A woman stands on a scale in a moving elevator. Her mass is 61.0 kg, and the combined mass of the elevator and scale is an additional 815 kg. Starting from rest, the elevator accelerates upward. During the acceleration, the hoisting cable applies a force of 9850 N. What does the scale read during the acceleration? Answer should be in N.

Question

shane_b · Answer

First you need to calculate the acceleration of the elevator $$F=ma$$$$9850N=(815kg+61.0kg)a$$$$a=11.24 m/s^2$$Now just calculate how much force she would be applying to the scale:$$F=ma$$$$F=(61.0kg)(11.24m/s^2)=685.6N$$That's the calculations...but you'd need to adjust for significant figures.

souvik · Answer

i think when its acceleration the reading of the scale would be...mg+ma
=61*9.8+61*11.24=1283.4 N

shane_b · Answer

@souvik: I believe you're including the acceleration due to gravity twice.  Given the tension is 9850N and the total acceleration is 11.24m/s^2, the *net* acceleration (upward) of the elevator will be:$$a_{net}=11.24 m/s^2 - 9.8m/s^2=1.44 m/s^2$$That's a pretty reasonable acceleration value for an elevator...it passes the sniff test.  However, 11.24m/s^2 would be more like the acceleration experienced on a roller coaster...not an elevator.