In $2010,$ the Vikings' stadium failed catastrophically due to the weight of the snow on the roof. Despite the

awful performance of the team in the NFL$,$ it was decided to design and create a new roof that was able to

support the weight of a snow fall. For the time being, assume that the top of the roof is a flat surface and

that any snow that falls on top will stick to the roof. Imagine that the density of snow is known, ${}_s,$ and that

the velocity at which it is dropping is a function of time $v_d=\frac{\frac{25t}{60}-\frac{1}{2}(\frac{t}{60}{)}^2}{50000}($in $\frac{m}{s},$ time in s$)$

between $0$ and $50$mins,$v_d=0$ after. The problem guides you on what to do$.$

a$)$ Calculate the mass flow rate of snow onto the roof as a function of the area of the roof $A_0.$ Use

appropriate integral equations to do so and select an appropriate Control Volume. Choose one that

is not moving or deforming.

b$)$ Calculate the total mass of the roof after $50$ minutes as a function of ${}_s$ and $A_0.$ Imagine that the

mass of the roof without snow is $M_0.$

Use $A_0=10000m^2,M_0={10}^{7}Kg,{}_s=\frac{100(kg)}{m^3}$

c$)$ EXTRA. To make the structure support the weight of the snow, we would like to find the force

needed to support the weight of the snow $($including the weight of the roof$).$ Use an appropriate

equation to calculate the force as a function of time.

d$)$ EXTRA. When $50$ minutes have passed, what would be the total force?

Do your problem here.

Governing Equation$($s$)$

Free Body Diagram