Physics Mechanics Question. See Attached image. A ball of mass m_A = 5.4 kg , co

Question

Physics Mechanics Question. See Attached image.

A ball of mass m_A = 5.4 kg , connected to a horizontal spring with a relaxed length og I_O = 115 mm and a spring constant of k = 70 N/m , falls from rest a frictionless channel and collides with another ball of mass m_B = 8 kg , which is attached to a rope with a length of 200 mm and is at rest. The value of a is 0.2 m and b is 0.5 m. What is the speed of ball A, in m/s, right before impact with ball B? If ball A comes to rest immediately after the impact, what is the speed of ball B, in m/s, right after impact with ball A? If ball A comes to rest immediately after the impact, find the maximum angle (IN RADIANS) that ball B will travel through after the impact.

Explanation / Answer

when ball collides with B then ball A comes down height h.

h = a + bcos(180-120) = 0.2 + 0.5cos60 = 0.45 m

length of spring = sqrt[ (0.45)^2 + (0.5sin60 - 0.2)^2] = 0.507 m

using energy conservation to find speed of A just before collision,

(mA gh ) + (70 (0.2 - 0.115)^2 / 2) + (0) = (0) + (70 (0.507-0.115)^2 /2 ) + ( mA v^2 /2)

(5.4 *9.81*0.45) + 0.253 = 5.38 + 2.7v^2

v = 2.63 m/s

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using momentum conservation,

mA v + mb * 0 = mA *0 + mb * vf

5.4 x 2.63 + 0 = 0 + 8vf

vf = 1.78 m/s

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using energy conservation,

mgh = mvf^2 /2

9.81 L ( 1- cos@) = 1.78^2 /2

0.20 ( 1 - cos@) = 0.161

@ = 78.74 deg

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