How much do the bed springs stretch when a person jumps on them?

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In summary, a person weighing 48 kg jumps from a 1.95 m platform onto an innerspring mattress with 20 vertical springs, each having a spring constant of 5000 N/m. Using the conservation of mechanical energy and the spring equation, the stretch of each spring is determined to be y=1.54 m. The spring constant does not need to be multiplied or divided by 20.
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vinnyzwrx
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Homework Statement


The innerspring mattress on your grandmother’s bed is held up by 20 vertical springs, each having a spring constant of 5000 N/m. A 48 kg person jumps from a 1.95 m platform onto the innersprings.
The acceleration of gravity is 9.8 m/s2 .
Assume: The springs were initially un- stretched and that they stretch equally (typical old fashioned bed).
Determine the stretch of each of the springs. Answer in units of m.


Homework Equations



consevation of mechanical energy using spring equation, 1/2kx2


The Attempt at a Solution



im not really sure how to setup the conservation of energy equation... if i have it right here then i should solve for y, but i don't see how to do that algebraically. i will always end up with a y on either side. unless I'm supposed to apply the quadratic formula... nope, still a wrong answer. am i setting up the conservation of energy equation right?

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  • #2
should the spring constant be multiplied by 20 to compensate for the 20 springs, or should the answer be divided by 20?

i don't see where i went wrong in my math...
 
  • #3
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Related to How much do the bed springs stretch when a person jumps on them?

1. How does landing on bed springs affect your body?

Landing on bed springs can have a significant impact on your body, depending on the height and force of the landing. Bed springs are designed to provide cushioning and support for sleeping, but they may not be able to adequately absorb the impact of a fall. This can lead to injuries such as bruising, sprains, and even fractures.

2. Are there any safety precautions to take when landing on bed springs?

It is always important to take precautions when jumping or falling onto bed springs. Make sure the bed is stable and securely attached to the frame. Also, avoid jumping or falling from high heights onto the bed, as this can increase the risk of injury.

3. Can landing on bed springs cause damage to the bed?

Bed springs are designed to withstand the weight of a person sleeping on them, but repeated jumping or falling onto them can cause damage over time. This can lead to sagging or broken springs, which can affect the comfort and support of the bed.

4. Is there a recommended way to land on bed springs to minimize impact?

If you must jump or fall onto bed springs, it is best to land on your feet with your knees bent to absorb the impact. This can help distribute the force and minimize the strain on your body and the bed springs.

5. What are the alternatives to landing on bed springs?

If you are looking for a softer landing surface, consider using a mattress topper or padding on top of the bed springs. Alternatively, you can also use a trampoline or other cushioned surface for jumping and falls. It is important to always prioritize safety and use caution when engaging in any activities involving bed springs.

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