The sign of work done by a force on a body is important to understand .State carefully if the following quantities are positive or negative :
(a) work done by a man in lifting a bucket out of a well by means of a rope tied to the bucket .
(b) work done by gravitational force in the above case ,
(c ) work done by friction on a body siding down an inclined plane ,
(d ) workdone by an applied force on a body moving on a rough horizontal plane woth uniform velocity .
(d) work done by the resistive force of air on a vibrating pendulum in bringing it to rest .

Explanation

We know that work `W = Fd cos theta` , where `theta ` is the angle between `vec(F ) and vec(d)` .
(a) Here , displacement of a bucket is in the direction of force exterted on bucket so `theta = 0^(@)`
` :. Cos 0^(@) =1 " " : W = Fd cos 0^(@) =Fd `
` :. ` Work is positive .
(b) Work done is negative ,because gravitational force is in the downward and displacement of bucket is upward direction so , `theta = 180^(@)`
` :.W = Fd cos 180^(@)`
` :. W = - Fd " " [ :. cos 180^(@) =-1]`
(c ) Work done is negative , because force of friction is acting against the displacemnt so `theta = 180^(@)`
` :. W = fd cos 180^(@)`
` :.W = Fd `
(e) Work done is negative , because the resistive force of air opposes the motion so , `theta = 180^(@)`
` :. W - Fd cos 180^(@)`
` :. W = - Fd `