Work (W) denoted as an uppercase W
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Is the application of force to an object that causes it to move some displacement (d)
Note: Work is a scalar quantity.
It has Magnitude
But no Direction
Kinetic Energy & Work
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Newton’s 2nd law of Motion (𝐹𝑛𝑒𝑡 = 𝑚𝒂)
𝒗𝑓2 − 𝒗2𝑖 = 2𝒂𝒅
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Substituting
_𝒗𝑓2 − 𝒗2𝑖 =
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𝐹𝑛𝑒𝑡
for a:
𝑚
2𝐹𝑛𝑒𝑡 𝑑
𝑚
Multiplying both sides of the equation by ½ m
_1⁄2 𝑚𝒗𝑓2 − 1⁄2 𝑚𝒗2𝑖 = 𝑭𝒏𝒆𝒕 𝒅
The left side of the mathematical relationship is equal to the change in Kinetic Energy of the system.
_𝐾𝐸 = 1⁄2 𝑚𝑣𝑓2 − 1⁄2 𝑚𝑣𝑖2
The right side of the mathematical relationship is equal to the amount of Work done by the
environment on the system.
_𝑊 = 𝑭𝒏𝒆𝒕 𝒅
Word-Energy Theorem
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states that the work done on an object is equal to its change in kinetic energy.
ΔKE = W
Note: this condition is true only when there is no friction.
Units (of work):
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Joule (J)
1 Joule is equal to the amount of work done by a 1 Newton force over a displacement of 1
meter.
1 Nm (1 Newton meter)
_1𝑘𝑔 ∙ 𝑚2 /𝑠 2
Calculating Work
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What if the force is not completely in the same direction as the displacement of the object?
When all the force is not in the same direction as the displacement of the object, we can use
simple trig (Component Vector Resolution) to determine the magnitude of the force in the
direction of interest.
Hence: 𝑊 = 𝐹𝑑𝑐𝑜𝑠𝜃
Work: Conditions
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A force acting in the same direction as an object’s motion does positive work
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A force acting with a component in the same direction as the object’s motion does positive
work
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A force acting at the right angles to the motion does no work
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A force acting opposite the motion does negative work
Problem Solving:
Example 1:
Little Johnny pulls his loaded wagon 30.0 meters across a level playground in 1 minute while applying a
constant force of 75.0 Newtons. How much work has he done? The angle between the handle of the
wagon and the direction of motion is 40°.
The moon revolves around the Earth approximately once every 29.5 days. How much work is done by
the gravitational force?
The crate below is pushed at a constant speed across the floor through a displacement of 10m with a
50N force.
a) How much work is done by the worker?
b) How much work is done by friction?
c) What is the total work done?
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Power = W/t (units are Joule/second(J/s) or Watts(W)
Simple machines
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Generally use a smaller force over a longer distance to get the same work done. A lever (like a
crowbar) can apply a greater force over a small distance.
Example 5
Recalling Johnny in Ex. 1 pulling the wagon across the school yard. He expended 1,720 Joules of energy
over a period of one minute. How much power did he expend?
Alternate representations for Power
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As previously discussed, 𝑃𝑜𝑤𝑒𝑟 =
𝑑
𝑡
𝑊𝑜𝑟𝑘
𝑇𝑖𝑚𝑒
(P = amount of work done per unit of time)
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Alternatively, 𝑃𝑜𝑤𝑒𝑟(𝑃) = 𝐹 ∙ since d/t = Velocity
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𝑃 = 𝐹 ∙ 𝑣 (Power is equals to Force times Velocity)
In this case here, we are talking about an average force and an average velocity
Example 4:
A corvette has an aerodynamic drag coefficient of 0.33, which translates to about 520.0 N of air
resistance at 26.8 m/s. In addition to this frictional force, the friction due to the tires is about 213.5 N.
Determine the power output of the vehicle at this speed.
Key Ideas
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Energy of motion is Kinetic Energy = 1⁄2 𝑚𝑣 2
Work = The amount of energy required to move an object from one location to another.
The Work-Energy Theorem states that the change in kinetic energy of a system is equal to the
amount of work done by the environment on that system.
Power is a measure of the amount of work done per unit of time.
Short review/quiz?
1. A force of 10 N works on a ball over a distance of 5 m. The force is parallel to the displacement
of the ball. What is the total work done by the force?
2. A force of 10 N works on a ball over a distance of 5 m. The force is perpendicular to the
displacement of the ball. What is the total work done by the force?
3. A force of 10 N works on a ball over a distance of 5 m. The force is antiparallel to the
displacement of the ball. What is the total work done by the force?
4. The work done by a given force over a given distance is proportional to?
a. Velocity
b. The cosine of the angel between the force and the displacement
c. The sine of the angle between the force and the displacement
d. The time during which the force acts
5. What is the sign of the work performed on an object in uniform circular motion? (what)
6. How much work is performed by gravity on an object of mass m in free fall over a distance of h
meters?
a. mh
b. mgh
c. mg/h
d. mh/g
7. A force of 1 N, parallel to the displacement of the object, acts on an object over a distance of 1
m. How much work is done?
8. How is work related to acceleration?
9. A constant force of 10 N causes a box to move at a constant speed of 2 m/s. How much work is
done in 10 seconds?
10. A mass is kept stationary by an external force. All of the following are true EXCEPT:
a. The point of application of the force does not move
b. No work is done on the mass
c. There is no net force on the mass
d. The external force may perform work on the mass
11. What is the magnitude of the work done by a force acting on a particle instantaneously?
a. Zero
b. Positive
c. Negative
d. None of the above
12. The Word-Energy Theorem states that the ____ done on an object is equal to its change in
kinetic energy.
13. The work done by friction over any distance is always ________.
14. The sum of the change in kinetic and potential energy is always ____
ANSWER KEY
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
50 N
0N
-50 N
B.
Zero (0)
B.
1 Joule
(idk yet, im trying to figure it out_
200 Joules
D.
A.
Work
Negative
Zero