Question

A motor is capable of raising 400kg of water in 5min from a well 120m deep. What is the power of the motor?

Answer 1

Answer:

1,568 Watts

Explanation:

Given:

• Mass of water = 400 kg

      = 400 kg * 9.8 m/s² (g) = 3920 N (Force)

• Height of the well = Displacement (s) = 120 m

• Time taken to raise the water from the well (t) = 5 minutes = 300 seconds

To find:

Power (P)

Method to find:

First, we need to find the work (W) done by the motor.

W = Fs    (Work Done = Force * Displacement)

⇒ W = 3920 * 120

⇒ W = 4,70,400 Joules

Now, we can find the power of the motor.

P = W/t   (Power = Work Done / Elapsed Time)

⇒ P = 4,70,400/300

⇒ P = 1,568 Watts

Hence, the power of the motor is  1.568 Watts.

Answer 2

$\maltese \: \red{\mid{\underline{\overline{\textbf{Answer}}}\mid}}$

It is given that :-

• Weight of water = 400kg
• Time taken to displace = 5min = 300s
• Displacement of water = 120m

Now, since weight is the acceleration due to gravity thus we can also say that the weight is also equal to force required to overcome it. Now we can say that the force applied on water = 400N.

Now work done on displacing water = Force × Displacement

= 400 × 120 = 48,000J.

Now, we know power is the rate of work done. Represented by :

$\maltese \: p = \frac{w}{∆t}$

After inputting the known values we get :-

$\maltese \: p = \frac{48000}{300}$

$\maltese \: p = \cancel \frac{48000}{300} = 160watt$

Therefore the power of motor is 160W.

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BY SCIVIBHANSHU

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