Question

CNM has decided to purchase some Swanky luxury water beds for the new dormitories. Each water bed has dimension of 1.83 m x 1.93 m x 0.248 m. The floor of the dorms will 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 are asked to determine the weight of a bed of water with dimensions 1.83m x 1.93m x 0.248m. To do that we will determine the mass using the following formula:

`m=\rho V`

Where:

`\begin{gathered} m=\text{ mass} \\ \rho=\text{ density} \\ V=\text{ volume} \end{gathered}`

To determine the volume we will use the fact that the bed has the shape of a rectangular prism and therefore its volume is the product of its dimensions, like this:

`V=\lparen1.83m)\left(1.93m\right)\left(0.248m\right)`

Solving the operations we get:

`V=0.88m^3`

The density of water is given by:

`\rho=1000\text{ kg/m}^3`

Substituting in the formula for the mass:

`m=\lparen1000\text{ kg/m}^3)\left(0.88m^3\right)`

Solving the operations:

`m=880kg`

Now, to determine the weight we use the following formula:

`W=mg`

Where:

`\begin{gathered} W=\text{ weight} \\ m=\text{ mass} \\ g=\text{ acceleration of gravity} \end{gathered}`

Substituting the values:

`W=\left(880kg\right)\left(9.8\text{ m/s}^2\right?`

Solving the operation:

`W=8624N`

Since the weight is 8624 N this means that the weight will not be tolerated.