Work done by a Force, Physics Assignment Help

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If a force 952_work,power and energy.pngis performing on a particle and displacement of particle becomes 1001_work,power and energy1.png then work done by this force 952_work,power and energy.pngis in interval A to B will be 92_work,power and energy2.png for constants force 952_work,power and energy.pngand if force 952_work,power and energy.pngis variable then we will have to split the path from A to B in small intervals and after that we will have to include all the small works.

803_work done by a force11.png

78_work done by a force12.png

678_work done by a force.png 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

Negative Work

Zero Work Done

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.

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.

Work given by a force is zero if

(i) F = 0           (ii) s = 0

(iii) cos Θ = 0  1101_linear motion.png 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.

 

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,

1005_work done by a force1.png

In terms of rectangular components,1217_work done by a force2.png      

431_work done by a force3.png

Graphically area inside the force-displacement graph is the work done.

783_work done by a force4.png

 

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.

2048_work done by a force5.png

Here 1787_work done by a force6.png are the displacements of points of application of forces 1165_work done by a force7.png respectively.

In case of tight body and pure translational motion we get 1241_work done by a force8.png

1620_work done by a force9.png

2145_work done by a force10.png When there is no reformation or deformation and no rotation is involved. 

 

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