Lesson_Text_3.1

# Lesson_Text_3.1 - 1 Lesson 3.1 Work and Power 1 Work done...

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1 Lesson 3.1 Work and Power 1. Work done by a constant force: Only a force can do work. A force does work when it produces displacement in the direction of the force. We will only consider here forces that remain constant, that is the force remains the same through out the displacement. Work done by a force is measured as the product of the component of the force in the direction of displacement and the magnitude of the displacement . x F A Fig. 1a Displacement is in the direction of the force. B θ F F cos θ x A Fig. 1b F cos θ is in the direciton of displacement B In fig. 1a above, a force F displaces an object from position A to position B, a displacement = x in the direction of the applied force. In this case, the work done is given by W = F x …. (i) In fig. 1b, the displacement is not in the direction of the force. The force makes an angle θ with the displacement vector. Therefore, the component of the force in the direction of displacement is F cos θ . Work is done by the component of the force in the direction of displacement. Therefore, the work done is given by W = F Cos θ x ……(ii) The unit of force is the newton (N) and the unit of displacement is the meter (m). Therefore, the unit of work is N.m which is called joule (J).

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2 While the work done by a positive force is positive, the work done by a negative force is negative. For example a book placed on a table can be lifted without causing acceleration by applying an upward force equal to the weight of the book. When the book is placed at a height y, the work done by the applied force is given by: W = mg y Here mg is the applied upward force equal to the weight of the book and y is the upward displacement. At the same time, the force of gravity acting in the opposite direction of motion also does work on the book. The force of gravity is –mg. The work done by this force in raising the book through a height y is given by: W = -mgy Fig.2 A n upw ard f orc e mg produc es an upw ard dis plac ement y m g m g m g The work done by the applied force to raise the book is positive, while the work done by the force of gravity is negative.
3 2. Work is represented by the area under force versus displacement graph . F x area = F . x =Work Fig. 3 Work done is area under the force-displacement graph Fig.3 above shows the graph of force (F) against x (displacement) where F remains a constant throughout the displacement. Because F does not change, the graph is a horizontal line (shown in red in the figure). The area under this horizontal line is a rectangle and its area is given by F . x which is a measure of the work done. This can be generalized and we can say that Work done by a force is given by the area under the force-displacement graph Example 4 : A tractor exerts a constant force of 5.0 × 10 3 N on a horizontal chain while moving a load a horizontal distance of 30 cm. How much work is done by the tractor? Solution

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## This note was uploaded on 05/01/2011 for the course PHY 2048 taught by Professor George during the Fall '10 term at Edison State College.

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Lesson_Text_3.1 - 1 Lesson 3.1 Work and Power 1 Work done...

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