A water bed has dimensions of 1.83mx1.86mx.238m. The floor of the bed room will tolerate an additional weight of no more than 6660N. Find the weight of the water in the bed and determine whether it should be purchased.
The weight of the water in the water bed is (volume* g* density of water)
= 810 m^3* 9.8 m/s^2 * 1000 m/m^3 = 9.61*10^3 N
That is more weight than the floor can support.
To determine the weight of the water in the water bed, we need to calculate the volume, gravity factor (g), and density of water.
First, let's calculate the volume of the water bed. The dimensions are given as 1.83m in length, 1.86m in width, and 0.238m in height.
Volume = length * width * height
Volume = 1.83m * 1.86m * 0.238m
Volume = 0.810 m^3
Next, we need to consider the gravity factor (g), which is the acceleration due to gravity. Its approximate value is 9.8 m/s^2.
Now, let's calculate the weight of the water in the bed using the formula:
Weight = volume * g * density of water
The density of water is approximately 1000 kg/m^3.
Weight = 0.810 m^3 * 9.8 m/s^2 * 1000 kg/m^3
Weight = 9.61 * 10^3 N (rounded to two decimal places)
The weight of the water in the bed is approximately 9610 N.
Since the weight of the water exceeds the additional weight tolerance of the floor, which is 6660 N, it is not advisable to purchase this water bed as it may exceed the floor's weight limit and cause potential structural problems.