# Newton's Cradle same diameter, different mass

lostagain
Homework Statement:
I have two cradles, one with 5 metal balls 2.54cm in diameter and 66g and one with 5 marble balls 2.54cm in diameter and 21g. The 1st metal ball was released with no applied force from 10cm which kicked the 5th ball out to 10cm's. I assumed since P and KE were both different for the metal and the marble balls, that the marble ball, when tested from the same drop height would not bounce as far. It did, 5th ball went out 10cm too.
How can the mass not affect the 5th ball more with the metal ball?
Relevant Equations:
Ball Type Weight Grams
Metal 66
Marble 21

V = SQRT(D * (acceleration due to gravity or 9.8 m/s^2))2
D = .1 in meters

P=MV
KE = =(MV^2) / 2
Ball drops cm P (Momentum)
Metal 10cm 92.4
Marble 10cm 29.4

Ball drops cm KE
Metal KE 10cm 64.68
Marble KE 10cm 20.58

## Answers and Replies

Science Advisor
Homework Helper
Gold Member
As long as all balls in a cradle have the same mass (which they do here), and as long as they're dense enough to allow us to ignore air resistance (this too is OK here), the mass doesn't matter.

Why? Because both KE and momentum/impulse are proportional to the ball mass M, so for any equation involving M we can remove M by either cancelling (when it appears in the numerator and denominator of a fraction) or dividing the whole equation by M.

Looked at another way: the metal ball scenario does affect the 5th ball more: it imparts approximately three times (66/21) the impulse to that ball compared to what is imparted to the fifth ball in the marble-ball cradle. But it needs three times the impulse to make the ball reach the same height, because the ball is three times as heavy.

lostagain