Work

 

- For work to be done on an object, the following two

  conditions MUST be met:

- A force must be applied to the object.

- The object must move with some component of the

   displacement in the direction of the applied force.

- A type of energy.

- A scalar quantity. (Energy is a scalar quantity.)

- Can still have a sign (+/-).

      - Positive work is work done in the direction of motion

      - Positive work will speed up an object.

      - Negative work is work done in the opposite direction

         of the motion.

      - Negative work will slow an object.

- Product of force and the component of displacement in

   the direction of the force OR

  Product of the component of the force in the direction of

  the displacement and the displacement.

     

            W = (F cos θ) s

 

where θ is the angle between the force and displacement

vectors. Note, this result is NOT a vector (but a scalar.)

Note also, this equation assumes force is constant.

Work (continued)

 

- (In SI units) Has units of N m, or, kg m2 / s2, or joules (J).

 

      1 N m = 1 J

 

- Can also be measured in calories, Calories, eV, BTU’s,

   ergs, ft lb, kW hrs, etc…

 

Common usage: Everyone knows what work means…

 

Physics usage: If the above-mentioned conditions are not met, no work is being done!

 

 

Kinetic Energy

 

- Energy associated with motion.

 

KE = ½ m v2

 

where m is mass, and v is speed.

 

Note the SI units will be kg m2 / s2, which is = joule.

Work Energy Theorem

 

The work done on an object by a net (external) force is equal to the change in the KE of the object.

 

W = ΔKE = KEf - KEi

 

One can see, positive work means KEf must be larger than

KEi, therefore, the object must be speeding up.

 

Conversely, negative work means KEf must be less than KEi, therefore, the object must be slowing down.

 

Work-Energy Theorem lets us solve “old” problems in a new way. In some cases, problems may be solvable that are difficult or impossible using kinematics and Newton’s 2nd Law.


Potential Energy

 

- Energy associated with position.

- Stored energy.

- Gravitational potential energy is energy an object has due

   to its position in a gravitational field.

 

PE = m g h

 

where m is mass, and g is g, and h is the height of the object above some specific reference level.

 

Note the SI units will be kg (m / s2) m which is …

 

The work done on an object by the force of gravity is equal to the negative of the change in the PE of the object.

 

Wg = -ΔPE = PEi - PEf

 

Positive work means PEf must be smaller than PEi, therefore, the object must be moving downwards.

 

This simple concept is only included here to confuse otherwise clear-thinking physics students.