Question

Find the mass of water lifted by a pump of 0.5hp to a height of 10m in 60sec​

Answer 1

228.36 kg is the required answer.

GIVEN:

• Power, p = 0.5 hp
• Height, h = 10 m
• Time, t = 60 sec

TO FIND:

Mass of water lifted, m

FORMULAE:

• Power = work done / time

• work done, w = force × distance

• According to Newton's second law of motion, force, f = ma

SOLUTION:

STEP 1:

• SI unit of power is watt.

• 1 horse power = 746 watt

• 0.5 horse power = 0.5 × 746 watt

• p = 746/2

• Power, p = 373 watt.

STEP 2:

f = ma

Here a = g , acceleration due to gravity.

g = 9.8 m/s²

f = m × 9.8

f = 9.8 × m

STEP 3:

work = force × displacement

Here displacement refers to the height.

work = force × height

= 9.8 × m × 10

work done = 98 × m

STEP 4:

POWER = WORK / TIME

$373 = \frac{98 \times m}{60} \\ \\ 373 \times 60 = 98 \times m \\ \\ m = \frac{373 \times 60}{98} \\ \\ m = \frac{22380}{98} \\ \\ m = 228.36 \: kg$

ANSWER:

Mass of the water lifted is 228.36 kg .

DIRECT FORMULA:

Power , p = (mgh) / t

IMPORTANT POINTS:

• Power is defined as the rate of doing work.

• It is a scalar quantity. It has magnitude alone. It does not have direction.

• Power is also equal to dot product of force and velocity.

• Work is a form of energy. It is a scalar quantity.

Answer 2

Answer:

hi

228.36 kg is the required answer.

GIVEN:

Power, p = 0.5 hp

Height, h = 10 m

Time, t = 60 sec

TO FIND:

Mass of water lifted, m

FORMULAE:

Power = work done / time

work done, w = force × distance

According to Newton's second law of motion, force, f = ma

SOLUTION:

STEP 1:

SI unit of power is watt.

1 horse power = 746 watt

0.5 horse power = 0.5 × 746 watt

p = 746/2

Power, p = 373 watt.

STEP 2:

f = ma

Here a = g , acceleration due to gravity.

g = 9.8 m/s²

f = m × 9.8

f = 9.8 × m

STEP 3:

work = force × displacement

Here displacement refers to the height.

work = force × height

= 9.8 × m × 10

work done = 98 × m

STEP 4:

POWER = WORK / TIME

\begin{gathered}373 = \frac{98 \times m}{60} \\ \\ 373 \times 60 = 98 \times m \\ \\ m = \frac{373 \times 60}{98} \\ \\ m = \frac{22380}{98} \\ \\ m = 228.36 \: kg\end{gathered}

373=

60

98×m

373×60=98×m

m=

98

373×60

m=

98

22380

m=228.36kg

ANSWER:

Mass of the water lifted is 228.36 kg .

DIRECT FORMULA:

Power , p = (mgh) / t

IMPORTANT POINTS:

Power is defined as the rate of doing work.

It is a scalar quantity. It has magnitude alone. It does not have direction.

Power is also equal to dot product of force and velocity.

Work is a form of energy. It is a scalar quantity.

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