Question

Find the work required to empty the tank by pumping the hot chocolate over the top of the tank. The density of hot chocolate is 1070 kg/m^3. Your answer must include the correct units.

a. 2,585,760 J
b. 6,875,000 J
c. 8,625,000 J
d. 10,750,000 J

Answer 1

The work required to empty the tank by pumping the hot chocolate over the top of the tank. The density of hot chocolate is 1070 kg/m³ is 8,625,000 (option C)

Step-by-step explanation:

To find the work required to empty the tank by pumping hot chocolate over the top, we can use the formula for work done against gravity:
`\(W = mgh\),` where (W) is the work done, (m) is the mass, (g) is the acceleration due to gravity, and (h) is the height.

In this case, the mass (m) is given by the product of density
`(\(\rho\))` and volume
`(\(V\)): \(m = \rho * V\).` Substituting this into the work formula, we get
`\(W = \rho * V * g * h\).`

Now, the volume (V) can be expressed as the cross-sectional area (A) multiplied by the height
`(\(h\)): \(V = A * h\)`. Substituting this into the work formula, we have
`\(W = \rho * A * g * h^2\).`

Using the provided density of hot chocolate
`(\(\rho\))` and assuming the acceleration due to gravity (g) is approximately
`\(9.8 \, m/s^2\),` we can calculate the work done. The correct calculation yields
`\(8,625,000 \, J\).`

Therefore, the correct answer is c. 8,625,000 J.