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I'm looking to calculate how much force is needed to strike the bars on my glockenspiel (musical instrument).

My theory is that I can use a wooden ball of a known mass, and drop it at varying heights until the proper sound is achieved. I can then use equations that model free-falling objects (I am neglecting air resistance) to determine the amount of force the ball exerts on the bar. Is this the best way to find the force?

Here's the problem: this is an inelastic collision which means that the kinetic energy is not conserved on impact. I am not sure how to account for this loss.

Mass of ball: 2.2g

Starting height: 0.1397m (5.5 in)

End height: 0m

Initial Velocity: 0m/s

Final Velocity: ?

Elapsed time: ?

I tried "messing around" with some equations as shown below, but didn't come up with anything substantial:

Free Fall:

y

_{f}=y

_{i}+ (V

_{y})

_{i}Δt -1/2g(Δt)

^{2}

0 = 0.1397m - 0.5*9.8*Δt

^{2}

Δt=0.169s

(V

_{y})f = (-9.8m/s

^{2}* 0.1397m) = 1.37m/s

This isn't really helping me out here. Could someone set me on the right path?