Download Unit 6: Work, Power and Energy Lab Activities and Handouts

Unit 6: Work, Power and Energy
Reading and Homework: Tipler Chapter 6 & 7.1 - 7.3
Problem Set
Reading
Chap/Sec
PS1
PS2
PS 3
PS 4
PS 5
PS 6
PS 7
PS 8
PS 9
PS 10
6/1
6/1
6/2
6/2-3
6/4
6/4
7/1
7/2
7/3
Problems
http://www.physicsclassroom.com/
Physics Tutorial  Work, Power & Energy  Lesson 1: Read
and answer all questions, checking yourself as you go and
briefly recording answers to the “Check your Understanding”
questions only. (There are 21 Questions all together)
20, 21, 22, 23, 24
(W-KE Theorem, constant F)
1, 2, 25, 26, 27, 29
(W-KE Theorem, variable F)
35, 36, 37, 38, 39
(Dot-Product)
46, 47, 48, 49, 50, 51
(Power)
10, 11, 55, 57, 58, 59
(Potential Energy)
12, 62, 63, 64, 65, 68
(Potential Energy and Equilibrium)
16, 18, 19, 20, 24, 31, 33, 37
(Cons. Of Mech. Energy)
43, 44, 46, 48
(W- E Theorem, Cons. of E)
Ch. 6: 4, 5, 6, 7, 9; Ch. 7: 2, 3, 4, 6, 53
(Review)
Lab Activities and Handouts:
•
•
•
•
Your Power Lab
Work-Kinetic Energy Lab
Pulley Lab
MOPS Activities (W & KE): 850, 870,
880
• “Cut Short” Lab
• Energy Skatepark Virtual Lab
• MOPS Activities (PE): 900, 910
Objectives
1. Recognize that a force does work on an object if the object moves through a
distance and there is a component of the force in the direction of the velocity
of the object. Distinguish this use of the word “work” from that used in
everyday language.
2. Identify the SI unit of work, the joule: 1 J = 1 N •m.
3. Express the work done by a constant force through a displacement in
mathematical terms: W = Fx Δx = F cos θ Δx
4. Recognize that the work done by a variable force can be related to the product
of average force and displacement or to the area under a graph of force as a
function of position.
5. Use integration to calculate the work done by a variable force F(x) on a object
as the object is displaced over a distance in one dimension.
AP Physics
W12
Unit 6 Objectives
1
6. Define kinetic energy: K = mv 2 .
2
7. Recognize the relationship between the Work-Kinetic Energy Theorem and
Newton’s Second Law.
8. Use the Work-Kinetic
Energy Theorem to solve problems involving constant and
€
variable forces.
9. Define the dot product (scalar product) of two vectors in terms of the angle
between the vectors and use unit vectors to write their dot product in terms of
the rectangular components of two vectors.
10. Apply the properties of the dot product to perform algebraic manipulations of
dot products and take the derivative of the dot product of two vectors.
11. Use dot-product notation to write a vector definition of the work done on a
s2
 
particle as it moves from point 1 to point 2: W = ∫ F ⋅ds .
s1
12. Use the vector definition of work to calculate the work done on an object as
the object is displaced in more than one dimension.
dW  
€
13. Define power as a rate at which a force
does work: P =
= F ⋅v.
dt
work done
14. Recognize that in cases of a constant force, power is P =
.
time
15. Calculate the mechanical advantage of simple machines (ramps and pulleys).
€
16. Define conservative or nonconservative forces and cite examples.
17. Define the change in Potential Energy of a system
in terms of the work done by
€
2 

