Question

In: Physics

A 679-kg elevator starts from rest and moves upward for 3.30 s with constant acceleration until...

A 679-kg elevator starts from rest and moves upward for 3.30 s with constant acceleration until it reaches its cruising speed, 1.63 m/s. (a) What is the average power of the elevator motor during this period? (b) How does this amount of power compare with its power during an upright trip with constant speed?

Solutions

Expert Solution

Power = Work/time

Work = force x distance

in the first case, the force exerted = F =ma

if the elevator started from rest and got to a speed of 1.63 m/s in 3.3 secs, then its accel was 1.63m/s / 3.3s = 0.494 m/s^2

then the force acting on the elevator is found from newton's second law:

sum of forces = ma
sum of forces = tension pulling up elevator - mg = ma
tension force on elevator = m(g+a) = 679kg(9.8+0.494)m/s/s
= 6989.62N

the distance the elevator travels in 3 seconds is:

dist = 1/2 at^2 = 0.5(0.494)(3.3)^2 = 2.69 m

the power = force x distance/ 3.3 s = 5697.6 Watts

in the second case, the power is NOT zero (wouldnt it be a wonderful world if we could run machines at constant speed and not do work)

Power = Work/time = Force x distance /time; but notice that we have a distance/time term, which we know to be velocity

in the case of constant motion, we have that Power = Force x velocity

here the force pulling up the elevator is equal to the weight of the elevator = mg = 6654.2N

so power = 6654.2N x 1.63 m/s = 10,846.34 W

the power output is greater at constant speed, since the elevator is traveling faster during cruising compared to the acceleration phase


Related Solutions

A 613-kg elevator starts from rest and moves upward for 2.50 s with constant acceleration until...
A 613-kg elevator starts from rest and moves upward for 2.50 s with constant acceleration until it reaches its cruising speed, 1.63 m/s. (a) What is the average power of the elevator motor during this period? (b) How does this amount of power compare with its power during an upward trip with constant speed? (Give the power during an upward trip with constant speed.)
A 621-kg elevator starts from rest and moves upward for 3.20 s with constant acceleration until...
A 621-kg elevator starts from rest and moves upward for 3.20 s with constant acceleration until it reaches its cruising speed, 1.65 m/s. (a) What is the average power of the elevator motor during this period? hp (b) How does this amount of power compare with its power during an upward trip with constant speed? (Give the power during an upward trip with constant speed.) hp
A 674-kg elevator starts from rest and moves upward for 2.90 s with constant acceleration until...
A 674-kg elevator starts from rest and moves upward for 2.90 s with constant acceleration until it reaches its cruising speed, 1.80 m/s. (a) What is the average power of the elevator motor during this period?______________ hp (b) How does this amount of power compare with its power during an upward trip with constant speed? (Give the power during an upward trip with constant speed.)____________________ hp
A 700-kg elevator starts from rest. It moves upward for 4.50 s with constant acceleration until...
A 700-kg elevator starts from rest. It moves upward for 4.50 s with constant acceleration until it reaches its cruising speed of 1.75 m/s. (a) What is the average power of the elevator motor during this time interval?
an elevator starts from rest and moves upward with a constant acceleration 1.2 abolt of mass...
an elevator starts from rest and moves upward with a constant acceleration 1.2 abolt of mass m in the elevator celling above the elevator nworks loose and falls dowen assume g = 9.8 what is the velocity of the bolt at is it hit the flor relative to the ground? what is the velocity of the bolt as it hits the floor relative to the elevator
An elevator with mass 500 Kg starts from rest and moves upward 20.0 m in 5.00...
An elevator with mass 500 Kg starts from rest and moves upward 20.0 m in 5.00 s. What is the average rate with which the force from the cable is doing work on the elevator? g = 9.8 m / s2
A 1325 kg elevator starts from rest and moves upwards for 4 seconds with a constant...
A 1325 kg elevator starts from rest and moves upwards for 4 seconds with a constant acceleration until it reaches a speed of 2.1 m/s. After 4 seconds, the speed of the elevator remains constant. A) What is the average power of the elevator motor during the first 4 seconds? B) What is the average power of the elevator when t=9 seconds?
A pendulum is swinging in an elevator that is accelerating upward at a constant acceleration a....
A pendulum is swinging in an elevator that is accelerating upward at a constant acceleration a. (a) Using the Lagrangian method, what is the equation of motion? Note be careful here, the velocity needs to be measured from an inertial reference frame. (b) What is the frequency of small oscillations?
A dentist's drill starts from rest. After 3.20 s of constant angular acceleration it turns at...
A dentist's drill starts from rest. After 3.20 s of constant angular acceleration it turns at a rate of 3.00 ✕ 104 rev/min. (a) Find the drill's angular acceleration. rad/s2 (b) Determine the angle (in radians) through which the drill rotates during this period. rad
A bicycle starts from rest with a constant acceleration 1 m/s^2. After 5 seconds of having...
A bicycle starts from rest with a constant acceleration 1 m/s^2. After 5 seconds of having started its movement, the brake pin of one of its handlebars, located 5 meters from the ground, is detached. What is the horizontal distance the plug travels from when it comes off until it falls to the ground? Note: Approximate result with only one decimal place
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT