# Area under the curve of a mass time graph

• blueblast
And don't worry, modern elevator cables are designed to hold much more weight than any elevator could possibly carry. In summary, the conversation discusses different methods for solving a physics problem involving force, time, mass, and change in velocity. One person suggests calculating the area under a graph to determine momentum, while another suggests looking at the graph and identifying periods of acceleration and constant velocity. The conversation also includes a discussion about feeling altered weight in an elevator and a fear of elevator cables snapping.
blueblast

## Homework Equations

Force * time = mass * change in velocity[/B]

## The Attempt at a Solution

What I did was I converted the y-axis from kilograms to Newtons, since the "mass" reading is the force that the scale experiences. Then, the area under the curve will be the change in momentum, and if you divide that by the mass(80 kg, it is given that the elevator is stationary at t = 0), you can get the change in velocity. How would you use this to solve this problem? I know there are other ways to solve this, I'm just curious if my method works.

This is from the 2013 F=MA exam.

Thanks,

blueblast

You need to deduct the student's resting weight from the curve before measuring the area under it, as most of the force measured by the scale is being used to resist that weight.

Having done that, if you make a graph of the area under the curve against time (ie the integral of the graphed function), that will show momentum, and you'll be able to see where the period of maximum momentum is.

blueblast
andrewkirk said:
You need to deduct the student's resting weight from the curve before measuring the area under it, as most of the force measured by the scale is being used to resist that weight.

Having done that, if you make a graph of the area under the curve against time (ie the integral of the graphed function), that will show momentum, and you'll be able to see where the period of maximum momentum is.

Could you possibly give me an example for one of the time periods?

Rather than go to all the trouble of calculating area under the graph, why not look at it and work out in what time period the lift is accelerating downwards, when it is accelerating upwards (ie slowing down), and when it is traveling at a constant rate. Think about yourself traveling in a lift. If it is going down, at what point in the ride do you feel lighter than usual, and at what point do you feel heavier than usual?

I love to jump in the air at these two times to feel the sensation of altered weight. is it just me or does anybody else like doing that?

andrewkirk said:
Rather than go to all the trouble of calculating area under the graph, why not look at it and work out in what time period the lift is accelerating downwards, when it is accelerating upwards (ie slowing down), and when it is traveling at a constant rate. Think about yourself traveling in a lift. If it is going down, at what point in the ride do you feel lighter than usual, and at what point do you feel heavier than usual?

I love to jump in the air at these two times to feel the sensation of altered weight. is it just me or does anybody else like doing that?

The only reason I actually want to get the values is because I solved it using a different way involving Newton's second law. That way seemed much more complicated than it needed to be, so I wanted to see if this method's values matched up with the more complicated way. I got the same results by subtracting the weight (800 N) from whatever value the y-axis displayed at the time(like you told me to do), then found the area under the curve. After that, I divided the area by the actual mass (80 kg), and got the same results as my other method :) Is this what you were suggesting initially?

Also, regarding your comment on jumping, I have always been afraid that the elevator cable will snap under my weight. A strange phobia of mine.

blueblast said:
Is this what you were suggesting initially?
Yes, that's right.

blueblast

## 1. What is the area under the curve of a mass time graph?

The area under the curve of a mass time graph represents the total amount of mass that has been measured over a specific period of time. It is a measure of the cumulative change in mass during the given time interval.

## 2. How is the area under the curve calculated?

The area under the curve is calculated by finding the sum of all the individual areas within the graph. This can be done by dividing the graph into smaller segments and using basic geometric formulas such as rectangles, triangles, and trapezoids to calculate the area of each segment. The sum of these individual areas will give the total area under the curve.

## 3. What units are used to measure the area under the curve?

The units used to measure the area under the curve of a mass time graph depend on the units used for the axes. For example, if the x-axis represents time in seconds and the y-axis represents mass in grams, then the area under the curve would be measured in gram-seconds (g*s).

## 4. What does the area under the curve tell us about the data?

The area under the curve can provide important information about the data being analyzed. It can tell us about the rate of change in mass over time, the total amount of mass that has been measured, and any patterns or trends that may be present in the data.

## 5. Can the area under the curve be negative?

No, the area under the curve cannot be negative as it represents a physical quantity (mass) and cannot have a negative value. If the graph dips below the x-axis, the area under that portion will be considered a negative value and will be subtracted from the total area under the curve.

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