where 1 and 2 shows the position of A and B respectively.
It is important to notice that work is a scalar physical quantity and it can be +ve, may be -ve and can be zero.
For work by constant force w = Fr cosΘ
Work may be positive negative or zero
Positive Work
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Negative Work
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Zero Work Done
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Work given by a force is positive if angle between the force and displacement is less than 90o. In other words work is positive if the element of force is in the direction of displacement. Positive work on an object increases its kinetic energy.
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Work done by a force is negative if angle between force and displacement is bigger than 90o.
In other words work is negative if the element of force is opposite to the displacement.
Negative work on an object decreases its K.E.
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Work given by a force is zero if
(i) F = 0 (ii) s = 0
(iii) cos Θ = 0 Θ = 90o.
When the force and the displacement are perpendicular, the work done is zero. A tension perpendicular to displacement doesn't modify magnitude of velocity and is only responsible for modification in direction of motion. So zero work gives no change in K.E.
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Work done by a Variable Force: When the direction and magnitude of a force vary in three dimensions, it may be expressed as a function of the position. For a variable force work is determined for infinitely small displacement and for this displacement force is taken to be constant.
Mg(h/x)
The total work done will be addition of infinitesimal small work,
In terms of rectangular components,
Graphically area inside the force-displacement graph is the work done.
Work Done by Several Forces: When several forces perform on a body then the net work done on the body is the algebraic sum of work done by individual forces.
Here are the displacements of points of application of forces respectively.
In case of tight body and pure translational motion we get
When there is no reformation or deformation and no rotation is involved.
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