Question

If you perform 40 J of work lifting a 10-N box from the floor to a shelf, how high is the shelf?

Answer 1

Before anything, if you are lifting the Work value have to be negative, reason is because the formula to the work of the weight is:

$w = p \times d \times cos \: \theta$
*Photo to help you to visualize. (P = Weight Force, F = Force)

If you are lifting, you are exercising a force that opposes the Weight Force, Force up (lifting) and Weight Force down (gravity pulling).
This forms a 180 angle and the cos 180 = -1.

Well let's do the question:

Work (W) = -40 J (Joule = Kg x m^2/s^2)
(negative, explanation given)

Weight Force (P) = 10 N (Newton = kg x m/s^2)

Distance (D) = ?

W = P x d x cos theta

-> -40 = 10 x d x -1
-> -40 = -10 x d
-> d = -40/-10 (J/N)
-> d = 4 meters

$d =j \div n \\ d = ((kg \times {m}^{2} ) \div {s}^{2}) \div ((kg \times m) \div {s}^{2}) \\ d = m \: (meters)$