Impact force due to angual movement?

[JBlackhole]

I am trying to estimate the force at impact due to an angular movement
Assumed a pendulum of mass 'm' and inertia 'I' attached to a infinitely stiff pendulum. See attached picture
The pendulum is given an horizontal acceleration 'a' which means that it will hit a infinitely stiff wall.
If the angle beta is very small could one use F=m*a?

Thanks

Regards

JXB

[IRstuff]

You know that the pendulum motion is circular, so why not decompose to the vertical and horizontal components?

TTFN

[RichardJ]

If the wall and the pendulum are infinitely stiff the coefficient of restitution will be 1, so the velocity of the pendulum will be reversed when it hits the wall (a perfect bounce, with no loss of energy). Further, if the wall and the pendulum are infinitely stiff they will not deform at all during the bounce, so the bounce will be instantaneous. That mean the acceleration will be infinite, and so will the force.

You can't calculate a realistic number for the force without realistic properties for the pendulum and the wall.

[wayne]

I think you need to review the physics a little more.

What's important is the kinetic energy (velocity) at the time the object hits the wall. An initial acceleration over some time interval(?)

creates velocity. This energy can be partially absorbed by the materails and partially imparted as kinetic energy.

At any rate, the force imparted is is a function of the kinetic energy at the time of impact and rigidity of both the ball and the wall. In F=ma for this problem, the acceleration is actually the decelleration during impact. If the wall and the ball were truly infinitly stiff, then the force is also infinite. If you
could some how estimate the average decelleration, perhaps you could estimate the force this way.

The problem as stated, and as shown, (small angle) suggets that the pendulum and the small angle form the normal to the wall is more or less trivial
to the problem.

Is there some more informaton available?

Wayne

[JBlackhole]

Wayne,

Thanks for your post. As suggested by others post my basic physic is a bit rusty. It was a bit silly of me to suggest that the wall is infinitely stiff. It isn't I am trying to size the wall!

The Kinetic energy of the pendulum is E=1/2*J*w^2

So if one assumes that all the energy is absorbed by the wall over a short time (say 0.5s) one might be able to estimate an impact force. Is this correct?

My line of thinking

1. Estimate kinetic energy of the ball (Eb)

2. Eb is totally absorbe by the wall

3. If one assumed the wall as a vertical beam (like a pillar), one could calculate the deflection of the beam under a force F. This delfection create strain energy (U)

4. The strain energy (U) must equal the kinetic energy (Eb).

Thanks

Regards

JXB

[f.kohlhepp]

In addition to all the great comments, let me show you a path forward and a place to look further:

[JBlackhole]

Fred,

Thanks for the provided files. I'll try to take the time later to go through the details. I have just spotted a small problem with the variable teta1 in the mcad file "pendulum". See attached picture.

Thanks

JXB

[RichardJ]

That's because version 11 is ignoring the time units, but later versions require that there are no units for rkfixed (or Odesolve). Multiply the second element of the Dtheta(t,theta) vector by s^2 to remove the units.

[f.kohlhepp]

Just another reason to hold onto version 11 by my fingernails!! ; )

[PhilipOakley]

Immovable object / irresistable force = inconceivable disturbance 😉

perfectly stiff objects don't do 'forces of compression'.

A thought experiment:

If you drop a dart onto your hand, the flight feathers don't reach your palm (something tells it to stop), but if you drop a stream of water onto your hand the tail of the column still reaches your palm. Now think about a firm jelly as an intermediate case, and what parameters you need to add to model the situation.

Philip

[wayne]

A couple of additional thoughts (if you havn't had enough yet)

1) A common material test for ducitility of a steel specimen is the Charpy V Notch test, which is a pendulum test.
Could look up the specifics of this.

2) The desing of a wall is a dynamics problem. For example the dynamic amplification factor for a beam in which a weight at
the center is supported just at the beam surface, but not by the beam, and then released onto the beam is 2. (the maximum
deflection of the beam is twice the static deflection). One way to solve for this much the same as I think your are suggesting:
Equate the difference in potential energy to the internal strain energy at the maximum deflection.

Good Luck.

Wayne

[jeanGiraud]

jmG