Answer to Question #201972 in Physics for Niii

Question

A 3.2 kg statue of Einstein is on a shelf 2.00 m above the floor.  You do 18 J of negative work to move the statue to the table top. How high is the table? Note: The diagram is not to scale. 

Answer 1

Sinnce the work was negative, the height of the statue was reduced. The initial potential energy was:

$$E_0 = mgh_0$$

where $m = 3.2kg$, $h_0 = 2.0 m$, $g = 9.8m/s^2$ is the gravitational acceleration. The new potential energy (on the table top) is then:

$$E = E_0 - A = mgh_0 -A$$

where $A = 18J$ is the work done. On the other hand, this energy is given as follows:

$$E = mgh$$

where $h$ is the height of the table. Combining the last two equations and expressing $h$, obtain:

$$mgh_0 -A = mgh\\ h = h_0 - \dfrac{A}{mg}\\ h = 2.0m - \dfrac{18J}{3.2kg\cdot 9.8m/s^2} \approx 1.4 m$$

Answer. 1.4 m.