A water bed has a dimension of 2m × 2m × 2m. The floor of the bed will tolerate an additional load of no more than 600N. Find the weight of the bed and determine whether it should be purchased.
Vw = 2 * 2 * 2 = 8 M^3 = 8*10^6 cm^3. =
Vol. of the water.
Dw = 1g / cm^3 = 0.001kg / cm^3. = Density of water.
Mass = Vw * Dw.
Mass = 8*10^6cm^3 * 10^-3kg/cm^3 = 8*10^3kg = 8000 kg. = Mass of water.
Wt. = mg = 8000kg * 9.8N/kg = 78,400 N.
= Wt of water.
To determine whether the water bed should be purchased, we need to find the weight of the bed and compare it to the floor's tolerance.
To find the weight of the bed, we need to know the density of water, which is 1000 kg/m^3. Since density is mass divided by volume, we can rearrange the formula to find the mass: mass = density × volume.
Given:
- Density of water = 1000 kg/m^3
- Dimensions of the water bed: 2m × 2m × 2m
First, calculate the volume of the water bed:
volume = length × width × height = 2m × 2m × 2m = 8 m^3
Next, calculate the mass of the water bed:
mass = density × volume = 1000 kg/m^3 × 8 m^3 = 8000 kg
Now, we need to convert the mass from kg to Newtons since the floor tolerance is given in Newtons. We can do this by using the conversion factor 1 kg = 9.8 N (approximate value for gravitational acceleration on Earth).
weight = mass × gravitational acceleration
weight = 8000 kg × 9.8 N/kg
weight ≈ 78,400 N
The weight of the water bed is approximately 78,400 Newtons.
Since the floor can tolerate an additional load of no more than 600 Newtons, and the weight of the water bed exceeds this tolerance, it should not be purchased.