An engineer is designing a system to raise the curtain in a theater. it should take exactly 8.0 seconds to rasie 200. kg by 6.8 meters. how mich work is needed to do this? how much power needes to gonto the motor to the job

The correct answer to the question is: Work: 13,328 J and Power: 1666 watt.

EXPLANATION:

As per the question, the mass of curtain is given as m = 200 Kg.

The curtain is raised to a height of 6.8 metre.

Hence, height h = 6.8 m.

The time taken to raise t = 8.0 seconds.

We are asked to calculate the work done by the machine.

The work done by the machine is nothing else than the potential energy gained by the curtain due to the lifting of it from ground to a height of 6.8 m.

Hence, work done W = Potential energy gain ( P.E )

The potential energy gained by the curtain is calculated as -

P.E = mgh

Here, g is known as acceleration due to gravity and it's value is g = 9.8 m/s2.

Hence, P.E = mgh

= 200×9.8×6.8 Joule

= 13,328 J.

Now, we have to calculate the power of the machine.

The power of the machine is defined as the rate of doing work or the work done per unit time.

Mathematically power P= W ÷ t

= 13,328 ÷ 8.0 watt.

= 1666 watt.

Hence, the work done and power of machine are 13,328 J and 1666 watt.