1. Newton’s laws of Motion
PHYS 101
Newton’s laws of Motion
Ionizing Radiation
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Work, Energy and Power
Wave properties
of light
Fluids
Nerve Conduction
Direct Current (DC)
Instructor: Sujood Alazzam
2017/2018

2. 6.3 Potential energy and Conservative forces
Lecture 6:
6.3 Potential energy and Conservative forces
6.9 Power

3. CHAPTER OUTLINE Work, Energy and Power: 6.1 Work 6.2 Kinetic energy.
6.3 Conservative forces and potential energy.
6.5 Observations of work and energy.
6.9 Power.

4. OBJECTIVES
We should be able to define potential energy, identify the standard unit of potential energy.
We should be able to define mechanical energy and relate it to the amount of kinetic energy and potential energy.
We should be able to define power and identify its units.

5. 6.3 POTENTIAL ENERGY AND
CONSERVATIVE FORCES

6. 6.3 POTENTIAL ENERGY AND CONSERVATIVE FORCES
 is the energy that is stored in an object due to its position relative to some zero position
For example, the heavy ball of a demolition machine is storing energy when it is held at an elevated position. This stored energy of position is referred to as potential energy.
Potential energy U=m g h

7. In Fig. 6.8a, a ball rises from an initial height h. to a height h
The gravitational force mg is opposite in direction to the displacement s = h – h.
so the work done is negative:

8. U- U.= m g (h – h. ) =W(grav) = =F x cos Ɵ
The magnitude of ∆ U is defined to be equal to the magnitude of W(grav), so we write:
U = U. +W(grav)
U- U.= m g (h – h. ) =W(grav) = =F x cos Ɵ

9. so we have the important result
The sum of the kinetic energy and the potential energy is called the total mechanical energy,
so we have the important result
K + U= K. + U.
E = K + U

10. Idea#3 - Do not delete this text. Is needed for animation to work.
Example
A woman skis from rest down a hill 20 m high (Fig. 6.9). If friction is negligible, what is her speed at the bottom of the slope?

11. Process connections– Do not delete this text box
1. The forces acting on the skier are her weight and a normal force due to the ground.
2. The normal force does no work because it is perpendicular to the displacement.
3. No work is done by applied forces, and the total energy E = K + U is constant
4. We choose the bottom of the slope as the level ,so the final potential energy is U = 0
5. The kinetic energy at the top is K.=0 since she starts from rest.
6. Her potential energy there is U = mgd
7. Her final kinetic energy at the bottom of the hill is K=½ mv2
Thus
K + U = K. + U. Becomes
½ m v2 = + m g d

12. Conservative force
Conservative force—a force with the property that the work done in moving a particle between two points is independent of the path it takes.

13. Idea#1 - Do not delete this text. Is needed for animation to work.
6.5 OBSERVATIONS ON WORK
AND ENERGY
we see that energy occurs in many forms. It has been found experimentally that energy can be changed into different forms, but it is never created or destroyed.
This is the principle of conservation of total energy.

14. SOLVING PROBLEMS USING
WORK AND ENERGY
These quantities are then
related by
E = E. + W. 1
The procedure includes
the following steps:
We draw a force diagram 3
calculate the work done and the mechanical energy 2
This step may be done mentally in simple cases, but it is very helpful in complex situations to actually draw the diagram.
That may be included in the potential energy, as well as the applied forces that do work.
We identify
the conservative forces

15. EXAMPLE
In the pole vault, an athlete uses a pole to convert the kinetic energy of running into potential energy when the pole is vertical (Fig. 6.I2). A good sprinter runs at a speed of 10 m s-1. Disregarding the additional height the athlete gains by using his arms to raise his center of gravity well above the position of his hands on the pole, how high can the athlete raise his center of gravity?

16. U. = 0 and K. =1/2 m v2 where v = 10 m s-1
Just before the athlete begins to use the pole,
U. = 0 and K. =1/2 m v2 where v = 10 m s-1
At the top of an ideal jump,
v = 0, so K =0 and U = mgh
where h is the height of his center of gravity above its initial position. Since only the force of gravity acts on the airborne jumper,
E = E.

17. 6.9 POWER
POWER:- When an amount of work W is done in a time t, the power is defined as the rate of doing work,
Like work and energy, power is a scalar quantity.

19. Average Power
When a quantity of work is done during a time interval , the average work done per unit time or average power is defined to be M.K.S System joule/sec (or) kg m2 s-3 (or) watt.

20. Alternative Formulae for Power
Thus the power associated with force F is given by
where v is the velocity of the object on which the force acts.
P = F . v = F v cos θ

21. This is a high power output for a human.
Example
A 70-kg man runs up a flight of stairs 3 m high in 2 s. (a) How much work does he do against gravitational forces? (b) What is his average power output?
The work done, W, is equal to his change in potential energy, mgh. Thus  W = mgh = (70 kg)(9.8 m/s2 )(3 m) = 2060 J
(b) His average power is the work done divided by the time,
P =  W/  t = 2060J /2 s = 1030 watt
This is a high power output for a human.

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