Here, you divided d by t. To move t to the other side, do the opposite, multiply by it.

t cancels on the right side

And you are left with the formula for d.

Speed and Velocity

How fast an object is traveling.

Velocity has direction, speed does not.

Acceleration

The change in velocity

Can be: • speeding up • slowing down • or changing direction

If an object is moving at a constant speed, acceleration = 0

Negative acceleration (deceleration) means the object is slowing down.

Using force to move an object a certain distance.

If there is no movement, there is no work done. If distance = 0, work = 0

The displacement must be in the direction of the force.

Does not depend on the time it takes to do the work

If Distance = 0, then

Work = 0.

The man is carrying his groceries 2 meters to the counter. He is holding the groceries with a force of 10 N, what is the work done on the groceries?

The force and the displacement are not in the same direction.

Therefore, Distance = 0,

Work = 0.If the man had been lifting the

groceries up, then there would be work.

The rate at which work is done.

More power means the same work can be done faster.

How could this person increase his power?

What is the power of this motor?

Power = Work/timeTime = 5 s

We must find the work first!Work = Force x

distance= 10 N x 2m = 20 J

Power = Work/time= 20J/5s=4 Watts

Momentum

The product of an object’s mass and velocity.

Can be thought of as how difficult it is to stop a moving object.

A stopped object has zero momentum.

Conservation of Momentum

In collisions, total momentum does not change. The momentum of the objects (together) before the collision is the same as the momentum of the objects (together) after the collision.

Distance vs. Time graphs

• In a distance vs. time graph, the slope of the line is the speed of the object.

• If you have a horizontal line, the object is stopped.

0 5 10

Time (hours)

No speed = stopped

0 5 10

Time (hours)

0 5 10

Time (hours)

Constant speed away from a point Constant speed toward a point

0 5 10

Time (hours)

0 5 10

Time (hours)

The line gets steeper – speeding up The line gets less steep – slowing down

Velocity vs. Time Graphs

• In a velocity vs. time graph, the slope of the line is the acceleration of the object.

• In this type of graph, a horizontal line means that the object is moving at a constant speed.

• 1. A ball moving at 30 m/s has a momentum of 15 kg·m/s. The mass of the ball is —

A 45 kg

B 15 kg

C 2.0 kg

D 0.5 kg

• 2. The weight lifter used a force of 980 N to raise the barbell over her head in 5.21 seconds. Approximately how much work did she do in raising the barbell?

F 380 J

G 982 J

H 2,000 J

J 10,000 J

3. How much work is performed when a 50 kg crate is pushed 15 m with a force of 20N?

F 300 J

G 750 J

H 1,000 J

J 15,000 J

4. According to this graph, what was the bicycle’s acceleration between 6 and 10 seconds?

A 0.0 m/s2

B 0.65 m/s2

C 1.6 m/s2

D 6.5 m/s2

5. If a force of 100 newtons was exerted on an object and no work was done, the object must have —

A accelerated rapidly

B remained motionless

C decreased its velocity

D gained momentum

6. A mechanic used a hydraulic lift to raise a 12,054 N car 1.89 m above the floor of a

garage. It took 4.75 s to raise the car. What was the power output of the lift?

A 489 W

B 1815 W

C 4796 W

D 30,294 W

• 9.The pictures show how an air bag functions in a collision. How much momentum in kg.m/s does the air bag absorb from the crash-test dummy if all of the crash-test dummy’s momentum is absorbed by the air bag?

P = m x v = 100 kg x 6.3 m/s = 630 kg x m/s

Integrated Physics and Chemistry (4) Science Concepts.

The student knows concepts of force and motion evident in everyday life. The student is expected to:

(B) Investigate and describe [applications of] Newton’s laws such as in vehicle restraints, sports activities, geological

processes, and satellite orbits.

Forces

• Force can be defined as a push or a pull.

• Forces can be balanced, which mean they are equal and opposite with no change in direction. If the forces on an object are balanced, it will either remain at rest or it will move at a constant speed in a straight line.

Unbalanced forces cause an object to accelerate (speed up, slow down or

change direction) in the direction of the

largest force.

Friction is a force that acts in the opposite direction to the motion of a moving object.

Newton’s Laws

Newton’s First Law: An object at rest will remain at rest and an object in motion will remain in motion at a constant velocity unless acted upon by an unbalanced force.

• The Law of Inertia.

