Solar panels are installed on a rectangular flat roof. The roof is 15 feet by 30 feet,and the mass of the panels and framing is 900 \mathrm{lb}_{\mathrm{m}}.
A) Assuming the weight of the panels is evenly distributed over the roof, how much pressure does the solar panel array place on the roof?
B) The density of fallen snow varies; here assume its ~30% of the density of liquid water. Estimate the total pressure on the roof if 4 inches of snow fall on top of the solar panels.
A) Pressure =\frac{\text { Force }}{\text { Area }} Area = Length × Width \quad Force = Mass × Acceleration
Pressure =\frac{\left(900~ \mathrm{lb}_{\mathrm{m}}\right)\left(32.2 \frac{\mathrm{ft}}{\mathrm{sec}^{2}}\right)}{(15~ \mathrm{ft})(30 ~\mathrm{ft})}\left(\frac{1~ \mathrm{lb}_{\mathrm{f}}}{32.2 \frac{\mathrm{lb}_{\mathrm{m}} \mathrm{ft}}{\mathrm{sec}^{2}}}\right)
Pressure =2 \frac{\mathbf{l} \mathbf{b}_{\mathbf{f}}}{\mathbf{f t}^{2}}
B) \text { Density }_{\text {snow }}=(30 \%) 63.3 \frac{\mathrm{lb}_{\mathrm{m}}}{\mathrm{ft}^3}=19.0 \frac{\mathrm{lb}_{\mathrm{m}}}{\mathrm{ft}^3}
\text{Force}_{\text {snow }}= \text{Volume}_{\text {snow }} × \text{Density}_{\text {snow }} × gravity
Pressure =\frac{\text { Force }_{\text {snow }}+\text { Force }_{\text {panels }}}{\text { Area }}
4 inches =0.333 ft
Pressure =\bf 8.33 \frac{\mathbf{l b}_{\mathbf{f}}}{\mathbf{f t}^{2}}