The nickel will be 8 times louder than the penny at the hitting speeds.
How to calculate the impact of each metal?
The sound intensity (loudness) produced by an impact is proportional to the kinetic energy of the impacting object.
K.E = ¹/₂ mv²
where;
- m is the mass of the object
- v is the speed of the object
For penny, the impact is;
K.E = ¹/₂ x (2.5) x (10)²
K.E = 125 J
For nickel, the impact is;
K.E = ¹/₂ x (5) x (20²)
K.E = 1,000 J
The ratio of their kinetic energy is;
nickel / penny = 1,000 J / 125 J
= 8
Thus, a nickel hitting a metal lid at speed of 20 inches/second creates a sound approximately 8 times louder than penny hitting a metal lid at a speed of 10 inches /second.