Orbits and Inertia

Newton’s Second Law:

• Force = mass x acceleration

• For a constant force, if mass increases acceleration decreases

• For a constant mass, if force increases, acceleration increases

The force on the ball and the force on the cannon are equal (See 3rd Law).

F = ma The ball’s mass is lower, so its acceleration is higher.

The cannon’s mass is greater, so its acceleration is lower.

Newton’s Third Law: For every action force, there is an equal and opposite reaction force.

A The ground pushes the rocket up while exhaust gases push down on the ground.B Exhaust gases push down on air while the air pushes

up on the rocket.C The rocket pushes exhaust gases down while the exhaust gases push the rocket up.D Gravity pulls the rocket exhaust down while friction pushes up against the atmosphere.

1. Which of these is the best description of the action- reaction force pair when the space shuttle lifts off from the launchpad?

2. After shooting a cannonball, a cannon recoils with a much lower velocity than the cannonball. This is primarily because, compared to the cannonball, the cannon has a —

F much greater massG smaller amount of momentumH greater kinetic energyJ smaller force applied to it

3. How many newtons of force does a 50.0 kg deer exert on the ground because of gravity?

F = m x a

50 kg x 9.8m/s2 = 490 N

4. Which factor would most likely cause a communications satellite orbiting Earth to return to Earth from its orbit?

F An increase in the satellite’s forward momentumG An increase in solar energy striking

the satelliteH A decrease in the satellite’s sizeJ A decrease in the satellite’s velocity

TAKS Review: Simple machines

(D) investigate and demonstrate [mechanical advantage and] efficiency of various

machines such as levers, motors, wheels and axles, pulleys, and ramps. (11th only)

Simple machines

Simple machines are tools that make work easier, usually do work

with a single movement

Simple machines

The amount of effort saved when using machines is called mechanical

advantage or MA

Mechanical Advantage

Mechanical advantage is how many times a machine multiplies the force that is put into it.

For example, if you put in a force of 10 N, and the machine puts out a force of 40 N, then the machine has multiplied your force ___ times.

The mechanical advantage is 4. (Remember Work remains the same!)

Mechanical advantage is calculated by the following formula:

MA = Resistance force= Fr Effort force Fe

For example, if a worker applies a force of 20 N to pry out a nail that has a resistance force of 500N, what is the mechanical advantage of the hammer the worker uses?

MA = Resistance force = Fr = 500 N= Effort force Fe 20 N

Ideal MA

If you do not know the forces applied, the mechanical advantage a machine should provide (called ideal MA) can be calculated by the following formula:

IMA = Effort distance

Resistance distance

Pulleys

The mechanical advantage of a pulley = the number of supporting strings. If you pull up on a string you count it. If you pull

down on a string you don’t count it.

What is the MA?

Levers

In a lever, the MA can be found by dividing the distance between the fulcrum and the effort by the distance between the fulcrum

and resistance.

Levers

So, to make a lever easier to use, move the fulcrum closer to the weight you are trying to move and further from where you are

pushing.

Which is easiest to move?

To increase the MA of a ramp (to make the ramp easier to climb), make the ramp longer with a more gradual incline.

How could you make this ramp easier to climb?

Wheel and axle

• To increase the MA of a wheel and axle, make the wheel larger and the axle smaller.

A gear system is a modified type of wheel and axle, where the larger gear acts as the wheel and the smaller gear acts like the axle. How could you change these gears to make the

smaller one turn faster?

Make the larger gear larger or the smaller gear

smaller.

Efficiency

• If a machine were perfect, all of the work that was put in would be used to do useful work.

• In real life, some work put into a machine is “lost” as heat or friction.

• We calculate efficiency to determine how much of the work put in actually produces useful work.

Efficiency

• Efficiency = Work out x 100%

Work in

• If a machine were perfect and there were no friction, efficiency would be 100%, because all of the work in would become work that came out.

• In real life, efficiency is always less than 100%!!!!

The diagram shows an electric motor lifting a 6 N block a distance of 3 m. The total amount of electrical energy used by the motor is 30 J. How much energy does the motor convert to heat?

F 9 JG 12 JH 18 JJ 21 J

Which lever arrangement requires the least effort force to raise a 500 N resistance?

What is the efficiency of an air conditioner if there is a work input of 320 J and a work output of 80 J?

