Physics Question?

Question

The answer is 681.66, but i don't get some of the steps to reach that answer. Can someone explain the steps to me?

A woman stands on a scale in a moving elevator. Her mass is 63.0 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 9500 N. What does the scale read during the acceleration?

Answer 1

At first, the woman is at rest. This means that the acceleration due to gravity as she is standing on the scale is g=9.81m/s^2.

When the elevator starts to accelerate, the value of g is increased. You have to find that new value.

As you might know, force equal mass times acceleration or F=ma, where in this case, F=9500N, m=total mass of the woman, elevator and scale, and a=g.

At the instant the tension is applied to the cable, the system is still at rest. So the net force acting on the system is zero. So assuming upward force is positive and downward force is negative, you have

0=9500N-m*g

So 9500N=(63.0 kg+815kg)*g

Solve for the new g.

The new g is g= (9500N)/(63.0 kg+815kg)=10.8m/s^2

So the new weight the scale registers is
(63.0kg)*(10.8m/s^2)=681.66N

Landy

Answer 2

Some of the answers are correct. But i would like to consider it this way. The total system, woman+elevator+scale is traveling upwards with some acceleration 'a' that we do not know. Only two forces are acting on this system. One 9500 N by the cable upwards and earth is pulling all of them downwards with [815+63]x9.8 = 8604.4 N. So the net force upward is 9500 - 8604 = 895.6 N. By Newton's second law a = 895.6/878 = 1.02 m/s^2. Now consider only the woman. What are the forces acting on her? Reaction due to scale upwards which gives us her weight as read by the scale, W say and the force applied by the earth on her = 63x9.8 = 617.4 N. So W - 617.4 is the net force, F acting on the woman which produces an acceleration of 1.02 m/s^2 upwards with which she is travelling upward along with the elevator and scale. So W - 617.4 = 63x1.02 = 64.26 N. Hence W = 617.4+64.26 = 681.66 N

Answer 3

Given the total mass of the system and the tension in the cable, the acceleration of the cab can be determined; remember that the tension of the hoist cable arises from the combined effect of gravity and the acceleration. From the acceleration, the apparent mass read by the scale can be determined; it too will be the sum of the gravitational weight (63 kg) plus the weight arising from the acceleration. The number 681.66 seems high to me, but I am not going to run the numbers myself -- that's your job.

Answer 4

I believe the answer is in terms of Newton, which is the weight, not the mass. I assume that force is (-) going down, (+) going up and acceleration is 9.8m/s^2.
To obtain the answer, you must first find the total acceleration the scale is "feeling".
Therefore you must calculate the woman's weight AND the force added by the elevator's weight as well.

Forces going downward:
woman's force(weight) = 63.0kg * 9.8m/s^2 = -617.4N

Forces going upward:
elevator & scale & woman's acceleration = 9500N/878kg = 10.82m/s^2

Now that the total acceleration is found, this is the acceleration the scale is "feeling"
weight of woman = 63.0kg(10.82m/s^2) = 681.66N

Answer 5

Welcome to physics my friend. the force of the woman on the spring is proportional to the upward acceleration of the car and the mass of the woman. while accelerating upward, the spring in the scale exherts a larger force on the woman because the elevator is also causing the scale to accelerate. therefore the relative weight of the woman increases as the elevator accelerates upward.


~Scholar~