You walk into an elevator step onto a scale and push the up...

You walk into an elevator, step onto a scale, and push the "up" button. You also recall that your normal weight is 625 $\mathrm{N}$ . Start each of the following parts with a free-body diagram. (a) If the elevator has an acceleration of magnitude $2.50 \mathrm{m} / \mathrm{s}^{2},$ what does the scale read? (b) If you start holding a 3.85 kg package by a light vertical string, what will be the tension in this string once the elevator begins accelerating?

Transcript

0:00 Hi there.

00:01 So for this problem we have a man that is inside an elevator and has a weight of 625 newtons and inside of the elevator he is over a scaled and what we need to measure is the what the scale read if the elevator has an upward acceleration because the problem says that he pushes the up button, so he has an upward acceleration, and that acceleration is of 2 .5 meters per second square.

00:51 Now, to do that first part, the value that we read in the scale, we know that the value that we are going to read in the scale is the value for the force, the force that the person exerts on the scale.

01:10 So what we need to do first is to draw all of the forces that are acting on this person inside the elevator.

01:17 So the first thing that we know is that this person and the weight is pointing downward.

01:25 We also have the normal force that is the force that the person exerts on the skill.

01:35 That is the same that the force that the skill exerts on the person.

01:40 So we have those two forces.

01:45 So when we apply newton's seconds law to sum all of the forces acting on the y company, we will have that this is.

01:52 The normal force minus.

01:56 Weight and this is equal because the system is moving upward positive mass times the acceleration now from here what the skill here this is going to read is the normal force because this is the force that the person is at searching on the scale in this in for this problem so in here we are going to solve for the normal force so in here we have mass times the acceleration plus the weight.

02:31 But we know that the weight is defined as the mass of the man times the acceleration due to gravity.

02:38 So we have mass times acceleration due to gravity.

02:41 We can simplify this folder by taking out the mass so that it is the mass times the sum of the acceleration of the elevator and the acceleration due to gravity.

02:54 So we just need to substitute those.

02:57 Values.

02:57 We know that the weight, we are given the weight of the person.

03:03 So from here we can obtain the mass of the person because that will be to divide the weight over the acceleration due to gravity.

03:13 So doing that, we know that the acceleration due to gravity is 9 .8 meters per second squared and so this will give us that the mass of a person is 63 .3.

03:27 0 .78 kilograms.

03:34 So knowing that value, we just substitute that in here...

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