F 4%G 25%H 240%J 400%

Which configuration of pulleys and belts shown below will result in the

fastest rotation of Spindle 2?

Integrated Physics and Chemistry (6) Science Concepts.

The student knows the impact of energy transformations in everyday life. The

student is expected to(A) describe the law of conservation of

energy.

Energy

• energy- the ability to do work

• unit: joule (J)

Types of Energy:

– kinetic energy- the energy of motion • the faster an object moves, the more kinetic energy

KE = ½ (mv2)

– potential energy- energy of position • stored energy – ex: a ball rolled to the top of a hill• GPE is potential energy due to gravity. GPE = mgh

(remember g = 9.8m/s2)

law of conservation of energy-

• energy may neither be created nor destroyed

• it can only be transformed into various forms—from kinetic to potential, from chemical to mechanical

• the total energy in the system is constant

Where is the PE greatest?Where is the PE least?

Where is the KE greatest?Where is the roller coaster moving

the fastest?

Types of Energymechanical energy- Moving objects

heat energy- usually results from friction—causes phase & temperature changes

chemical energy- stored in chemical bond bonds Example, released when starting a fire, burning fuel, digesting food

nuclear energy- Nuclear reactions; produces the sun’s energy due to nuclear fusion--hydrogen changes to helium

electromagnetic energy- Charges—microwaves, X-rays, light

Energy conversions

Powerful PlanktonThe U.S. Naval Research Laboratory has created an experimental marine fuel cell that could produce enough electricity to power ocean-monitoring devices. This fuel cell runs on seawater and sediment, with the help of plankton. Some

plankton on the surface of ocean sediments use dissolved oxygen to break down organic matter, releasing energy; this is an aerobic process. The

plankton in the deeper sediments break down organic matter without using oxygen; this is an anaerobic process. These two processes create a

difference in voltage between the surface of the sediment and the sediment farther down in the seabed. The voltage difference can be used to produce electricity-up to 5.0 x 10 – 2 watts of power. Energy supplied by this type of fuel cell can be obtained as long as there is organic matter in the sediment.

Fuel cells powered by plankton from the seabed can be used to operate instruments that monitor ocean currents and water temperature. These fuel

cells get their energy by converting —

F chemical energy to electrical energyG electrical energy to mechanical energyH hydroelectric energy to geothermal energyJ mechanical energy to chemical energy

Which process best shows the conversion of solar energy to

chemical energy?

F Prevailing winds causing windmills to spin

G Green plants making their own food

H Uranium producing heat to make steam

J Tides generating electricity

What is the potential energy of the rock?

A 59,900 joulesB 64,600 joulesC 93,100 joulesD 121,600 joules

Which of the following is an example of solar energy being

converted into chemical energy?

F Plants producing sugar during the day

G Water evaporating and condensing in the water cycle

H The sun unevenly heating Earth’s surface

J Lava erupting from volcanoes for many days

An inventor claims to have created an internal combustion engine that converts

100 kJ of chemical energy from diesel fuel to 140 kJ of mechanical energy. This claim

violates the law of conservation of —

F momentum

G inertia

H energy

J mass

Integrated Physics and Chemistry (6) Science Concepts.The student knows the impact of energy transformations in everyday life.

The student is expected to(B) investigate and demonstrate the movement of heat through solids,

liquids, and gases byconvection, conduction, and radiation

Remember the properties of solids, liquids and gases…

• heat- energy caused by the internal motion of molecules

• heat transfer- the movement of heat from a warmer object to a cooler one

3 methods of heat transfer

1. conduction- heat transferred by direct contact of molecules

• takes place in solids, liquids, & gases, but does best in solids

• one particle must contact another for this to occur. In solids, the particles are close to each other, which makes contact easier.

Conductors vs. Insulators

conductors- substances that conduct heat better & more rapidly than others (silver, copper, iron)

insulators- substances that do not conduct heat easily (glass, plastic, wood, rubber)—wearing several layers of clothing in extremely cold weather

3 Methods of Heat Transfer

2. convection- takes place in liquids & gases as up-and-down movements called convection currents.

• Important: Does not occur in solids

Convection – look for arrows or circular motion

3 Methods of Heat Transfer

3. radiation- heat energy transfer through empty space

• This is how the sun heats the earth

Which method is shown?

Radiation

Conduction

Which method is shown?

