Bathroom scale being compressed but jumping on it

In summary, the conversation discusses the concept of using a bathroom scale to measure weight and how to find the compression of the spring when a person jumps on it from a certain height. The conversation covers using formulas such as Hooke's law and energy equations to solve for the spring constant and the displacement of the scale. It also mentions the conversion of gravitational potential energy to stored energy in the spring. The final conclusion is that the compression of the spring can be found by equating the gravitational potential energy to the energy stored in the spring.
  • #1
kavipach
20
0

Homework Statement


If you stand on a bathroom scale, the spring inside the scale compresses 0.55mm, and it tells you your weight is 760N.
Now if you jump on the scale from a height of 1.3 m, what does the scale read at its peak?
 
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  • #2
What are your thoughts on the question? Post your attempt.
 
  • #3
well i tried a few things... i found the persons mass which is 77.55kg.Since F=ma,and we have m, i tired using kinamatics to find a but finding the velocity of the person just before impact. Then i got stuck. I don't know how to go about this question.
 
  • #4
kavipach said:
well i tried a few things... i found the persons mass which is 77.55kg.Since F=ma,and we have m, i tired using kinamatics to find a but finding the velocity of the person just before impact. Then i got stuck. I don't know how to go about this question.

So when the person stands on the scale, they weigh 760N. This means that the spring compresses. Do you know a formula that relates force and extension?
 
  • #5
ya hookes law...F=kx.
 
  • #6
where k equals spring constant and x equals displacment
 
  • #7
kavipach said:
ya hookes law...F=kx.

yes

kavipach said:
where k equals spring constant and x equals displacment

good.


So can you find the spring constant,k using the information in the first line of the question?
 
  • #8
according to this the constant equals to 1381818.2 is this right
 
  • #9
kavipach said:
according to this the constant equals to 1381818.2 is this right

1381818.2 N/m yes, remember to put in your units.


So second line now. If the person is at 1.3m in the air, what type of energy does he have? This energy is converted into the energy needed to compress the spring a displacement,x, at the peak.
 
  • #10
potential energy?
 
  • #11
kavipach said:
potential energy?

yes. What is the formula for gravitational potential energy? And what is the formula for the energy stored by a spring?
 
  • #12
The formula for gravitational potential energy is U=mgy where u equals the p.e, m equals mass and y is the displacement. the formula for the energy storedd in a spring is U=1/2kx^2
 
  • #13
kavipach said:
The formula for gravitational potential energy is U=mgy where u equals the p.e, m equals mass and y is the displacement. the formula for the energy storedd in a spring is U=1/2kx^2

So if all the gravitational energy is converted to energy stored in the spring, that makes

gravitational p.e. = energy stored in the spring.


Can you find the compression,x for the scale now?
 
  • #14
ya i think i can..thanks for all the help..your a life saver
 

1. How does a bathroom scale measure weight?

A bathroom scale measures weight by using a spring or strain gauge to calculate the force exerted on it when an object (such as a person) stands on it.

2. Why does a bathroom scale compress when I step on it?

A bathroom scale compresses because it is designed to measure weight by measuring the force or pressure exerted on it. When you step on the scale, the force of your weight causes the scale to compress.

3. Can I trust the accuracy of a bathroom scale that compresses?

Yes, you can trust the accuracy of a bathroom scale that compresses. As long as the scale is properly calibrated and functioning correctly, the compression of the scale will not affect its ability to accurately measure weight.

4. Is it normal for a bathroom scale to jump or fluctuate when I step on it?

Yes, it is normal for a bathroom scale to jump or fluctuate slightly when you step on it. This can be due to the sensitivity of the scale and the movement of the person standing on it. However, if the scale is jumping excessively or giving inconsistent readings, it may be a sign of a malfunction and should be checked or replaced.

5. How can I ensure the accuracy of my bathroom scale?

To ensure the accuracy of your bathroom scale, it is important to regularly calibrate it according to the manufacturer's instructions. Additionally, make sure the scale is placed on a flat and stable surface and that you are standing still and evenly distributed on the scale when taking a measurement.

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