1. Work
AP Physics C

2. Energy Energy is the ability to do work.
It is the capability to produce a change.
There are not different kinds or forms of energy.
Energy is stored in different modes.

3. Some Energy Considerations
Energy can be transformed from one form to another
Essential to the study of physics, chemistry, biology, geology, astronomy
Can be used in place of Newton’s laws to solve certain problems more simply

4. Energy Storage Non Mechanical Energy is stored at the atomic level.
heat energy, light energy, sound energy, nuclear energy, or chemical energy
Mechanical energy is associated with the motion and position of an object.
kinetic energy, gravitational potential energy, elastic potential energy, electric potential energy, magnetic potential energy
By identifying the change, you can identify the means of energy storage and transfer

5. Transfer of energy
Transferring energy into or out of a system is doing work.
Energy is transferred into or out of a system by three modes.
Heat (Q) is energy transfer due to a difference in temperature
Radiation (R) is energy transfer by photons/EM waves
Work (W) is energy transfer by external forces

6. Work Provides a link between force and energy
The work, W, done by a constant force on an object is defined as the product of the component of the force along the direction of displacement and the magnitude of the displacement

7. There are many different TYPES of Energy.
Energy is expressed in JOULES (J)
4.19 J = 1 calorie
Energy can be expressed more specifically by using the term WORK(W)
Work = The Scalar Dot Product between Force and Displacement. So that means if you apply a force on an object and it covers a displacement you have supplied ENERGY or done WORK on that object.

8. Scalar Dot Product?
A product is obviously a result of multiplying 2 numbers. A scalar is a quantity with NO DIRECTION. So basically Work is found by multiplying the Force times the displacement and result is ENERGY, which has no direction associated with it.
A dot product is basically a CONSTRAINT on the formula. In this case it means that F and x MUST be parallel. To ensure that they are parallel we add the cosine on the end.
W = Fx
Area = Base x Height

9. Work, cont. F is the magnitude of the force
∆x is the magnitude of the object’s displacement
q is the angle between

10. Work, cont. This gives no information about
the time it took for the displacement to occur
the velocity or acceleration of the object

11. WORK
In order for work to be done, a force must be applied to an object AND the force must cause a displacement.
If the force and displacement are:
in the SAME direction, the force helps cause the displacement
In the OPPOSITE direction, the force hinders the object’s displacement

12. When Work is Zero Displacement is horizontal Force is vertical
cos 90° = 0

13. The meaning of positive/negative work
If the energy transfer is from the environment to the system:
Work is positive
The energy of the system increases
Velocity or height increases
If the energy transfer is from the system to the environment:
Work is negative
The energy of the system decreases
Velocity or height decreases

14. Work Can Be Positive or Negative
Work is positive when lifting the box
Work would be negative if lowering the box
The force would still be upward, but the displacement would be downward

15. Work and Dissipative Forces
Work can be done by friction
For now, the phrase “Work done by friction” will denote the effect of the friction processes on mechanical energy alone
The energy lost to friction by an object goes into heating both the object and its environment
Some energy may be converted into sound

16. Work
The VERTICAL component of the force DOES NOT cause the block to move the right. The energy imparted to the box is evident by its motion to the right. Therefore ONLY the HORIZONTAL COMPONENT of the force actually creates energy or WORK.
When the FORCE and DISPLACEMENT are in the SAME DIRECTION you get a POSITIVE WORK VALUE. The ANGLE between the force and displacement is ZERO degrees. What happens when you put this in for the COSINE?
When the FORCE and DISPLACEMENT are in the OPPOSITE direction, yet still on the same axis, you get a NEGATIVE WORK VALUE. This negative doesn't mean the direction!!!! IT simply means that the force and displacement oppose each other. The ANGLE between the force and displacement in this case is 180 degrees. What happens when you put this in for the COSINE?
When the FORCE and DISPLACEMENT are PERPENDICULAR, you get NO WORK!!! The ANGLE between the force and displacement in this case is 90 degrees. What happens when you put this in for the COSINE?

17. Example
A box of mass m = 2.0 kg is moving over a frictional floor ( uk = 0.3) has a force whose
magnitude is F = 25 N applied to it at an angle of 30 degrees, as shown to the left. The box is observed to move 16 meters in the horizontal direction before falling off the table.
a) How much work does F do before taking the plunge?

18. Example cont’
What if we had done this in UNIT VECTOR notation?

19. Example cont’ How much work does the FORCE NORMAL do and Why? Fn
There is NO WORK since “F” and “r” are perpendicular. Ff
How much work does the frictional force do?
Note: This “negative” does not specify a direction in this case since WORK is a SCALAR. It simply means that the force is involved in slowing the object down. J

20. What if the FORCE IS NOT CONSTANT?
The function here MUST be a “FORCE” function with respect to “x” or “r”. Let’s look at a POPULAR force function.
Is this function, with respect to “x” ?
NO!
You can still integrate the function, it simply needs to be modified so that it fits the model accordingly.

21. Work-Energy Theorem
Kinetic energy is the ENERGY of MOTION.

22. Example W=Frcosq
A 70 kg base-runner begins to slide into second base when moving at a speed of 4.0 m/s. The coefficient of kinetic friction between his clothes and the earth is He slides so that his speed is zero just as he reaches the base (a) How much energy is lost due to friction acting on the runner? (b) How far does he slide?
-560 J
= N
1.17 m

23. Another varying force example..
A ball hangs from a rope attached to a ceiling as shown. A variable force F is applied to the ball so that:
F is always horizontal
F’s magnitude varies so that the ball moves up the arc at a constant speed.
The ball’s velocity is very low
Assuming the ball’s mass is m, how much work does F do as it moves from q = 0 to q = q1?

24. Example Cont’
Tcosq T
Tsinq mg

25. Example Cont’
The energy of POSITION or STORED ENERGY is called Potential Energy!

26. Something is missing….
Consider a mass m that moves from position 1 ( y1) to position 2 m,(y2), moving with a constant velocity. How much work does gravity do on the body as it executes the motion?
Suppose the mass was thrown UPWARD. How much work does gravity do on the body as it executes the motion?
In both cases, the negative sign is supplied

27. The bottom line..
The amount of Work gravity does on a body is PATH INDEPENDANT. Force fields that act this way are CONSERVATIVE FORCES
FIELDS. If the above is true, the amount of work done on a body that moves around a CLOSED PATH in the field will always be ZERO
FRICTION is a non conservative force. By NON-CONSERVATIVE we mean it DEPENDS on the PATH. If a body slides up, and then back down an incline the total work done by friction is NOT ZERO. When the direction of motion reverses, so does the force and friction will do NEGATIVE WORK in BOTH directions.

28. Force can be found using the DERIVATIVE
Since work is equal to the NEGATIVE change in potential energy, the FORCE of an object is the derivative of the potential energy with respect to displacement. Be very careful handling the “negative” sign.