Question

a ball of clay, moving in the +x - direction with a speed of 14.4\frac{m}{s}, collides with the first in a line of n = 10 stationary identical balls of clay, causing a chain - reaction of collisions. each time a new ball of clay is struck, it sticks to the clump that struck it. the only forces acting on any of the balls of clay are from the other balls of clay. find the speed in meters per second of the giant clump of clay balls that emerges after all of the collisions have occurred. provide at least two decimal places

Explanation:

Step1: Apply the law of conservation of momentum

The law of conservation of momentum states that \(p_{initial}=p_{final}\). Let the mass of each clay ball be \(m\). The initial momentum is \(p_{initial}=m\times14.4\) (since only the first ball is moving initially). The final mass is \(M=(N + 1)m=(10+ 1)m = 11m\), and let the final velocity be \(v\). So, \(p_{final}=11m\times v\).

Step2: Solve for the final velocity

Since \(p_{initial}=p_{final}\), we have \(m\times14.4=11m\times v\). Canceling out the mass \(m\) (because \(m
eq0\)) from both sides of the equation, we get \(v=\frac{14.4}{11}\).

Answer:

\(v = 1.31\space m/s\)