You pick up a 3.4-kg can of paint from the ground and lift it to a height of 1.8 m. (a) how much work do you do on the can of paint? (b) you hold the can stationary for half a minute, waiting for a friend on a ladder to take it. how much work do you do during this time? (c) your friend decides not to use the paint, so you lower it back to the ground. how much work do you do on the can as you lower it?

(a) For the work-energy theorem, the work done to lift the can of paint is equal to the gravitational potential energy gained by it, therefore it is equal to

where m=3.4 kg is the mass of the can, g=9.81 m/s^2 is the gravitational acceleration and is the variation of height. Substituting the numbers into the formula, we find

(b) In this case, the work done is zero. In fact, we know from its definition that the work done on an object is equal to the product between the force applied F and the displacement:

However, in this case there is no displacement, so d=0 and W=0, therefore the work done to hold the can stationary is zero.

(c) In this case, the work done is negative, because the work to lower the can back to the ground is done by the force of gravity, which pushes downward. Its value is given by the same formula used in part (a):

this could be newton#'s law of cooling. the cooling curve is exponential