Calculate Force of Rod at Fixed Pivot Point

[sportymat]

Hello,

I have not studied any physics or mechanics in a number of years so apologise in advance.

Part of my dissertation involves the manufacture of a test rig that will continually strike an implement just above the floor, at a known force.

The rig is comprised of a rod with a known mass which is fixed at one end to a pivot point. The other end is weighted. The rod will be raised to a known angle and then left to rotate freely under gravity until it strikes the ground.

As i see it, the variables that can be manipulated in order to achieve the desired force, are length of rod, mass at end point of rod, relative angle of rod to the ground.

How would i go about calculating the necessary parameters to achieve a certain end force?

Thanks

 

[wreckemtech]

dPE=-dKE

The potential energy stored as the rig is raised will be converted to kinetic energy on the way down. KE=mV^2. Your issue is going to be a little complicated though. Because the rod also has mass of a known linear density and each differential slice dx will be raised a distance of x(sin(theta1)-sin(theta2)) you'll need to account for that too. So you'll need to do some integral calculus to figure out the total difference in kinetic energy between top and bottom. That will be the energy expended in the collision when it strikes bottom. Friction (if any) in your pivot will need to be subtracted.

The speed at which this energy is expended will factor into how much peak force is generated. You may be able to model it after something like a ball bearing hitting the floor, or you may have to determine it experimentally. You should be able to figure out the deceleration (acceleration), and then plug that into F=ma, and solve for F. Or use the impulse equation: http://en.wikipedia.org/wiki/Impulse_(physics )

That's the short answer.

 

[sportymat]

Thank you for your reply,

I again apologise for my lack of knowledge on this subject, so if i am thinking incorrectly please let me know.

I was looking at calculating linear impact forces earlier today in which, Impact force = KE/D (D = distance traveled by object), could this not be used in a similar fashion to calculate the force of the impact.

when attempting to calculate KE, I am struggling to calculate the Velocity of the striking implement at the end of the rod when it is free falling under gravity, so any help here would be appreciated? For example if the rod is 1.5m long and has mass 3kg, is raised at an angle of 30 degrees to the horizontal and has a point mass located at the far end of the rod of mass 20kg, how would we calculate KE and therefore the impact force. (assuming that there is no friction in the system)

Thanks

 

[wreckemtech]

The final kinetic energy, mass times mv^2 will be equal to the vertical distance fallen times gravity times mass, mgh.

Set the two equal to each other, and mass cancels out. So you can solve for final velocity. But your device is complicated by the fact that the rod has mass as well, and will add to the total kinetic energy (and momentum) of the device at impact.

 

[sportymat]

Is this the case even though the mass will move in an arc around the pivot point?

Thanks

 

[wreckemtech]

Yes. The mass moving in an arc really doesn't affect the net KE being generated as a result of it changing elevation. And I'm assuming that the head of the striking implement will be more-or-less perpendicular to the surface of the object it's striking. This means all the velocity will be instantaneously confined to the up-and-down axis.

If you're a decent mathematician, that should be enough to calculate the average velocity for your mass at impact. Which will give you a momentum to plug into the impulse equation. Sorry I'm kind of pressed for time at present, so I don't have time to go into all the equations in-depth. It may take you a page or two of calculations, but definitely do-able to a reasonable degree of accuracy.