Chapter 13: Work and Power

Work and Energy

Energy is one of the most important unifying concepts in all of the physical science.
Conservation of energy states that in any isolated system the total energy of all forms is constant
* Conservation laws play a vital role in all of physical science.
* Conservation of mass: Matter cannot be created or destroyed.
* Kinetic energy is energy associated with mass in motion.
* Conservation of energy can be generalized to include energy associated with every kind of physical phenomenon.
* Force acting on a body does work on the body only when the body moves.

* Work Wk = when a body moves a distance s along a straight line while a constant force of magnitude F, directed along the line, acts on it.

* The work W done by this force when its point of application undergoes a displacement and the component of the force in the direction of the displacement.The componenet of F in the direction of s is F cos@ .Then

W = (F cos @) s


* Alternative interpretation:
W = F s

* Work is a scalar quantity, even though force and displacement is vector.
* When force and displacement are perpendicular, the force does no work.
* The joules is the unit of work and of energy of all kinds.

Scale for work

1 joule = (1newton) (1meter)
1 J = 1Nm
1 dyn = 10-5
1cm = 10-2
1J = 0.7376 ft.lb
1ft.lb = 1.356 J

Power

Power deals with the description of how quickly work is done or the time rate at which work is done or energy transferred.

Average power = Work done---------------Pav = W
--------------------time interval---------------------t

SCALE FOR POWER
1J/s = Watt
1hp = 550ftlb/s = 33000ftlb/min
1hp = 746W = 0.746kW
1kWh = 3.6 X 10^6 J = 3.6MJ

Formulas of POWER;
P = F.v----------------P = mav-------- P = mg(d / t)

P = F(d / t)----------------P = Wk / t

Sample Problem
1. A jet airplane engine develops a thrust ( a forward force on the plane) of 15,000N ( roughly 3000lb). When the plane is flying at 300m/s (roughly 600 mph), what horsepower does the engine develop?
P = F.v = (15000N) (300m/s) = 4.5X 10^6 W or 6030hp

2. As part of a charity fund-raising drive a Philippine marathon runner of mass 50.0kg runs up the stairs to the top of the Peninsula hotel, one of the tallest building in the Philippines (443m), in 15.0minutes.Find the average power output of the runner in watts, Kilowatts, and lastly in horsepower.

W = mgh = (50.0kg)(9.80m/s2)(443m) = 2.17 X 10^5 J

P = Wk / t = 2.17 X 105 J = 241 W or 0.241kW or 0.323hp
-------------------900s
Vave = d / t = 443m / 900s = 0.492 m/s

P = F.Vave = mg Vave = (50.0kg)(9.80m/s2)(0.492m/s) = 241 W

3. A boy with a mass 60kg walks up a flight of stairs 12m high in 30 seconds. What power has he used?
P = mg(d / t) = 60kg (10m/s^2)[(12m)/30s] = 240watts

4. A jet engine develops a thrust ( or forward force) of 1.5 X 10^4 N. When the plane is flying at 300m/s, what power in kilowatts is developed?
P = F.v = (15000N) (300m/s) = 4.5X 10^3 kW

5. A motor is rated at 20kW.At what speed in m/s can this motor raise a load weighing
2.5X 10^5N?

V = P / F

V= (20kW) (1000w/kW) = 2.0X10^4W = 0.8 X 10^-2m/s or 0.08m/s
------------------2.5X 10^5N--------2.5X 10^5N