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Work in 1 dimension

- 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

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.

Work in 2 dimensions

- 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.

The work done may be positive, zero, or negative, depending on the angle between the force and the displacement

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

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

Work and Energy

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

Kinetic Energy KE

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

KE=1/2mv2

Potential Energy PE

- 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

PE=mgy

Work-Energy Principle or Theorem

- 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.

Wnet=ΔKE

Potential energy can also be stored in certain materials when they are compressed; the figure below shows potential energy yielding kinetic energy.

Hooke’s Law

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

Elastic potential energy

- The force increases as the spring is stretched or compressed
- Potential energy of the compressed or stretched spring measured from its equilibrium position

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 gravity

If the object were to return to the starting point no net work would be done

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

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

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

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

6-10 Power

Power is the rate at which work is done

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

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

Efficiency

- The ratio of power output to input
- Always less than 1 because engines always lose some input power to friction

Efficiency=Poutput

Pinput

References

- Giancoli, Douglas. Physics: Principles with Applications 6th Edition. 2009.
- Walker, James. AP Physics: 4th Edition. 2010
- www.hyperphysics.com

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