Question

Chapter 07, Problem 48


Two particles are moving along the x axis. Particle 1 has a mass m1 and a velocity v1 = +5.0 m/s. Particle 2 has a mass m2 and a velocity v2 = -7.9 m/s. The velocity of the center of mass of these two particles is zero. In other words, the center of mass of the particles remains stationary, even though each particle is moving. Find the ratio m1/m2 of the masses of the particles.

Answer 1

We can find the ratio m1/m2 of the masses of the particles using the formula for the velocity of the center of mass:

V_cm = (m1 * v1 + m2 * v2) / (m1 + m2)

Since the velocity of the center of mass is zero, we can set up the equation:

0 = (m1 * 5.0) + (m2 * -7.9) / (m1 + m2)
0 = (5 * m1 - 7.9 * m2) / (m1 + m2)

Now, we want to find the ratio m1/m2, so we'll manipulate the equation accordingly:

0 = 5 * m1 - 7.9 * m2
5 * m1 = 7.9 * m2

Now, we can find the ratio m1/m2:

m1/m2 = 7.9/5

m1/m2 = 1.58

Therefore, the ratio m1/m2 of the masses of the particles is 1.58.