Consider a glancing collision between two identical spheres of 0.038 kg, with on

Question

Consider a glancing collision between two identical spheres of 0.038 kg, with one of the spheres initially at rest. Initially the incoming projectile has a velocity of 1.30 m/s to the right and after the collision we observe that this sphere leaves the collision region with a velocity of 0.50 m/s at an angle of 26° to its initial direction. (Assume that the +x-axis is to the right and the +y-axis is up along the page. Angles are measured counterclockwise from the +x-axis. Do not assume this collision is elastic.)

Find the x-component and the y-component of the velocity of the second sphere

Explanation / Answer

Apply conservation of momentum to the spheres

m1 v1i + m2 v2i = m1 v1f cos theta 1 + m2 v2f cos theta 2

m1 = m2

so above equaiton changes as

0+ 1.30 = v1f cos theta 1 + 0.50 cos 26

v1f cos theta 1 = 0.85 m/s

apply conservation of mometum along y axis

0+0 = - m v1f sin theta1 + m v2f sin thet2

v 1f sin thet1 = v2f sin theta 2

=0.5 sin 26

=0.219 m/s

the x-component and the y-component of the velocity of the second sphere is

0.85 m/s and 0.219 m/s

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