In 37.0 s, a pump delivers 552 dm3 of oil into barrels on a platform 29.0 m above the pump intake pipe. The density of the oil is 0.82 g/cm3.
(a) Calculate the work done by the pump.
(b) Calculate the power produced by the pump
To calculate the work done by the pump, we can use the formula:
Work = Force x Distance
To find the force, we need to calculate the weight of the oil being lifted. The weight is given by:
Weight = Mass x Gravity
The mass of the oil can be calculated using its volume and density:
Mass = Volume x Density
Now, let's calculate the work done by the pump:
(a) Calculate the work done by the pump:
Step 1: Compute the mass of the oil being lifted.
Mass = Volume x Density
Mass = 552 dm3 x (0.82 g/cm3) = 452.64 g
Step 2: Convert the mass from grams to kilograms. Since 1 kg = 1000 g, the mass is:
Mass = 452.64 g ÷ 1000 = 0.45264 kg
Step 3: Calculate the weight of the oil using the formula:
Weight = Mass x Gravity
Weight = 0.45264 kg x 9.8 m/s^2 = 4.438272 N
Step 4: Calculate the distance the oil is lifted:
Distance = 29.0 m
Step 5: Calculate the work done by the pump using the formula:
Work = Force x Distance
Work = 4.438272 N x 29.0 m = 128.488288 J
Therefore, the work done by the pump is approximately 128.49 J.
(b) Calculate the power produced by the pump:
Power is defined as the rate at which work is done. It can be calculated using the formula:
Power = Work / Time
Step 1: Calculate the power produced by the pump using the formula:
Power = Work / Time
Power = 128.488288 J / 37.0 s = 3.47075733333 W
Therefore, the power produced by the pump is approximately 3.47 W.
To calculate the work done by the pump, we first need to find the mass of the oil delivered by the pump. We can do this by multiplying the volume of the oil by its density. The formula to calculate the mass is:
Mass = Volume × Density
Let's calculate the mass:
Volume = 552 dm³
Density = 0.82 g/cm³ = 0.82 g/mL
To convert dm³ to cm³, we multiply by 1000 since 1 dm³ = 1000 cm³:
Volume = 552 dm³ × 1000 cm³/dm³ = 552,000 cm³
Mass = Volume × Density = 552,000 cm³ × 0.82 g/cm³ = 452,640 g
Now that we have the mass, we can calculate the work done by the pump. The formula for work is:
Work = Force × Distance
In this case, the force is the weight of the oil, and the distance is the vertical distance the oil is lifted. The formula to calculate weight is:
Weight = Mass × Gravitational Acceleration
Gravitational Acceleration is approximately 9.8 m/s². We need to convert the mass from grams to kilograms:
Mass = 452,640 g × 0.001 kg/g = 452.64 kg
Weight = Mass × Gravitational Acceleration = 452.64 kg × 9.8 m/s² = 4,434.432 N
Distance = 29.0 m
Now let's calculate the work done by the pump:
Work = Force × Distance = 4,434.432 N × 29.0 m = 128,431.808 J
Therefore, the work done by the pump is 128,431.808 Joules.
To calculate the power produced by the pump, we can divide the work done by the time it takes to do the work. The formula for power is:
Power = Work / Time
Time = 37.0 s
Now let's calculate the power:
Power = Work / Time = 128,431.808 J / 37.0 s ≈ 3,472.481 W
Therefore, the power produced by the pump is approximately 3,472.481 Watts.