A water bed has dimensions of 1.83 m 2.17 m 0.247 m. The floor of the bedroom will tolerate an additional weight of no more than 6660 N. Find the weight of the water in the bed and determine whether it should be purchased.
Find the cubic meters water volume of the water bed. Do this by multiplying its width * length * height.
Water weighs 1000kg/m^3, convert the volume to kg of mass.
The force on the floor will be F=m*g.
Is this > 6660N ?
Bad purchase! Don't forget the g = 9.8 m/s^2 (= 9.8 Newtons/kg) factor when computing the weight.
To find the weight of the water in the bed, we can use the formula:
Weight = density × volume × gravity
1. First, let's calculate the volume of water in the bed:
Volume = length × width × height
Given:
Length (l) = 1.83 m
Width (w) = 2.17 m
Height (h) = 0.247 m
Volume = 1.83 m × 2.17 m × 0.247 m
Volume ≈ 0.887 m³
2. Next, let's find the density of water:
The density of water is approximately 1000 kg/m³.
3. Now, we can calculate the weight of the water:
Weight = 1000 kg/m³ × 0.887 m³ × 9.8 m/s²
Weight ≈ 8705 N
The weight of the water in the bed is approximately 8705 N.
4. Finally, we can determine whether the water bed can be purchased based on the additional weight tolerated by the floor.
Given:
Additional weight tolerated by the floor = 6660 N
Since the weight of the water (8705 N) is greater than the additional weight tolerated by the floor (6660 N), the water bed should not be purchased as it exceeds the weight limit.
To find the weight of the water in the bed, we need to determine the volume of the water and then use its volume to calculate the weight.
The volume of the water can be found by multiplying the dimensions of the water bed:
Volume = Length × Width × Height
Volume = 1.83 m × 2.17 m × 0.247 m
Next, we need to convert the volume to liters because the weight of water is often measured in kilograms or liters:
Volume (in liters) = Volume in cubic meters × 1000
After converting the volume to liters, we can calculate the weight of the water using the following equation:
Weight of water (in kilograms) = Volume (in liters) × density of water
The density of water is approximately 1000 kg/m³.
Finally, we can convert the weight from kilograms to Newtons since the floor's weight tolerance is given in Newtons:
Weight (in Newtons) = Weight of water (in kilograms) × 9.8 m/s² (acceleration due to gravity)
By substituting the values into the equations, we can find the weight of the water in the bed.
Let's go ahead and calculate the weight:
Volume = 1.83 m × 2.17 m × 0.247 m = 0.922559 m³
Volume (in liters) = 0.922559 m³ × 1000 = 922.559 liters
Weight of water (in kilograms) = 922.559 liters × 1000 kg/m³ = 922.559 kg
Weight (in Newtons) = 922.559 kg × 9.8 m/s² = 9049.5182 N
The weight of the water in the bed is approximately 9049.52 N.
Since the weight of the water in the bed is less than the additional weight tolerated by the floor (6660 N), it is safe to say that the water bed should be purchased.