Finding a sensor for vibration of impact event, preferably for interface with arduino
A dumbell falling from 1m height will hit the ground at about 4.4m/s. But what acceleration will it experience when it hits? This depends on the distance it travels during deceleration. Assuming the coatings on the dumbell and floor have some give in them, lets assume that it takes 1mm to decelerate. In this case, the dumbell will experience nearly 100G deceleration. So, you just need to find a device which can cope with these kind of accelerations.

How about the ADXL377 from Analog Devices? It's even advertised for this very application.



Personally, I'd be more worried about the Arduino and the tape holding it onto the dumbell. How much load will it have to take during the impact?

F = ma
= 0.1kg * 1000m/s/s
= 100N
= 10kg

That's a lot of load. You'd better screw the accelerometer on with some nice bolts, to transmit the acceleration to it accurately, and use anti-vibration mounts for the Arduino.