Spheres A (mass 0.020 kg), B (mass 0.030 kg), and C (mass 0.050 kg), are each ap

Question

Spheres A (mass 0.020 kg), B (mass 0.030 kg), andC (mass 0.050 kg), are each approaching the origin as they slide on a frictionless air table (Figure 1) . The initial velocities of A and B are 1.50 m/s and0.50 .m/s All three spheres arrive at the origin at the same time and stick together.

x-component of the initial velocity of C be if all three objects are to end up moving at 0.50 m/s in the +x-direction after the collision

What must the y-component of the initial velocity of C be if all three objects are to end up moving at 0.50 m/s in the +x-direction after the collision

Explanation / Answer

Now for calculating the velocity of C in x-component, we need to consider that momentum before and after collision are same.

pi = pf.

Here we need to give ' + & - " signs according the the direction of the spheres with respect to the x axis.

[- 1.5 * 0.02] + [- 0.5 * 0.03]cos 60 + [0.05 * Cx] = [0.02 + 0.03 + 0.05] * 0.5

We get Cx= 1.75 m/s.

Same for y- component,

Since the spheres are moving in x direction after collision, final momentum in y direction would be Zero,neither we would have component of A sphere, so we have

[- 0.5 * 0.03]sin 60 + [0.05 * Cy] = 0

Cy= 0.26 m/s.

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