How many g-forces are experienced by this object

[markmac]

Hello everyone. I know this may be a simple problem for some, however I am having a hard time figuring it out.

I need to figure out how many g-forces are experienced when dropping a 210 pound (95.2kg) object a distance of 1.5 feet. Thus I can figure out how much that object "weighed" at the time of impact.

Thanks for any help you can provide!

 

[Tide]

You know the speed at impact and the "final" speed. What you don't know is how long it takes to decelerate the object. You need more information or must find a way of estimating the deceleration time.

 

[markmac]

I guess I didn't think of that. It is not an extremely accurate problem, so I would say equivalent to dropping a sandbag on the ground. I would say that would be a fairly immediate deceleration time?

Thanks for your help

 

[markmac]

Anyone have any ideas on this? This problem has been driving me nuts! LOL

 

[mezarashi]

G forces: the G is used to mean multiples of 9.8 m/s/s. So an acceleration of 2 G would be 19.6 m/s/s. The "weight" of the object at impact, or rather its impulse as usually used in science, depends on the time of impact. Try jumping off a height (not recommended of more than 3 inches) without bending your knees (with them straight). Trust me, this will hurt. Now jump off a height of 1 meter but with knees allowed to bend as it receives the impact. You feel less force, less pain.

The simple governing equation is:

Ft = mv

F - force, t - time, m - mass, v - velocity before impact.

Two unknowns, force and time. Conclusion, unless you can figure out time, you can't figure out much.

 

[mezarashi]

I would say that would be a fairly immediate deceleration time?

Nothing can be stopped in zero time. Note from the equation earlier that as the time approaches zero, for any given m (mass) and v (final velocity), Force must approach infinity, which is silly. Zero-time impacts don't exist in the physical world.

 

[markmac]

G forces: the G is used to mean multiples of 9.8 m/s/s. So an acceleration of 2 G would be 19.6 m/s/s. The "weight" of the object at impact, or rather its impulse as usually used in science, depends on the time of impact. Try jumping off a height (not recommended of more than 3 inches) without bending your knees (with them straight). Trust me, this will hurt. Now jump off a height of 1 meter but with knees allowed to bend as it receives the impact. You feel less force, less pain.

Ok, for sake of simplifying this problem, how would I determine the G forces I would experience if I tried the experiment above, jumping off a height of 3 inches, and not bending my knees... Taking for granted that I just "fell" from that height, and landed on the ground? And for argument sake, say I weighed 210 pounds (which I do not LOL), and it was a 1.5 foot drop instead of 3 inches?

As for the time thing, can I not figure out how long that object was falling, if I know that it fell 1.5 feet, and the gravitational acceleration is 9.8m/s/s or 32ft/s/s?

Thanks for everyone's help! Muchly appreciated. I did not realize that it would be this complicated!

 

[mezarashi]

Refer to the Ft = mv equation above (it's Newton's 2nd law by the way)

As for the time thing, can I not figure out how long that object was falling, if I know that it fell 1.5 feet, and the gravitational acceleration is 9.8m/s/s or 32ft/s/s?

From this information, you can determine the final velocity through kinematics or kinetics. So you will know v. You know m because you just told me your weight. But I know nothing about the time of impact. How long it will take to stop you once you touch the floor (the floor is elastic, it will yield a bit. your joints are a bit elastic too, they will give way a bit and spend some time, maybe a couple milliseconds).

Because I cannot tell how much time it takes, I cannot solve the equation: F = mv/t. All I can say is that if t is very small, then F is very big. If t is very big, then F is very small.

 

[markmac]

Thanks for your help mezarashi!

As I mentioned before, I am not looking for an exact precise answer. I am just looking for a ballpark figure. So could you figure out how many G forces I would experience (roughly) if I fell from 1.5 feet on to the ground, weighing 210 pounds? I know there are a LOT of variables involved in figuring out something like this precisely, but a ballpark figure would be beneficial!

Thanks again for your help!

 

[mezarashi]

Well your welcome markmac. Hope to help you understand the physics of things as much as you can. As for the ballpark figure, I'm really afraid I have no experimental experience with jumping off things and measuring my impact. I would suggest if you really must. To get a large enough scale so that you can jump on it, then see how far the scale jumps just as you land. That would be the force you are feeling. Try jumping with knees bent, without, etc and see the difference =D

 

[markmac]

Unfortunately, the whole scale idea is out of the question, that is why I turned to physics equations!

Thanks anyway!