In 35.0 s, a pump delivers 0.574 m3 of oil into barrels on a platform 25.5 m above the intake pipe. The oil's density is 0.820 g/cm3.
To find the work done by the pump, we need to calculate the gravitational potential energy of the oil that is lifted.
Work done = Change in potential energy
Potential energy = mgh
Here's how we can calculate it step by step:
Step 1: Convert the density to kilograms per cubic meter.
Density in kg/m^3 = density in g/cm^3 * 1000
Density in kg/m^3 = 0.820 g/cm^3 * 1000 = 820 kg/m^3
Step 2: Calculate the mass of the oil delivered.
Mass = density * volume
Mass = 820 kg/m^3 * 0.574 m^3 = 471.28 kg
Step 3: Calculate the change in potential energy.
Change in potential energy = mass * gravitational acceleration * change in height
Gravitational acceleration (g) = 9.8 m/s^2
Change in height = height of platform = 25.5 m
Change in potential energy = 471.28 kg * 9.8 m/s^2 * 25.5 m = 118,735.04 Joules
Therefore, the work done by the pump is 118,735.04 Joules.