Convection

Radiation

Convection/Conduction

Radiation/ Convection

Conduction

The primary way liquids and gases transmit heat is by the process of —

A reflection

B conduction

C radiation

D convection

A man who was sleeping wakes up because he hears the smoke alarm go off in his house. Before opening the bedroom door, the man feels the door to see whether it is warm. He is assuming that heat would be transferred through the door by _________________________Conduction

A solar heater uses energy from the sun to heat water. The heater’s panel is painted black to —

F improve emission of infrared radiation

G reduce the heat loss by convection currents

H improve absorption of infrared radiation

J reduce the heater’s conducting properties

In which container is the substance unable to transfer heat by convection?

Container P and Container Q each were filled with 0.5 liter of water. The water was heated to 90°C. The

table shows the temperatures after both containers were allowed to cool for 3 minutes. Compared to

Container Q, Container P is a better A conductor C radiator

B absorber D insulator

TAKS Review: Waves

The student knows the effects of waves on everyday life. The student is expected to

(A) demonstrate wave types and their characteristics through a variety of activities such as modeling with ropes and coils, activating tuning forks, and

interpreting data on seismic waves. (10th only)

(B) demonstrate wave interactions including interference, polarization, reflection, refraction, and resonance within various materials. (11th only)

2. Longitudinal (compression)

1. Transverse

Types of Waves

Parts of a Wave

Calculating Wave Speed

Speed = Wavelength • Frequency

Measured in Hz

Interference

Constructive

Destructive

Reflection

Angle of incidence = Angle of reflection

Refraction

Refraction is the bending of light as it passes from one medium to

another.

Refraction

Pencil appears bent in a glass of water.

Spear fishing: the fish is actually lower

than it appears to be.

Refraction

A prism separates white light into its

components

DiffractionWhen a wave meets an obstacle it bends around the

obstacle.

Resonance

Resonance occurs when two nearby objects share the same vibrational frequency.

When one of the objects is vibrating, it forces the second object into vibrating.

The result is a large vibration = a large sound (in sound waves)

Resonance

Example: Two similar tuning forks.

When one tuning fork is sounded, the second tuning fork is energized by the specific frequencies emitted by the first, and begins to

vibrate and sound as well!

Other examples of resonance:

• Plucked strings on musical instruments (guitar)

• Air blown across a tube (flute) or bottle of water

• Vocal cords

Polarization

At 0°C sound travels through air at a speed of 330 m/s. If a sound wave is produced with a wavelength of 0.10 m, what is the wave’s frequency?

F 0.0033 HzG 33 HzH 330 HzJ 3300 Hz

• Which illustration best demonstrates compression waves?

Which wave has the greatest velocity?

When trying to spear a fish in water, a person needs to take into account the way light bends as it moves from water into air. The bending of light as it passes from one medium into another is known as —

F reflectionG refractionH diffractionJ polarization

One tuning fork is struck and placed next to an identical fork. The two forks do not touch. The second tuning fork starts to vibrate because

of —

F interference

G the Doppler effect

H resonance

J standing waves

The pitch of a sound made by plucking a guitar string is

determined by the —

A frequency of the vibration produced

B strength of the plucking forceC distance between the stringsD shape of the guitar body

The diagram shows waves approaching a barrier. Which pattern will be formed after the waves pass through the opening in the barrier?

Electric Circuits

IPC 6F – Investigate and compare series and parallel circuits. (10th grade only)

Circuits

To have an electric circuit, you need:

• a closed conducting path which extends from the positive terminal to the negative terminal.

• An energy source, such as a battery.

Will the bulb light?

Closed loop!

Series circuit

• each device is connected in a manner such that there is only one pathway by which charge can traverse the external circuit.

What happens if the first light bulb burns out?

Parallel Circuits

• multiple pathways by which charge can flow through the external circuit.

What happens if the first light bulb burns out?

Circuit Math

Current (Amps)

Voltage (Volts)

Resistance (Ώ)

Which switch, if opened, will cause the lightbulb to stop glowing?

F QG RH SJ T

What is the current in a copper wire that has a resistance of 2 ohms and is connected to a 9-volt electrical source?

F 0.22 ampG 4.5 ampsH 11.0 ampsJ 18.0 amps

How much current is flowing through this circuit?

A 0.32 AB 3.1 AC 4.0 AD 12.5 A

Which circuit is built so that if one lightbulb goes out, the other three lightbulbs will continue to glow?

TAKS Review - Formulas

Documents