You walk into an elevator, step onto a scale, and push the 'up' button. You recall that your normal weight is 625 625 625 N. Draw a free-body diagram. When the elevator has an upward acceleration of magnitude 2.50 2.50 m/s 2 , what does the scale read?

Hey, everyone in this problem, we're told that a boy with a normal weight of 980 moons is standing on a wah scale kept in a lift that is moving upward, the lift has an upward acceleration of 3 m per second squared. We're asked to find the reading on the scale. We're given four answer choices all in Newtons. Option A 1080. Option B 1180. Option C 1280 or option D 1380. Now, if we have a question that's asking for the reading on this scale, OK. What we want to find is his normal, right? So the reading on the scale tells us that we're looking for the normal four. All right. So let's go ahead and draw a free body diagram to get a sense of what's going on. We have this boy standing in the elevator, he's going to have the weight acting downwards, here's force of gravity acting downwards and there's gonna be a normal force pointing upwards because he's standing on the sur. Now this elevator is going to be accelerating of words OK. So it's accelerating upwards. And we're gonna say that that is the positive direction and we're gonna have positive acceleration so that upward direction is going to be our positive acceleration or sorry, our positive direction. OK. If we want to find the normal force and then let's consider our some forces no, some of the forces in the y direction according to Newton's second law is gonna be equal to the mass multiplied by the acceleration. Now, what forces do we have? Well acting in the positive direction, we have the normal force and, and acting in the negative direction, we have the weight W so we get that N minus W is gonna be equal to the mass multiplied by the acceleration. Now, we want to find the normal force. Then we're given the weight and the problem we're giving the acceleration but we need to find the mass M. OK? And we can do that because we're given the normal weight. OK? So let's go ahead and calculate that. So we're looking to calculate the mass M I recall that the weight W it's just equal to the mass um multiplied by the acceleration due to gravity. OK. So in this normal case, the boy has a weight of 980 nos that's gonna be equal to their mass multiplied by that acceleration due to gravity. 9.8 m per second squared by dividing both sides by 9.8 m per second. Squared, we get that the mass is going to be equal to 100 kg. All right. So going back to our equation with our forces N minus W is equal to M multiplied by A, we can rearrange to get N by itself. And we're gonna add the weight to both sides. So we get that N is equal to the weight. Well, what's the mass multiplied by the acceleration again, that's the mass we just found. And now we can substitute in all of those values to solve for the normal. So we have N is equal to 980 newtons plus the mass 100 kg multiplied by the acceleration 3 m per second squared. When we look at our units, we have newtons in the first term and we have kilogram meter per second squared in the second term and recall that those two things are equivalent. OK? So we're adding newtons to newtons and so we're good there. And when we add these together, we're gonna get that, that normal force is equal to 1280 nos. OK? And so the reading on this scale is therefore going to be 1280 noons which corresponds with answer choice. C thanks everyone for watching. I hope this video helped you in the next one.

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6. Intro to Forces (Dynamics)

Vertical Forces & Acceleration

Physics

6. Intro to Forces (Dynamics)

Vertical Forces & Acceleration

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Problem 8a

Textbook Question

You walk into an elevator, step onto a scale, and push the 'up' button. You recall that your normal weight is $625$ N. Draw a free-body diagram. When the elevator has an upward acceleration of magnitude $2.50$ m/s², what does the scale read?

Verified step by step guidance

Step 1: Begin by identifying the forces acting on you while standing on the scale in the elevator. These forces include your weight (gravitational force, Fg = mg) acting downward and the normal force (Fn) exerted by the scale acting upward. The scale reading corresponds to the magnitude of the normal force.

Step 2: Write Newton's second law for the vertical direction: $ F_{net} = ma $. Here, $ F_{net} $ is the net force acting on you, $ m $ is your mass, and $ a $ is the acceleration of the elevator. The net force is given by $ F_{net} = F_n - F_g $, where $ F_n $ is the normal force and $ F_g $ is your weight.

Step 3: Calculate your mass using your normal weight. Recall that $ F_g = mg $, where $ g $ is the acceleration due to gravity (approximately $ 9.8 \, \text{m/s}^2 $). Rearrange to find $ m = \frac{F_g}{g} $. Substitute $ F_g = 625 \, \text{N} $ and $ g = 9.8 \, \text{m/s}^2 $ to determine your mass.

Step 4: Substitute the values of $ m $, $ g $, and $ a $ into the equation $ F_n = F_g + ma $. Here, $ F_g $ is your weight, $ m $ is your mass, and $ a $ is the upward acceleration of the elevator ($ 2.50 \, \text{m/s}^2 $). This equation accounts for the additional force required to accelerate you upward.

Step 5: Solve for $ F_n $, which represents the scale reading. The result will be the sum of your normal weight and the additional force due to the elevator's upward acceleration. Ensure all units are consistent during substitution and calculation.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Free-Body Diagram

A free-body diagram is a graphical representation used to visualize the forces acting on an object. In this case, it would illustrate the forces on the person in the elevator, including gravitational force (weight) acting downward and the normal force exerted by the scale acting upward. This helps in analyzing the net force and acceleration of the object.

Newton's Second Law of Motion

Newton's Second Law states that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass, expressed as F = ma. In the context of the elevator, this law helps determine the net force when the elevator accelerates upward, allowing us to calculate the apparent weight shown on the scale.

Apparent Weight

Apparent weight is the normal force experienced by an object in a non-inertial frame, such as an accelerating elevator. It differs from true weight due to the effects of acceleration. When the elevator accelerates upward, the apparent weight increases, which is what the scale measures, reflecting the combined effect of gravitational force and the additional force due to the elevator's acceleration.

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You walk into an elevator, step onto a scale, and push the 'up' button. You recall that your normal weight is 625625625 N. Draw a free-body diagram. When the elevator has an upward acceleration of magnitude 2.502.50 m/s2, what does the scale read?

Key Concepts

Free-Body Diagram

Newton's Second Law of Motion

Apparent Weight

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You walk into an elevator, step onto a scale, and push the 'up' button. You recall that your normal weight is $625$ N. Draw a free-body diagram. When the elevator has an upward acceleration of magnitude $2.50$ m/s², what does the scale read?