Work and Energy Study Guide

Previous scribe was abducted by aliens and hasn't scribed ever since, so I inherited his scribing powers under the "first come, first serve" rule.

The study guide is straightforward. Basic stuff. Grade 12 physics students can do this in their sleep.


10.1 WORK AND ENERGY STUDY GUIDE

Note: Capitalized words are the answers to fill-in-the-blanks.

Work
Work is the product of the FORCE exerted on an object and the DISTANCE the object moves in the DIRECTION of the force. The equation used to calculate work is W = Fd. In this equation, W stands for WORK, F stands for FORCE, and d stands for DISTANCE. Work has no direction, so it is a scalar quantity. The SI unit of work is the JOULE. When a force of one NEWTON moves an object a distance of one METRE, one JOULE of work is done. Work is done on an object only if the object MOVES. Work is done only if the FORCE and the DISTANCE are in the same direction.

Work and Direction of Force
If a force is exerted IN THE DIRECTION OF the motion, work is done. If a force is exerted PERPENDICULAR to the motion, no work is done. If a force is exerted at another angle to the motion, only the component of the force IN THE DIRECTION OF the motion does work. The magnitude of this component is found by multiplying the force applied by the COSINE of the angle between the force and the DIRECTION OF THE MOTION. When friction opposes motion, the work done by friction is NEGATIVE. When work is done on an object, ENERGY is transferred. Work is the transfer of energy as the result of MOTION. This transfer can be POSITIVE or NEGATIVE.

Power
Power is the RATE of doing work, or the RATE at which ENERGY is transferred. The equation used to calculate power is P = W/t. In this equation, P stands for POWER, W stands for WORK, and t stands for TIME. The unit of power is the WATT. One JOULE of energy transferred in one second equals one watt. This is a very small unit, so power is often measured in KILOWATTS.

1. Symbol for kinetic energy: K
2. Calculation of kinetic energy: mv^2/2
3. Symbol for work: W
4. Calculation of work: Fd
5. Statement that the work done on an object is equal to the object’s change in kinetic energy: Delta K = W
6. Equivalent to 1 kg*m^2/s^2: 1 J

7. Through the process of doing work, energy can move between the environment and the system as the result of FORCES.
8. If the environment does work on the system, the quantity of work is POSITIVE.
9. If the environment does work on the system, the energy of the system INCREASES.
10. If the system does work on the environment, the energy of the system DECREASES.
11. In the equation W = Fd, Fd holds only for CONSTANT forces exerted in the direction of displacement.
12. In the equation W = Fd cos theta, angle theta is the angle between F and the X-AXIS.


13. W > 0: B, E, F
14. W = 0: A, D
15. W < 0: C


16. What was the magnitude of the force acting on the crate? 30.0 N
17. How far did the crate move horizontally? 0.50 m
18. What does the area under the curve of this graph represent? work
19. How much work was done in moving the crate 0.1 m? 3.0 J

20. Rate of doing work: power
21. Unit of power: watt
22. Symbol for power: P
23. Calculation of power: W/t
24. 1000 watts: kW

Next scribe is KAMIL.

Derivation for Circular Motion Formulas

Deriving a formula for velocity, acceleration, and the centripetal force when in a circular motion...


LEGEND
v = velocity (or speed, if direction is not indicated)
d = displacement (or distance, if direction is not indicated)
t = time (interval)
R = radius
a = acceleration
a_c = centripetal acceleration
F = force
F_net = net force
F_c = centripetal force
m = mass


1.
The distance an object moves in a circular motion is the circumference of the circular motion, which is equal to 2*pi*R. Using the definition of circumference (c=π*2*r) and the definition of velocity (v=d/t), we can derive this formula: v=2*π*R/t.

2.
Draw the circular motion, two radii, and two velocity vectors. Add the two radii vectors to get the net radius. Add the two velocity vectors to get the net velocity.

3.
Since the change in radii over the radius equals the change in velocities over a velocity (ΔR/R = Δv/v), using the definition of velocity (v=ΔR/Δt) and acceleration (a=Δv/Δt), we can derive this formula: a=v^2/R.

4.

Using the acceleration formula that we recently derived (a=v^2/R), we can use substitute velocity with v=2*π*R/t to get a more fancy-looking formula for centripetal acceleration (a=4*π^2*R/T).

5.
Using Newton's Second Law of Motion (F_net=m*a), we can substitute acceleration with a=v^2/R to get the formula for centripetal force (F_c=m*v^2/R), which can be derived even further using v=2*π*R/t to get F_c=4*π^2*R/t^2.

• Centripetal Force lab is due and was handed in today.
• Centripetal Acceleration and Centripetal Force assignments is due tomorrow.
• Next scribe is ERIC.