# Calculate the total potential energy, in Btu, of an object

Calculate the total potential energy, in Btu, of an object that is 20 ft below a datum level at a location where $g=31.7f\frac{t}{{s}^{2}}$ and which has a mass of 100 lbm.
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habbocowji
Step 1
The total potential energy simply is:
$PE=mgz$
$=100×31.7×20×\frac{1}{25037}Btu$
$=2.53Btu$

trisanualb6

Step 1
Given:
The mass is $m=100lbm$
The gravitational acceleration is
The height below the datum level is $h=20ft$
Step 2
The expression of the total potential energy change is given by,
1) $U=-m×g×h$
Here, U is the total potential energy change, m is the mass, g is the gravitational acceleration, and h is the height below the datum level.
Substitute the known values in the equation (1).
$U=-100lbm×31.7ft/{s}^{2}×20ft$
$U=-63400\frac{f{t}^{2}×lbm}{{s}^{2}}×\frac{0.000039948089Btu}{1\frac{f{t}^{2}×lbm}{{s}^{2}}}$
$U=-2.53255Btu$
Therefore, the total potential energy change is -2.53225 Btu.