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Question

Four billiards balls, each of mass 0.5 kg, all are traveling in the same direction on a billiard table, with speeds of 2 m/s, 4 m/s, 8 m/s, and 10 m/s. What is the linear momentum of this system?


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Solution

Step 1: Given data

Mass of four balls = 0.5kg

Speed of ball1=2m/s,ball2=4m/s,ball3=8m/s,ball4=10m/s

Step 2: Calculating the momentum of each ball

Linear momentum- A system's linear momentum is just the sum of its constituent parts' linear momentum.

The momentum in terms of the velocity and mass of the ball is,

P=m×v[whereP=momentumofbody,v=velocitywithwhichthebodyismoving,M=massofthemovingbody]

Momentum for ball1

P1=m1×v1P1=0.5×2P1=1kgms-1...........equation(1)

Momentum for ball2

P2=m2×v2P2=0.5×4P2=2kgms-1...........equation(2)

Momentum for ball3

P3=m3×v3P3=0.5×8P3=4kgms-1...........equation(3)

Momentum for ball4

P4=m4×v4P4=0.5×10P4=5kgms-1...........equation(4)

Step 3: Calculating linear momentum of the system,

We will add an equation (1),(2),(3),and(4) so that we get net linear momentum.

P=P1+P2+P3+P4P=1+2+4+5P=12kgms-1

Hence, the net linear momentum of this system is 12kgms-1.


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