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A 650 kg elevator starts from rest. It moves upward for 4.50 s with constant acceleration until it reaches its cruising speed, 1.75 m/s.
(a) What is the average power of the elevator motor during this period? W
(b) How does this power compare with the motor power when the elevator moves at its cruising speed? Pcruising = W

Sagot :

5789.8 W  is the average power of the elevator motor during this period and 1.115 * 10⁴ W this power compare with the motor power when the elevator moves at its cruising speed.

What is an explain acceleration?

The rate with which the speed and direction of a moving object vary over time. A point a object going straight ahead is pushed when it accelerates or decelerates.

Briefing:

Mass of elevator = 650 kg

Time = 4.50 sec

Speed of the elevator = 1.75 m/s

Calculating the elevator's acceleration is necessary.

Using the acceleration formula

a = vf - vi / t

a = 1.75 / 4.50

a = 0.38 m/s2

(a). We must determine the net force acting on the elevator.

Using the force formula

T = mg + ma

T = m (g +a)

T = 650 (9.8 + 0.38)

T = 6617 N

We must determine the average velocity.

Using the average velocity formula

v' = vf + vi / 2

v' = 1.75 / 2

v' = 0.875 m/s

We must determine the average power.

Using the power formula

P = T * v'

P = 6617 * 0.875

P = 5789.8 W

(b). We must determine the motor's power input.

Using the power formula

P = F * v

P = mg * v

P = 650 * 9.8 * 1.75

P = 1.115 * 10⁴ W.

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