In 39.0 s, a pump delivers 549 dm3 of oil into barrels on a platform 22.0 m above the pump intake pipe. The density of the oil is 0.82 g/cm3.

(a) Calculate the work (kJ) done by the pump
(b) Calculate the power (kW) produced by the pump

W = Fd --> W = mad
D = m/v
P = W/t --> this is the easy part

It would be nice to know the mass of the oil in kg and have lengths in meters

m = 549dm^3 * 10^-3m^3/dm^3 * .82g/cm^3 * 10^-3kg/g * 10^6cm^3/m^3

Then the work done to raise it 22m is:
m g h

then the power is indeed work per unit time

To solve this problem, we need to use the formulas for work (W), force (F), distance (d), and power (P).

(a) To calculate the work done by the pump (W), we need to determine the force (F) exerted by the pump and the distance (d) over which the force is applied.

1. Determine the mass of the oil delivered:
The density of the oil is given as 0.82 g/cm3. To convert this to kg/m3, we need to multiply by 1000 (since there are 1000 cm in a meter):
Density = 0.82 g/cm3 * 1000 kg/m3 = 820 kg/m3

The volume of oil delivered (V) is given as 549 dm3. To convert this to m3, we need to divide by 1000 (since there are 1000 dm in a meter):
Volume = 549 dm3 / 1000 = 0.549 m3

Now, we can calculate the mass (m) of the oil:
Mass = Density * Volume = 820 kg/m3 * 0.549 m3 = 449.28 kg

2. Determine the force exerted by the pump:
We know that force is equal to mass multiplied by acceleration. In this case, the acceleration is equal to the acceleration due to gravity (g), which is approximately 9.8 m/s2:
Force = m * g = 449.28 kg * 9.8 m/s2 = 4401.84 N

3. Determine the distance over which the force is applied:
The distance (d) is given as 22.0 m.

Now, we can calculate the work done by the pump:
Work (W) = Force (F) * Distance (d) = 4401.84 N * 22.0 m = 96839.28 J

To convert the work to kilojoules (kJ), divide by 1000:
Work (W) = 96839.28 J / 1000 = 96.84 kJ

Therefore, the work done by the pump is approximately 96.84 kJ.

(b) To calculate the power (P) produced by the pump, we need to divide the work (W) by the time (t) taken to do the work.

Given that the time taken is 39.0 s, we can calculate the power:
Power (P) = Work (W) / Time (t) = 96.84 kJ / 39.0 s

To convert the power to kilowatts (kW), divide by 1000:
Power (P) = (96.84 kJ / 39.0 s) / 1000 = 2.4877 kW

Therefore, the power produced by the pump is approximately 2.49 kW.