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### Work and Energy

Chapter 12

Students Will Be Able To:

- Explain the meaning of work.
- Explain how work and energy are related.
- Calculate work.
- Calculate power.

Work

- It is the transfer of energy to a body by the application of a force that causes the body to move in the direction of the force
- It is only done when a force causes a change in the position or the motion of an object in the same direction of the applied force
- Therefore, for work to occur, an object must move

Work

- Can be calculated by the following equation
- Work = force x distance (W= Fd)
- W= work
- F= force
- d= distance

Work

- Units for work include
- N • m
- J
- Stands for joule
- Is the main unit used for work
- kg • m2/s2
- 1J = 1 N • m= 1kg • m2/s2

Example- Work

- Imagine a father playing with his daughter by lifting her repeatedly in the air. How much work does he do with each lift, assuming he lifts her 2.0 m and exerts an average force of 190 N?

W = Fd

= 190N x 2.0m

= 380 N • m

= 380 J

Power

- It is a quantity that measures the rate at which work is done or energy is transformed
- Can be calculated by the following equation
- Power = work/time (P= W/t)
- P= power
- W= work
- t= time

Power

- Units for power include
- J/s
- W
- Stands for watt
- Is the main unit used for power
- 1W= 1J/s

Example- Power

- It takes 100 kJ of work to lift an elevator 18 m. If this is done in 20 s, what is the average power of the elevator during the process?
- 100kJ x 1000J/1kJ = 100000 J
- P = W/t

= 100000 J / 20 s

= 50000 J/s

= 50000 W

Students Will Be Able To:

- Explain how machines make work easier.
- Explain how to calculate mechanical advantage.
- Define efficiency.
- Describe the six types of simple machines.

Machines

- Machines multiply and redirect forces
- Help do work by redistributing the work that is put into them
- Can also change the direction of the input force
- Able to increase or decrease force by changing the distance over which the force is applied
- Different forces can do the same amount of work
- Due to decreasing the distance while increasing the force OR decreasing the force while increasing the distance

Mechanical Advantage

- Mechanical advantage tells how much a machine multiplies force or increases distance
- Calculated by the following equation
- Input force is the force applied to the machine
- Output force is the force applied by the machine to overcome resistance

Mechanical Advantage

- Amount of energy the machine transfers to the object cannot be greater than the amount of energy transferred to the machine
- Some energy transferred is changed to heat due to friction
- An ideal machine with no friction would have the same input work and output work

Example- Mechanical Advantage

- Calculate the mechanical advantage of a ramp that is 5.0 m long and 1.5 m high.
- Input distance= 5.0 m and output distance= 1.5 m
- Mechanical advantage = 5.0m/ 1.5m

= 3.33

Efficiency

- Is a measure of how much of the work put into a machine is changed into useful output work by the machine
- Calculating efficiency
- Efficiency = output work/input work X100%
- Efficiency of a machine is always less than 100%
- Lubricants can make machines more efficient by reducing friction

Example- Efficiency

- A sailor uses a rope and an old, squeaky pulley to raise a sail that weighs 140 N. He finds that he must do 180 J of work on the rope in order to raise the sail by 1 m (doing 140 J of work on the sail). What is the efficiency of the pulley? Express your answer as a percentage.
- Efficiency = output work/input work X100%

= 140 J/ 180 J X 100%

= 77.8%

Simple Machines

- One of the six basic types of machines, which are the basis for all other forms of machines
- Divided into two families
- Lever family
- Simple lever
- Pulley
- Wheel and axle
- Inclined plane family
- Simple inclined place
- Wedge
- Screw

Levers

- Have a rigid arm that turns around a point called the fulcrum
- Input arm is the part of the lever on which effort force is applied
- Output arm is the part of the lever that exerts the resistance force
- Divided into three classes based on the location of the fulcrum and of the input and output forces

First Class Levers

- Most common type
- Fulcrum is located between the effort and resistance forces (input and output forces)
- Multiplies and changes the direction of the force
- Example- claw hammer, pliers

Second Class Levers

- Fulcrum is located at one end of the arm and the input force (effort force) is applied to the other end
- Always multiplies force
- Example- wheelbarrow, nutcrackers, hinged doors

Third Class Levers

- Effort force is between the output force (resistance force) and fulcrum
- Responsible for multiplying distance rather than force
- They have a mechanical advantage of less than 1
- Example- human forearm

Pulleys

- Are modified levers
- The point in the middle of a pulley is like the fulcrum of a lever
- A single, fixed pulley has a mechanical advantage of 1
- It is attached to something that doesn’t move
- Force is not multiplied but direction is changed
- A moveable pulley has one end of the rope fixed and the wheel free to move
- It multiplies force
- Multiple pulleys are sometimes put together in a single unit called a block and tackle

Wheel and Axles

- Is a machine with two wheels of different sizes rotating together
- Is a lever or pulley connected to a shaft
- The steering wheel of a car, screwdrivers, and cranks are common wheel-and-axel machines

