# I I need help with a Rigid Pendulum Calculation please

1. Jul 12, 2017

### babu9000

I have a rigid body pendulum that is used to strike an object at the bottom of its swing. Ultimately I would like to know how much forced is the object being struck with. Could I do this with just knowing the velocity of the weight? I was thinking then I could get P=MV. Can someone please help e figure this out. Please see the attached diagrams.

Last edited by a moderator: Jul 12, 2017
2. Jul 12, 2017

### jbriggs444

No, knowing the velocity and mass of the rigid pendulum is not sufficient to determine the force with which it will strike a stationary object. Nor is it sufficient to tell you how much momentum is transferred from pendulum to target during the collision.

If, however, you are able to observe how far the pendulum rebounds, you could make a determination of how much momentum was transferred. That is the essential idea behind a ballistic pendulum.

3. Jul 12, 2017

### babu9000

Is there a formula I can use to determine force or energy?

4. Jul 12, 2017

### jbriggs444

Energy will be lost in the inelastic collision. But momentum will be conserved(*). Do you know the formula for momentum?

You know the momentum of the target prior to the collision. That's zero. If you know the momentum of the pendulum before and after the collision, you can calculate how much momentum winds up in the target afterward. If you know how much momentum winds up in the target afterward and you know its mass then you can determine its velocity. If you know the target's velocity and its mass then you can determine its kinetic energy.

(*) The axle about which the pendulum turns will exert a force during the collision. A proper analysis of the problem would involve angular momentum as well as linear momentum.

Force is more problematic. If the materials are soft, the collision could take place over a longer interval and involve smaller forces. If the materials are hard, the collision would take place over a shorter interval and involve larger forces. Force is not usually an easy thing to determine for a collision. Nor is it very useful.

You seem to want to calculate a number. But it is not clear that you will know what to do with any number that you calculate. What is the actual goal of this exercise?

5. Jul 12, 2017

### babu9000

I am trying to figure out force or energy imparted on the stationary object. I don't have a good way to measure the height on recoil and the material is plastic and soft.

I was trying fine Velocity and Force and make an assumption of .1s for time. I tried setting up a standard force gauge, but it cannot capture the impulse.

Mass= .594kg

Length (L) = .283m

Gravity(g) = 9.8m/s2

Pe = Ke

(Mass*Gravity*Height) = (½mv^2)

Re-written for pendulum as

V=sqrt(2*g*L(1-cosθ)

Force is calculated as [Mass*(Change in Velocity /Change in Time)]

F= m*(ΔV/ΔT)

at 90 degrees I got 2.93 lbf
at 179 degrees I got 4.11 lbf

6. Jul 12, 2017

### jbriggs444

Garbage in, garbage out. You cannot get accurate numbers out if you do not have accurate numbers to put in.

Since this is a pendulum on an axle, we are talking rotational kinetic energy given by $KE = \frac{1}{2}I \omega^2$ where I is the moment of inertia of the pendulum and $\omega$ is its rotation rate (e.g. in radians/sec).

You can obtain the moment of inertia for a long thin uniform beam about an axis at one end from Google. Your pendulum may be neither a uniform beam nor a mass on the end of a beam of negligible mass -- that complicates things. You may have to work to get a good number for its moment of inertia. [Treat it as a beam plus a mass and add the two moments of inertia -- that would work]

The relevant angular momentum L will be $L = I \omega$.

The angular impulse (change in angular momentum) is given by the difference between angular momenta before and after the collision. It is also given by torque multiplied by time. And torque is given by force times length of the moment arm.

So you start with potential energy. You use that as rotational kinetic energy just prior to impact. You try to measure final potential energy. You use that as rotational kinetic energy just after impact. You use the two rotational energies to determine angular velocities just before and after impact. That gives you the change in angular momentum. That is the rotational impulse that is delivered by/to the target. You divide by the length of the moment arm to get the associated linear impulse.

If you are smart you stop there.

Otherwise, you divide by the estimated time of collision to get the estimated force of impact.

Last edited: Jul 12, 2017