1. بسم الله الرحمن الرحيم
Dr- Sonia Reda

2. Kinetic energy and Work
chapter 7
Kinetic energy and Work By
Dr\ Sonia Reda
Dr- Sonia Reda

3. chapter 7 Kinetic energy and Work
What is energy
7.3 Kinetic energy
7.4 Work
7.5 Work and kinetic Energy
7.6 Work done by the gravitational force
7.7 Work done by a Spring force
Power

4. Outline Chapter 7 Work and Kinetic energy
Work done by a net force results in kinetic energy
Some examples: gravity, spring, friction

5. However, this definition is too vague to be of help to us now.
What is Energy?  
The term energy is so broad that a clear definition is difficult to write.
Technically,
Energy is a scalar quantity associated with the state (or condition) of one or more objects.
However, this definition is too vague to be of help to us now.
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6. Kinetic Energy
Kinetic energy K is energy associated with the state of motion of an object.
For an object of mass m whose speed v is well below the speed of light, Kinetic energy K is:
Unit for Kinetic energy is:
Kinetic energy is a scalar quantity.
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7. Work
Work W is energy transferred to or from an object by means of a force acting on the object.
Energy transferred to the object is positive work,
Energy transferred from the object is negative work.
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8. Properties of Work
Only the force component along the object’s displacement will contribute to work.
The force component perpendicular to the displacement does zero work.
A force does positive work when it has a vector component in the same direction displacement,
A force does negative work when it has a vector component in the opposite direction.
Work is a scalar quantity.
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9. Finding an Expression for Work
                                                                                                                                    
we can use Eq to write, for components along the x axis,
v2 =vo2 + 2axd
By multiplying the above Eq with ½ m
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10. Finding an Expression for Work
                                                                                                                                    
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11. Work-Kinetic Energy Theorem
Change in KE work done by all forces
Chap 7.3
DK  Dw
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12. Vector sum of all forces acting on the body
Work-Kinetic Energy Theorem SF x
Vector sum of all forces acting on the body xf xi
Work and Energy
7.3 Work and Kinetic energy
Note that in the slide F is the net force acting on the body.
= 1/2mvf2 – 1/2mvi2
= Kf - Ki
= DK
Work done by net force
= change in KE
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13. Checkpoint 1
A particle moves along an x axis. Does the kinetic energy of the particle increase, decrease, or remain the same if the particle’s velocity changes
(a) from −3 m/s to −2 m/s and
(b) from −2 m/s to 2 m/s?
(c) In each situation, is the work done on the particle positive, negative, or zero?
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14. Example 7-3
During a storm, a crate of crepe is sliding across a slick, oily parking lot through a displacement
while a steady wind pushes against the crate with a force The situation and coordinate axes are shown in Fig. 7-5.
(a) How much work does this force do on the crate during the displacement?
                           .
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15. Work done by the wind force on crate :
(a)  How much work does this force from the wind do on the crate during the displacement?
SOLUTION: 
Work done by the wind force on crate :
The wind force does negative work, i.e. kinetic energy is taken out of the crate.
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16. (b)  If the crate has a kinetic energy of 10 J at the beginning of displacement , what is its kinetic energy at the end of ?
SOLUTION: 
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17. Work done by ALL forces = change in KE
Gravitation and work
Work done by me (take down as +ve)
= F.(-h) = -mg(-h) = mgh h
Work done by gravity
= mg.(-h) = -mgh F
________
Total work by ALL forces (W) = mg
=DK
Lift mass m with constant velocity
This example resolves the situation when there are 2 forces, which are equal and opposite. The change in KE is zero.
Work done by ALL forces = change in KE
DW = DK
What happens if I let go?
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18. Work Done by a Spring Force
The spring force given by Hooke’s Law:
The work done by spring force:
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19. Compressing a spring =DK What happens if I let go?
Compress a spring by an amount x F
-kx x
Work done by me Fdx = kxdx = 1/2kx2
Work done by spring -kxdx =-1/2kx2
Here also the two forces are equal and opposite
Total work done (DW) =
=DK
What happens if I let go?
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20. Moving a block against friction at constant velocityd
Work done by me = F.d
Work done by friction = -f.d = -F.d
Total work done =
Here again the two forces are equal and opposite
The force here (friction) is different from the gravity force or the spring force.
Friction is NOT a conservative force
What happens if I let go?
NOTHING!!
Gravity and spring forces are Conservative
Friction is NOT!!
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21. Sample Problem 7-8
In Fig. 7-11, a cumin canister of mass m = 0.40 kg slides across a horizontal frictionless counter with speed v = 0.50 m/s. It then runs into and compresses a spring of spring constant k = 750 N/m. When the canister is momentarily stopped by the spring, by what distance d is the spring compressed?
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22. SOLUTION: 
We assume the spring is massless. Work done by the spring on the canister is negative. This work is :
Kinetic energy change of the canister is :
Therefore,
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23. Power The rate at which work is done by a force is called the power.
The average power due to the work done by a force during that time interval as
We define the instantaneous power P as the instantaneous rate of doing work, so that
W = F . Δx
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24. The units of power
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25. Sample Problem 7-10
Figure 7-14 shows constant forces and acting on a box as the box slides rightward across a frictionless floor. Force is horizontal, with magnitude 2.0 N; force is angled upward by 60° to the floor and has magnitude 4.0 N. The speed v of the box at a certain instant is 3.0 m/s.
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26. (a)  What is the power due to each force acting on the box at that instant, and what is the net power? Is the net power changing at that instant?
SOLUTION: 
The kinetic energy of the box is not changing. The speed of the box remains at 3 m/s. The net power does not change.
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27. (b) If the magnitude of is, instead, 6
(b)  If the magnitude of is, instead, 6.0 N, what now is the net power, and is it changing?
SOLUTION: 
There is a net rate of transfer of energy to the box. The kinetic energy of the box increases. The net power also increases.
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28. THANK
شكـراً
YOU
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