Physics 3.3Physics 3.3

WorkWork

Work is defined as Force in the direction of Work is defined as Force in the direction of motion x the distance moved.motion x the distance moved.

Work is also defined as the change in total Work is also defined as the change in total energy. energy.

Work is given in Work is given in NN·m·m, or , or JoulesJoules.. Work is a scalar quantity. Why? Work is a scalar quantity. Why? Lift a weight, put it back where it came from, Lift a weight, put it back where it came from,

displacement is zero, but displacement is zero, but workwork was done. was done.

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A constant force of 1900 newtons is A constant force of 1900 newtons is required to keep and automobile having a required to keep and automobile having a mass of 1.0 E3 Kg moving at a constant mass of 1.0 E3 Kg moving at a constant speed of 20. meters per second. The work speed of 20. meters per second. The work done in moving the automobile a distance of done in moving the automobile a distance of 2.0 E3 meters is: 2.0 E3 meters is:

W = Fd = W = Fd = ∆E∆ETT

PowerPower

Power is the rate at which work is donePower is the rate at which work is done Power is a scalar quantity.Power is a scalar quantity. Power equal work divided by time.Power equal work divided by time. P = W / tP = W / t Units of power are the watt (j / s).Units of power are the watt (j / s).

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A 3.0 kilogram block is initially at rest on a A 3.0 kilogram block is initially at rest on a frictionless, horizontal surface. The block is frictionless, horizontal surface. The block is moved 8.0 meters in 2.0 seconds by the moved 8.0 meters in 2.0 seconds by the application of a 12 – newton horizontal application of a 12 – newton horizontal force. What is the average power force. What is the average power developed while moving the block?developed while moving the block?

P = W / t = Fd / t = FvP = W / t = Fd / t = Fv

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A motor having a power rating of 500. watts A motor having a power rating of 500. watts is used to lift an object weighing 100. is used to lift an object weighing 100. newtons. How much time does the motor newtons. How much time does the motor take to lift the object a vertical distance of take to lift the object a vertical distance of 10.0 meters?10.0 meters?

P = Fd / tP = Fd / t

Potential and Gravitational Potential Potential and Gravitational Potential Energy:Energy:

The energy an object has because of its The energy an object has because of its height. height.

PE = mass x acceleration due to gravity x PE = mass x acceleration due to gravity x heightheight

∆∆PE = mg∆h.PE = mg∆h. Units of gravitational potential energy is Units of gravitational potential energy is

joules or kg∙m² / s². joules or kg∙m² / s².

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An object weighing 15 newtons is lifted from An object weighing 15 newtons is lifted from the ground to a height of 0.22 meter. The the ground to a height of 0.22 meter. The increase in the object’s gravitational increase in the object’s gravitational potential energy is approximately:potential energy is approximately:

∆∆PE = mg∆h.PE = mg∆h.

Hooke’s Law ForceHooke’s Law Force

The force (FThe force (Fss) placed on a spring is equal to ) placed on a spring is equal to the spring constant the spring constant kk times the change in times the change in distance from the rest position distance from the rest position ∆x.∆x.

FFs s = = k k ∆x∆x

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A 10-newton force is required to hold a A 10-newton force is required to hold a stretched spring 0.20 meters from its rest stretched spring 0.20 meters from its rest position. What is the spring constant?position. What is the spring constant?

FFs s = = k k ∆x∆x

Potential Energy of a SpringPotential Energy of a Spring

A compressed or stretched out spring A compressed or stretched out spring stores potential energy and can be stores potential energy and can be calculated 2 ways:calculated 2 ways:

1.1. The area of a FThe area of a Fss vs vs ∆x graph.∆x graph.

2.2. PEPEss = ½kx² = ½kx²

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A 10.-newton force is required to hold a A 10.-newton force is required to hold a stretched spring 0.20 meter from its rest stretched spring 0.20 meter from its rest position. What is the potential energy stored position. What is the potential energy stored in the stretched spring?in the stretched spring?

PEPEss = ½kx² = ½kx²

Kinetic EnergyKinetic Energy

The energy associated with motion.The energy associated with motion. The unit of kinetic energy is joules orThe unit of kinetic energy is joules or

kg∙m² / s².kg∙m² / s². KE = ½mv².KE = ½mv².

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The kinetic energy of a 980-kilogram race The kinetic energy of a 980-kilogram race car traveling at 90. meters per second is car traveling at 90. meters per second is approximately:approximately:

KE = ½mv².KE = ½mv².

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An Object moving at a constant speed of 25 An Object moving at a constant speed of 25 meters per second possesses 450 joules of meters per second possesses 450 joules of kinetic energy. What is the object’s mass?kinetic energy. What is the object’s mass?

KE = ½mv².KE = ½mv².

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If the speed of a car is doubled, the kinetic If the speed of a car is doubled, the kinetic energy of the car is:energy of the car is:

KE = ½mv².KE = ½mv².

Work and EnergyWork and Energy

Work changes into potential of kinetic Work changes into potential of kinetic energy. energy.

When there is friction, work also changes When there is friction, work also changes into internal energy.into internal energy.

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An average force of 20. newtons is used to An average force of 20. newtons is used to pull back the string of a bow and arrow 0.60-pull back the string of a bow and arrow 0.60-meters. As the arrow leaves the bow, its meters. As the arrow leaves the bow, its kinetic energy is:kinetic energy is:

W = Fd = W = Fd = ∆E∆ETT

Conservation of Energy:Conservation of Energy:

Energy cannot be created or destroyed. Energy cannot be created or destroyed. Ideal mechanical systemIdeal mechanical system

– Total energy equals potential and kinetic Total energy equals potential and kinetic energies. There is no friction or air resistance. energies. There is no friction or air resistance.

Non-ideal mechanical systemNon-ideal mechanical system– Total energy equals potential, kinetic, and Total energy equals potential, kinetic, and

internal energies. There is friction and/or air internal energies. There is friction and/or air resistance.resistance.

A Pendulum and a Mass on a Spring A Pendulum and a Mass on a Spring

Both can be used to show the relationship Both can be used to show the relationship between KE and PE.between KE and PE.

During an oscillation, the rest position During an oscillation, the rest position represents 0 PE and max KE. represents 0 PE and max KE.

The two points where there is a change in The two points where there is a change in direction, and furthest from the rest position direction, and furthest from the rest position is where KE is zero, and PE is maximum.is where KE is zero, and PE is maximum.