∆ energy when impacted by robot's arm

[Haim]

Hi,

This problem relates to my final's project.

I'm trying to quantify an impact on a human hand from a robot. I've thought about it in Watts, Joules and Newton's. But I ran into a problem when I thought about it like this:

If I have the mechanism (in the drawing)- its energy when falling equals to T=mgh from its center of mass. Which means that in an impact when the rod stops- my hand will absorb all the energy. BUT if I'll get hit from point A it will hurt much more than point B since its linear speed is greater. But the rod will stop either way! Meaning I will absorb all the amount of energy...

Am I wrong? Is the amount of energy is different along the rod (I know it does not make any sense).

I will appreciate any help!

 

[Stephen Tashi]

You have to consider that the materials involved (including you hand) are compressible. When a real hand collides with an object, both it and the object deform. In you situation, the rod does not stop moving the instant it hits the hand. A graph of the force on the hand due to the rod would would show a force that varied in time.
To model the situation realistically would take some very sophisticated software. Obviously, you hand is attached to you own arm and the rest of your body. If something hits you hand, there is compression and motion in body parts other than your hand. The rod also deforms in a collision.

You could try modeling the situation by replacing the hand with a mass on the end of a hooke's law spring that is fixed at the other end. Perhaps you can analyze the maximum force that appears between the rod and the mass.

 

[CWatters]

The problem is that humans are not ideal scientific measuring machines. There is no SI unit of "hurt". It's far from clear which will hurt more... getting your hand cut off quickly or slowly. Perhaps option A is actually less painful than option B.

In the situation you are looking at is the human free to move? In which case an impact might be the best way to describe the situation, or could they become crushed between the robot and another object? In which case it might be better to worry about the ultimate force or pressure the robot can exert.

Something to be aware of is that many electrical motors are essentially constant velocity devices. The more you increase the load the more power they try to deliver. eg The more you try and slow one down the more it tries to maintain it's velocity. So a robot that can only cause minor impact damage might be capable of serious crush damage unless some type of limiting system is employed.

 

[zevik]

Haim:

Indeed, if you place your hand at point A, the impact speed will be larger, but the falling robot will not come to a full stop. Its center of mass will continue downwards. So part of the robot's kinetic energy is not transferred to the hand. Hence, your hand absorbs less than mgh in this case.
To calculate how much kinetic energy your hand absorbed, you will need to balance forces AND moments.

Sorry to say, but the other answers by Stephen Tashi and CWatters are missing the point and complicate things unnecessarily. Sorry guys, but of course you may add complications such as the correction from the Earth's recoil, or the non-rigidity of the robot, the arm, the coupling to earth. Considering all these things before even solving the most basic question is worse than not understanding the basic question.

- A bored physicist