Force in spring due to falling object

Click For Summary

Discussion Overview

The discussion revolves around calculating the force exerted on a crane due to a falling object attached via a non-elastic cable, modeled using a spring system. Participants explore the relationships between potential energy, spring extension, and the forces involved in this scenario.

Discussion Character

  • Technical explanation
  • Mathematical reasoning
  • Debate/contested

Main Points Raised

  • Christopher proposes a model using a spring with spring constant k, extension x, and a falling object of mass m under gravitational acceleration g, leading to the expression F=sqrt(2mgkh).
  • One participant suggests that the formula is valid if the additional height difference during deceleration can be neglected, specifically when the force due to the spring is much greater than the weight of the object (F>>mg).
  • Christopher seeks clarification on whether h in the potential energy equation mgh should include the extension x, indicating uncertainty about how to proceed if the height difference cannot be neglected.
  • Another participant indicates that if the height difference cannot be neglected, the problem leads to a quadratic equation that can be solved, with the new height being the original height plus the extension x.
  • Christopher expresses confusion about the calculations, questioning whether he should perform the calculations twice and how to structure the equations correctly.

Areas of Agreement / Disagreement

Participants have not reached a consensus on the correct approach to account for the height difference during the deceleration process, and there are multiple competing views on how to handle the calculations.

Contextual Notes

The discussion highlights the dependence of the calculations on the assumptions made about the height difference and the relationship between h and x, which remains unresolved.

ChristopherJ
Messages
4
Reaction score
0
Hi,

I'm designing a crane that is supposed to withstand forces due to a falling object attached to the crane with a non-elastic cable. I have some troubles to calculate what force that will be due to the falling object.

I figured that one way is to simplify this system with a spring with spring constant k, extension of the spring x, non-elastic cable of length h, object with mass m, gravitational constant g.

Then, the spring is hanging vertical, attached in the upper end to a rigid mount and the cable in the free hanging end, and in the free end of the cable the object is attached. If the object is falling from the point where the cable is attached to the spring it will fall the distance h. Then the following expressions may be used.

1. Potential energy due to a height, E=mgh
2. Potential energy in the spring due to an extension, E=0.5kx^2
3. Hooke´s law due to an extension, F=kx

1 and 2 gives mgh=0.5kx^2 which gives x=sqrt(2mgh/k). This combined with 3 gives F=kx=sqrt(2mgkh).

Am I right in my reasoning and the last expression? For which cases is this then true?

I would be most grateful for response.

Regards
Christopher
 
Physics news on Phys.org
The formula is good if you can neglect the additional height difference during the deceleration process. You can neglect it if F>>mg.
 
Okey, so you mean that h in mgh is the length of the cable plus x, i.e. h ist the distance from the point of release to where it comes to a stop? If I can't neglect that, how should I do the calculations then? Since x depends on h, which depends in x?
 
Last edited:
If I can't neglect that, how should I do the calculations then? Since x depends on h, which depends in x?
You will get a quadratic equation, which can be solved. The "new h" is just the old h (constant) plus x.
 
mfb said:
You will get a quadratic equation, which can be solved. The "new h" is just the old h (constant) plus x.

I'm not sure I'm following. If the new h is the old h plus x, then I can perform the calculations twice and the second time just add x to h? Or how would the equation look like?
 

Similar threads

Undergrad Drawbridge falling before caught by rope/cable - Max force
  • · Replies 13 ·
Replies
13
Views
3K
Undergrad Questions about a spring and its principle
  • · Replies 9 ·
Replies
9
Views
3K
Undergrad Newton's 2nd law for an object in free fall
  • · Replies 15 ·
Replies
15
Views
2K
High School Help me understand jerk of a falling object hitting an "ideal foam"
  • · Replies 7 ·
Replies
7
Views
2K
Undergrad Work-Energy Theorem for Moving Block and Spring System?
  • · Replies 4 ·
Replies
4
Views
3K
Undergrad Force on Body Attached to Spring at Displacement x - A.P. French
  • · Replies 6 ·
Replies
6
Views
2K
Undergrad How to Calculate force exerted on a falling body?
  • · Replies 12 ·
Replies
12
Views
3K
Undergrad Does the spring force do work on the spring itself?
  • · Replies 9 ·
Replies
9
Views
3K
Undergrad Solving the Block-on-Spring Problem Using Forces
  • · Replies 11 ·
Replies
11
Views
5K
Undergrad What is the Formula for Calculating the Length of a Hanging Spring?
  • · Replies 27 ·
Replies
27
Views
5K