Ch 6 Work and Energy1

• Work is when a force is applied and an object is displaced

• If no displacement occurs or no force is applied then no work is done.

• The definition of work when the force is parallel to the displacement

Work in 1 dimension

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In the SI system, the units of work are joules:

As long as this person does not lift or lower the bag of groceries, he is doing no work on it. The force he exerts has no component in the direction of motion.

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• If the force is at an angle to the displacement you must determine the component of the force that is directed parallel to the displacement.

Work in 2 dimensions

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Work done by forces that oppose the direction of motion, such as friction, will be negative.

-Ffr

Fp

x

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The work done may be positive, zero, or negative, depending on the

angle between the force and the displacement

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If there is more than one force acting on an object, we can find the work done by each force, and also the work done by the net force

Wtotal=W1 + W2 + W3 … = Σ W

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6-3 & 6-4 KE, PE and Work Energy Principle• Kinetic energy (KE) is energy of motion

• Gravitational potential energy (PE; often just called potential energy) is energy of position

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Mechanical Energy is the sum of the kinetic and potential energy of an object

Energy was traditionally defined as the ability to do work. Not all forces can do work, but ME can

ME= KE + PE

Work and Energy

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• For objects moving at speeds much slower than the speed of light Kinetic energy is calculated by

Kinetic Energy KE

KE=1/2mv2 10

• An object can have potential energy by virtue of its position or height– A wound-up spring– A stretched elastic

band– An object at some

height above the ground

Potential Energy PE

PE=mgy

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• The net force done on an object is equal to the change in the object’s kinetic energy

• Work and kinetic energy can be equated and have the same units; joules.

Work-Energy Principle or Theorem

Wnet=ΔKE

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Potential energy can also be stored in certain materials when they are

compressed; the figure below shows potential energy yielding

kinetic energy.

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The force required to compress or stretch a spring is:

where k is the spring constant, and needs to be measured for each spring.Negative because it is a restoring force, acting in the opposite direction of displacement

Hooke’s Law

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• The force increases as the spring is stretched or compressed

• Potential energy of the compressed or stretched spring measured from its equilibrium position

Elastic potential energy

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6-5 Conservative and Nonconservative Forces

Conservative forces are ones that do not depend on, or are independent, of the path taken. An example is gravityIf the object were to return to the starting point no net work would be done

http://hyperphysics.phy-astr.gsu.edu/hbase/pegrav.html16

• Nonconservative forces are ones that do depend on the path taken.

• Also called dissipative forces because the energy is not stored as mechanical energy but changed into a different type such as heat energy

• An example is friction

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Potential energy can only be defined for conservative forces.

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6-6 Mechanical Energy and Its Conservation•If there are no nonconservative forces, the sum of the changes in the kinetic energy and in the potential energy is zero

• If only conservative forces are acting the total ME of the system stays constant or is conserved

•This is the principle of conservation of mechanical energy

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Total mechanical energy ME= KE + PE therefore

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Energy conservation• The total energy is neither increased nor

decreased, only transformed from one form to another and transferred from one object to another. The total amount remains the same.

This is the Law of Conservation of Energy

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6-10 Power

Power is the rate at which work is done

The difference between walking and running up these stairs is power – the change in gravitational potential energy is the same.

In the SI system, the units of power are watts:

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Efficiency• The ratio of power output to input

• Always less than 1 because engines always lose some input power to friction

Efficiency=Pou

tput

Pinput

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• Giancoli, Douglas. Physics: Principles with Applications 6th Edition. 2009.

• Walker, James. AP Physics: 4th Edition. 2010

• www.hyperphysics.com

References

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