Calculating Distance Using Force, Mass, and Acceleration

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Homework Help Overview

The problem involves calculating the distance a rock falls based on its weight, the force at impact, and the acceleration due to gravity. The original poster presents a scenario where a rock weighing 68 kg is dropped from a height, and the impact force is given as 15 kN. There is a focus on understanding the relationship between force, mass, and distance fallen.

Discussion Character

  • Exploratory, Assumption checking, Conceptual clarification

Approaches and Questions Raised

  • Participants discuss the relationship between force and distance, questioning the adequacy of the provided information. Some suggest using kinetic energy equations to relate the fall distance to the impact force, while others note the need for additional details about the surface upon impact.

Discussion Status

The discussion is ongoing, with participants exploring different interpretations of the problem. Some have raised concerns about missing information and the implications of different types of collisions. There is an acknowledgment of the complexity involved in relating the variables presented.

Contextual Notes

Participants note that the impact force may vary based on the nature of the surface and that the problem lacks specific details regarding the conditions of the fall. The original poster also mentions that the question was posed by a friend involved in rock climbing, which adds context to the discussion about safety and forces involved in climbing scenarios.

bradosaurus
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Homework Statement




A rock is dropped from x(meters) height. The rock weighs 68 kg, and its force at impact with the ground is 15 kiloNewtons. If the acceleration due to gravity is 9.8m/s^2, what is the distance/height the rock has fallen?


Homework Equations




F=m*a

15kN=15000kg*m/s^2

666.4N=68kg*9.8m/s^2

The force exerted by the rock at stationary position is 666.4 Newtons.

The rock fall distance is x meters.


The Attempt at a Solution




666.4N*x=15000N

(666.4kg*m/s^2)*x=15000kg*m/s^2

x=(15000kg*m/s^2)/(666.4kg*m/s^2)

x=22.51


This was all I could come with, but it is simply the ratio of the force. How do I find distance?
 
Last edited:
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Please state the complete problem exactly as given. As you've written it, there's not enough information. (The impact force depends on the nature of the surface being hit.)
 
Doc Al said:
Please state the complete problem exactly as given. As you've written it, there's not enough information. (The impact force depends on the nature of the surface being hit.)

Shouldn't there be a formula for the kinetic energy of a mass falling distance x and a formula for the F generated by an unknown kinetic energy when it hits? The two could then be equated resolving x.

I don't see elastic/inelastic collisions mentioned.
 
AC130Nav said:
Shouldn't there be a formula for the kinetic energy of a mass falling distance x
That one's easy.
and a formula for the F generated by an unknown kinetic energy when it hits?
That one's not so easy. More information is needed.
 
Doc Al said:
More information is needed.

Thank you for your responses. This was a question posed to me by a friend of mine who rock climbs. He inferred that the distance of the fall could be calculated using the force, mass and gravitational constant. Is it correct to say that the energy spent to stop will be the same for different stopping distances while the required force will be variable?

The question may be better understood as follows:

A person who weighs 68 kg falls an unknown distance. The climber's rope has a breaking strength of 15 kN, and a dynamic elongation of 29%. Barring any other variables (friction, etc.), what is the furthest distance the climber could fall before the rope fails?
 

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