internal conservative forces: ΔU = − ∫ F ⋅ ds .
1
18. Solve problems using potential energy concepts in 2 special cases:
• Gravitational Potential Energy: U = U 0 + mgy (near the earth’s surface)
1
• Potential Energy of€a Spring: U = kx 2 (U0 = 0 at x0).
2
19. Recognize force as the negative
derivative of potential energy and use it to
€
identify situations in which a system is in stable and non-stable equilibrium.
20. Define the total mechanical
energy of a system in terms of its kinetic and
€
potential energy and recognize that in the absence of non-conservative or
external forces, total mechanical energy of a system is conserved.
21. Recognize that the total energy of the universe is constant and that energy can
be converted from one form to another or one system to another, but cannot be
created or destroyed.
22. Describe how the energy of a system can be changed by work or by heat and
how to account for this using the Work-Energy Theorem.
AP Physics
2
W12
Unit 6 Objectives
23. Use energy conservation principles as an alternative to Newton’s Laws to solve a
variety of mechanics problems that require the determination of an objects
speed as a function of its position. These problems include:
Projectiles
Springs
Pendulums
Roller Coasters
Kinetic Friction
From the AP Board:
Work, Energy, Power
A. Work and the work-energy theorem
a. Students should understand the definition of work, including when it is positive, negative, or zero, so they can:
i. Calculate the work done by a specified constant force on an object that undergoes a specified displacement.
ii. Relate the work done by a force to the area under a graph of force as a function of position, and calculate this work
in the case where the force is a linear function of position.
iii. Use integration to calculate the work performed by a force F(x) on an object that undergoes a specified displacement
in one dimension.
iv. Use the scalar product operation to calculate the work performed by a specified constant force F on an object that
undergoes a displacement in a plane.
b. Students should understand and be able to apply the work-energy theorem, so they can:
i. Calculate the change in kinetic energy or speed that results from performing a specified amount of work on an
object.
ii. Calculate the work performed by the net force, or by each of the forces that make up the net force, on an object that
undergoes a specified change in speed or kinetic energy.
iii. Apply the theorem to determine the change in an object’s kinetic energy and speed that results from the application
of specified forces, or to determine the force that is required in order to bring an object to rest in a specified distance.
B. Forces and potential energy
a. Students should understand the concept of a conservative force, so they can:
i. State alternative definitions of “conservative force” and explain why these definitions are equivalent.
ii. Describe examples of conservative forces and non-conservative forces.
b. Students should understand the concept of potential energy, so they can:
i. State the general relation between force and potential energy, and explain why potential energy can be associated
only with conservative forces.
ii. Calculate a potential energy function associated with a specified one- dimensional force F(x).
iii. Calculate the magnitude and direction of a one-dimensional force when given the potential energy function U(x) for
the force.
iv. Write an expression for the force exerted by an ideal spring and for the potential energy of a stretched or compressed
spring.
v. Calculate the potential energy of one or more objects in a uniform gravitational field.
C. Conservation of energy
a. Students should understand the concepts of mechanical energy and of total energy, so they can:
i. State and apply the relation between the work performed on an object by non- conservative forces and the change in
an object’s mechanical energy.
ii. Describe and identify situations in which mechanical energy is converted to other forms of energy.
iii. Analyze situations in which an object’s mechanical energy is changed by friction or by a specified externally applied
force.
b. Students should understand conservation of energy, so they can:
i. Identify situations in which mechanical energy is or is not conserved.
ii. Apply conservation of energy in analyzing the motion of systems of connected objects, such as an Atwood’s
machine.
iii. Apply conservation of energy in analyzing the motion of objects that move under the influence of springs.
iv. Apply conservation of energy in analyzing the motion of objects that move under the influence of other non-constant
one-dimensional forces.
c. Students should be able to recognize and solve problems that call for application both of conservation of energy and
Newton’s Laws.
D. Power
Students should understand the definition of power, so they can:
a. Calculate the power required to maintain the motion of an object with constant acceleration (e.g., to move an object along
a level surface, to raise an object at a constant rate, or to overcome friction for an object that is moving at a constant
speed).
b. Calculate the work performed by a force that supplies constant power, or the average power supplied by a force that
performs a specified amount of work.
AP Physics
3
W12