Middle School

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A 193 kg curtain needs to be raised 7.5 m, at constant speed, in as close to 5.0 s as possible. The power ratings for three motors are listed as 1.0 kW, 3.5 kW, and 5.5 kW. Which motor is best for the job?

Answer :

Answer:

best motor for above purpose is 3.5 kW

Explanation:

As we know that power is defined as the rate of work done

Here we have to raise the curtain so work is done against gravity

So we have

W = mgH

here we know

m = 193 kg

[tex]g = 9.8 m/s^2[/tex]

Now we have

[tex]W = (193)(9.8)(7.5)[/tex]

[tex]W = 14185.5 J[/tex]

now power used in it

[tex]P = \frac{14185.5}{5}[/tex]

[tex]P = 2.8 kW[/tex]

So best motor for above purpose is 3.5 kW

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Rewritten by : Barada

Final answer:

To find the best motor for the job of raising a curtain, we can calculate the power required for each motor. The motor with a power rating of 5.5 kW is the best option, as it has the highest power output.

Explanation:

To find the motor that is best for the job, we need to calculate the power required to raise the curtain. Power is given by the equation P = W/t, where P is power, W is work done, and t is time. In this case, the work done is equal to the weight of the curtain multiplied by the height it is raised, which is W = mgh. Plugging in the values, we can calculate the power required for each motor:

Motor 1: P = (193 kg)(9.8 m/s^2)(7.5 m) / 5.0 s = 2867.2 W

Motor 2: P = (193 kg)(9.8 m/s^2)(7.5 m) / 5.0 s = 10021.6 W

Motor 3: P = (193 kg)(9.8 m/s^2)(7.5 m) / 5.0 s = 15663.6 W

Therefore, the motor with a power rating of 5.5 kW (or 5500 W) is the best option for the job, as it has the highest power output.

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