find the mass of water lifted by a pump of power 0.5 hp to a height of 5m in 98 second.
Answers
Work is defined as force times distance, W = F*d. In lifting a mass, m, up a height h against the force of gravity, mg, you perform the following amount of work:
W = F*d = -mgh
Where F=mg, g = the acceleration due to gravity at the surface of the Earth (-9.8 m/s2), and d = h = 5 m.
The motor provides the force that lifts the mass up a height h against the force of gravity. Horsepower is a unit of power, which is work performed per unit time, P = W/t. If you know the power and the amount of time, the work that's performed by the motor is given by:
W = P*t, where P = power and t = time.
Now set the two work equations equal to one another and solve for mass (m):
-mgh = P*t
m = -(P*t)/(g*h)
You know P, t, g, and h. Plug in their values in to get the mass. Be sure to fist convert the horsepower into mks metric units (google it). Remember that g is negative, so the mass m will be positive.
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