Question

CNM has decided to construct new dormitories for incoming freshmen students. CNM has also decided to purchase some swanky luxury water beds for the new dormitories. Each waterbed has dimensions of 1.83 m x 1.93 m x 0.248 m. The floor of the dorms with tolerate an additional weight of no more than 7150 N. Find the weight of the water in your bed and determine whether CNM should make the purchase?

Answer 1

We will have the following:

FIrst, we determine the volume of water each bead will have:

$V=\left(1.83m\right)\left(1.93m\right)\left(0.248m\right)\Rightarrow V=0.8759112m^3$

Now, we also know that the density of water is approximately 1000kg/m^3; so we determine the mass of water each bed would have:

$0.8759112m^3*1000kg/m^3=875.9112kg$

Now, using this mass we determine the force it would apply on the floor:

$F=m*A\Rightarrow F=\left(875.9112kg\right)\left(9.8m/s^2\right)$$\Rightarrow F=8583.92976N$

So, the force the water bed would apply on the floor is greater than the limit the floor can withstand. So, CNM should not make the purchase.