Impact time for a simple collision

[DODonoghue]

Hi,

I have what seems like a relatively simple problem: I have 2 cylindrical copper masses that oscillate on the same vertical shaft, with the lower mass being 80g and the higher mass being 30g. There is a compression spring (stiffness = 5 N/mm) attached to the top of the heavier (lower) mass, however the masses are not connected. My question is when the masses impact what is the impact time, assuming the impact is perfectly elastic and no friction between the masses and the shaft?

Is the impact time dependent on the velocities of the masses at the time of impact or just on the masses and stiffness of the spring? My initial thinking was that the impact time can be found by taking the half period (half of compression-extension cycle) for the lighter mass and the spring, however the heavier mass is ignored in this instance. Also the velocities at impact are ignored.

Any suggestions would be greatly appreciated!

 

[IRstuff]

I think you would have to define what you mean by impact time first.

In the general sense, the answer is yes, the time is dependent on velocity, since the velocity represents some amount of kinetic energy that must be transferred away from the moving object, and the process that removes that energy may be limited in its ability to remove energy

TTFN
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[Dougt115]

IF you have the relative velocities of the two masses.
Assuming no friction.
And knowing the spring constant, k.

Time for the relative velocities to go from max to zero is half the time.

V2 = V1 - K*X * t

Solve for T when V2 = 0 and V1 is max relative velocity.

If you do not know the compression of the spring then use an energy equation.
where
Energy of the masses before collision must equal the energy stored in the spring.


1/2* M1*(V1)^2 = 1/2*K*X^2

 

[DODonoghue]

Hi thanks for this!

@IRstuff The impact time is from the initial contact between the lighter mass and the spring attached to the heavier mass, until the masses are no longer in contact, i.e. the spring is compressed until the relative velocity between the masses is zero; the potential energy in the spring is then released resulting in the masses moving apart. Once the spring returns to its initial position the impact is complete.

@Dougtt115 I don't understand how you determined the first equation (V2 = V1 - k*x*t). Could you explain this?

Thanks again!

 

[IRstuff]

Why is the lower mass moving?

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[DODonoghue]

It is a drop-test where a sequence of vertically stacked masses impact one another in a controlled manner. The sequence happens as such: Upon being dropped the lowest mass impacts a spring at the base. It rebounds off the spring and impacts the next mass in the chain (which is lighter). This lighter mass then moves away at a higher velocity, before impacting the next mass in the system. This process continues for a number of impacts between pairs of masses. I am just interested in a single collision between the two free moving masses and their impact time. Remember there is a compression spring between the masses, but the masses are not connected.