Figuring acceleration using time and the reading of a weight scale help please

In summary, the student is trying to find the acceleration of the elevator while standing on a scale. The first 5 seconds show the student's normal weight of 500 N, with no acceleration. In the next 5 seconds, the scale reads 700 N, resulting in an acceleration of 0.4 m/s/s. However, the student realizes they must use their mass instead of weight in the formula, and adjusts their calculations accordingly. The final answer for the acceleration is -3.92 m/s/s, as the student is moving downwards in the last 5 seconds.
  • #1
benji
48
0
I'm new to this stuff, so the question may be really simple, but I just can't work it right...

Alright, so the question I'm trying to figure is this:

The student's normal weight is 500 N. He stands on a scale in an elevator and records the scale reading as a function of time.

So for the first 5 seconds the scale is at 500 N, thus the acceleration is 0 m/s/s. Then the next 5 seconds the scale reading is at 700. Now how do I go about figuring the acceleration?

I know F=ma. The only way I could think of solving this problem is putting the difference in for the force variable, the students weight in for the mass variable and then solving for acceleration.

So for example for the second 5 seconds I used 200=500a and I got 0.4 m/s/s. This doesn't seem like the right answer so I must be missing something or just going about the problem completely the wrong way. If someone could point me in the right direction I'd really appreciate it!
 
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  • #2
You have it mostly right, the 'm' in the equation is the student's mass, not weight. weight = mass*gravity.
 
  • #3
500/9.8 = 700/x

Cross multiply, solve for x, subtract g, and that is your acceleration upward.
 
  • #4
ek said:
500/9.8 = 700/x

Cross multiply, solve for x, subtract g, and that is your acceleration upward.

If I did it this way I do 500/9.8=700/x and x=13.72m/s/s. But then the last 5 seconds of the boys motion is downward and the scale reads 200N (300N0 lighter (when he was going up in the second 5 seconds the scale was 200N heavier [700N]). When I do 500/9.8=300/x I get x=5.88m/s/s. That doesn't seem right... So I assume I add 5.88m/s/s to gravity, then I get 15.68m/s/s.

...is that correct?
 
  • #5
No. You are using the formula [itex]F_{net}=ma[/itex], meaning the net force is accounted for (including gravity). You should really be starting all these problems with a free-body diagram, BTW.

Review your work with this in mind and remember that your final answer should be negative because you defined the upward direction as positive.
 
  • #6
benji said:
If I did it this way I do 500/9.8=700/x and x=13.72m/s/s. But then the last 5 seconds of the boys motion is downward and the scale reads 200N (300N0 lighter (when he was going up in the second 5 seconds the scale was 200N heavier [700N]). When I do 500/9.8=300/x I get x=5.88m/s/s. That doesn't seem right... So I assume I add 5.88m/s/s to gravity, then I get 15.68m/s/s.

...is that correct?
Your first part is right. 13.72 - 9.8 is the acceleration.

For the second part, since it's the opposite direction, you subtract that number from 9.8, instead of the other way around, to get the acceleration downwards. In this case it would be 9.8-5.88=3.92 m/s^2.
 

1. How do I calculate acceleration using time and a weight scale reading?

To calculate acceleration, you will need to measure the change in velocity over a certain amount of time. This can be done by taking two weight scale readings at different times and using the formula a = (vf-vi)/t, where a is acceleration, vf is final velocity, vi is initial velocity, and t is time.

2. What units should I use for time and weight scale readings?

Time should be measured in seconds, and weight scale readings should be measured in units of force, such as Newtons or pounds. It is important to ensure that all units are consistent in order to get an accurate calculation of acceleration.

3. Can I use any weight scale to measure acceleration?

No, not all weight scales are suitable for measuring acceleration. It is important to use a scale that is specifically designed to measure force or weight in order to get accurate readings. A bathroom scale, for example, is not suitable for measuring acceleration.

4. How many weight scale readings do I need to calculate acceleration?

In order to calculate acceleration, you will need at least two weight scale readings taken at different times. However, the more readings you take, the more accurate your calculation will be. It is recommended to take multiple readings and then calculate the average for a more precise result.

5. Are there any factors that may affect the accuracy of my acceleration calculation?

Yes, there are several factors that may affect the accuracy of your acceleration calculation. These include human error in taking the weight scale readings, external forces acting on the object being measured, and the accuracy and precision of the weight scale itself. It is important to take precautions and use proper techniques to minimize these factors and improve the accuracy of your calculation.

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