Use of energy or force in spring question

In summary, the problem at hand is to determine the force constant of a bungee cord for a bungee jumper who is dropped from a height of 36m above a river and needs to stop 4m above the river. The initial calculation using Hooke's Law and equating 700N to -k * 7 results in a force constant of 100. However, this is not the correct method as it does not take into account the jumper's inertia. Instead, the energy at the start and end points should be considered. The force method is incorrect because it does not account for the residual velocity that may cause the jumper to crash into the ground. Therefore, the energy method should be used to solve this type
  • #1
frostchaos123
17
0
Question is:
A balloon is 36m on top of a river, a bungee jumper has a unstretched cord of 25m attached to him and his weight is 700n

If he is to stop 4m above the river what should the force constant of the cord be?

My calculation is that since the cord can only extend 7m, using hooke's law I equate 700n = -k * 7 which gives 100. However I was told that the force method is not correct and I should consider energy at start and end points instead.

So my question why is the force reasoning incorrect and if there is a general way to tell how to choose, whether by force or by energy to solve a given problem?
 
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  • #2
That would be correct if the 700N man was statically loaded (i.e. wasn't dropped or falling). But since he is dropped from some height that person with the stiffness you calculated would overshoot and crash into the ground because he has inertia. It takes more force to stop something moving than to hold something up if that makes sense.
 
  • #3
I see. In this case would it be correct to say that force should not be used, because even though the forces cancel out each other, there is a residual velocity that continues downwards and crash the person into the ground?
 

1. How does the use of energy or force affect the behavior of a spring?

The use of energy or force can cause a spring to expand or contract, depending on the direction of the force applied. This is due to the spring's natural tendency to return to its original shape after being stretched or compressed.

2. What factors affect the amount of energy stored in a spring?

The amount of energy stored in a spring is affected by its stiffness, also known as its spring constant, as well as its length and the amount of force applied to it. A stiffer spring with a higher spring constant will store more energy than a less stiff spring.

3. How is the use of energy or force in a spring related to Hooke's Law?

Hooke's Law states that the force applied to a spring is directly proportional to the amount of stretch or compression of the spring. This means that the more energy or force applied to the spring, the more it will stretch or compress, following a linear relationship.

4. Can the use of energy or force in a spring ever cause permanent deformation?

Yes, if the amount of force applied to a spring exceeds its elastic limit, it can cause permanent deformation and the spring will not return to its original shape. This is known as plastic deformation and can occur in materials with low elasticity, such as plastic or rubber springs.

5. How is the use of energy or force in a spring important in everyday life?

The use of energy or force in springs is important in many everyday objects, such as car suspension systems, pogo sticks, and door hinges. It allows these objects to absorb and release energy, making them more efficient and durable. Springs also play a crucial role in many industrial and technological applications, such as in shock absorbers and mechanical clocks.

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