The Hoover Dam is 726 ft high. Find the potential energy of 1.00 million ft3 of water
at the top of the dam.(1 ft3 of water weighs 62.4 lb.)
You are mixing weight with mass.
PE=weight*height=density*volume(height)
= 62.4 lbs/ft^3*1E6 ft^3*726ft= you do it (this is in ft-lbs of energy)
Did it like this
1.00E6*62.4*736=4.53ftlb
To find the potential energy of 1.00 million ft3 of water at the top of the dam, you can use the formula for potential energy:
Potential energy = mass * acceleration due to gravity * height
First, we need to calculate the mass of the water. Since 1 ft3 of water weighs 62.4 lb, the mass of 1 ft3 of water can be calculated as:
mass = weight / acceleration due to gravity
mass = (1 ft3 * 62.4 lb) / 32.2 ft/s^2
Next, we need to convert 1.00 million ft3 to ft^3.
1.00 million ft3 = 1,000,000 ft3
Now we can calculate the potential energy using the formula:
Potential energy = mass * acceleration due to gravity * height
Potential energy = (mass of water) * 32.2 ft/s^2 * 726 ft
Substituting the values, we get:
Potential energy = [(1,000,000 ft3 * 62.4 lb) / 32.2 ft/s^2] * 32.2 ft/s^2 * 726 ft
After simplifying the equation, the units cancel out, leaving us with:
Potential energy = (1,000,000 ft3 * 62.4 lb) * 726
Calculating further:
Potential energy = 62,400,000 lb * 726
Therefore, the potential energy of 1.00 million ft3 of water at the top of the Hoover Dam is 45,190,400,000 lb-ft.
To find the potential energy of the water at the top of the Hoover Dam, we can use the formula:
Potential Energy = mass * gravitational acceleration * height
First, let's calculate the mass of the water:
1 million ft3 of water = 1,000,000 ft3
1 ft3 of water weighs 62.4 lb
So, the mass of 1 million ft3 of water is:
Mass = Volume * Density
= 1,000,000 ft3 * 62.4 lb/ft3
= 62,400,000 lb
Next, we need to convert the height of the Hoover Dam from feet to meters because the standard unit for gravitational acceleration is in m/s^2.
1 ft = 0.3048 m
So, the height of the dam in meters is:
Height = 726 ft * 0.3048 m/ft
= 221.05 m
Now, let's proceed to calculate the potential energy:
Potential Energy = Mass * Gravitational acceleration * Height
Since the gravitational acceleration near the Earth's surface is approximately 9.8 m/s^2, we can substitute the values into the formula:
Potential Energy = 62,400,000 lb * 9.8 m/s^2 * 221.05 m
Calculating this expression will give us the potential energy of the water at the top of the Hoover Dam.