Inclined Planes

- Is a sloping surface that reduces the amount of force required to do work
- Multiplies and redirects force
- Turns a small input force into a large output force by spreading the work out over a large distance
- Less force is required if a ramp is longer and less steep

Wedge

- Is a modified inclined plane
- Functions like two inclined planes back to back
- Turns a single downward force into two forces directed out to the sides
- Example- nails

Screw

- Is an inclined plane wrapped around a cylinder
- Example- spiral staircases, jar lids

Compound Machines

- Is a machine made of more than one simple machine
- Examples of compound machines
- scissors, which use two first class levers joined at a common fulcrum
- a car jack, which uses a lever in combination with a large screw

Students Will Be Able To:

- Explain the meaning of energy.
- Distinguish between kinetic and potential energy.
- Recognize the different ways that energy can be stored.
- Calculate kinetic and potential energy.

Energy

- Energy is the ability to do work or to cause change
- When you do work on an object, you transfer energy to that particular object
- Whenever work is done, energy is transformed or transferred to another system
- Energy is measured in joules
- Work is also measured in joules

Potential Energy

- Is the energy that an object has because of the position, shape, or condition of the object
- Is stored energy
- 3 types exist
- Chemical
- Energy stored in chemical bonds between atoms
- Elastic
- Energy stored in stretched or compressed elastic materials
- Gravitational
- Energy stored in the gravitational field which exists between two or more objects

Gravitational Potential Energy

- Depends on mass, height, and acceleration due to gravity
- Can be calculated by the following equation
- PE = mass x free fall acceleration x height (PE = mgh)
- PE= gravitational potential energy
- m= mass
- g= free fall acceleration (9.8 m/s2)
- h= height
- Usually measured from the ground but can also be measured from two objects

Example- Gravitational PE

- A 65 kg rock climber ascends a cliff. What is the climber’s gravitational potential energy at a point 35 m above the base of the cliff?
- PE = mgh

= 65 kg x 9.8 m/s2 x 35 m

= 22295 kg•m2/s2

= 22295 J

Kinetic Energy

- Is the energy of a moving object due to the object’s motion
- Depends on mass and speed
- Depends on speed more than mass
- Can be calculated by the following equation
- Kinetic Energy = ½ mass x speed squared

KE = ½ mv2

Example- KE

- What is the kinetic energy of a 44 kg cheetah running at 31 m/s?
- KE = ½ mv2

= ½ (44 kg)(31m/s)2

= 21142 kg•m/s2

= 21142 J

Other Forms of Energy

- The amount of work an object can do because of the object’s kinetic and potential energies is called mechanical energy
- Mechanical energy is the sum of the potential energy and the kinetic energy in a system
- In addition to mechanical energy, most systems contain non-mechanical energy
- Non-mechanical energy does not usually affect systems on a large scale

Other Forms of Energy

- Atoms and molecules have kinetic energy
- The kinetic energy of particles is related to heat and temperature
- Chemical reactions involve potential energy
- The amount of chemical energy associated with a substance depends in part on the relative positions of the atoms it contains
- Living things get energy from the sun
- Plants use photosynthesis to turn the energy in sunlight into chemical energy

Other Forms of Energy

- The sun gets energy from nuclear reactions
- The sun is fueled by nuclear fusion reactions in its core
- Electricity is a form of energy
- Electrical energy is derived from the flow of charged particles, as in a bolt of lightning or in a wire
- Light can carry energy across empty space
- Light energy travels from the sun to Earth across empty space in the form of electromagnetic waves

Energy Transformations

- Energy readily changes from one form to another
- Potential energy can become kinetic energy
- As a car goes down a hill on a roller coaster, potential energy changes to kinetic energy
- Kinetic energy can become potential energy
- The kinetic energy a car has at the bottom of a hill can do work to carry the car up another hill

Energy Transformations

- Mechanical energy can change to other forms of energy
- Mechanical energy can change to non-mechanical energy as a result of friction, air resistance, or other means

Students Will Be Able To:

- Describe how energy is conserved when changing from one form to another.
- Apply the law of conservation of energy to familiar situations.

The Law of Conservation of Energy

- Energy may change from one form to another, but the total amount of energy never changes
- Energy doesn’t appear out of nowhere
- Whenever the total energy in a system increases, it must be due to energy that enters the system from an external source
- Energy doesn’t disappear,but it can be changed to another form

Energy Systems

- Scientist study energy systems
- Boundaries define a system
- Systems may be open or closed
- When the flow of energy into and out of a system is small enough that it can be ignored, the system is called a closed system
- Most systems are open systems, which exchange energy with the space that surrounds them

Mass Energy

- Mass as thought of as energy when discussing nuclear reactions
- The total amount of mass and energy is conserved
- 2 processes involved
- Nuclear fusion
- Two nuclei are fused together
- Nuclear fission
- Two nuclei are broken apart

Food Energy

- Chemical potential energy from food that is stored in your body is used to fuel the processes that keep you alive
- The food calorie is used to measure how much energy you get from various foods
- One calorie is equivalent to 4180 J

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