mass is traveling to the right with a speed A 10.5kg mass is traveling to the ri
ID: 2099560 • Letter: M
Question
mass is traveling to the right with a speed
A 10.5kg mass is traveling to the right with a speed of 2.50m/s on a smooth horizontal surface when it collides with and sticks to a second 10.5kg mass that is initially at rest but is attached to a light spring with force constant 120N/m . Find the frequency of the subsequent oscillations. Find the amplitude of the subsequent oscillations. Find the period of the subsequent oscillations. How long does it take the system to return the first time to the position it had immediately after the collision?Explanation / Answer
omega = sqrt(K/m) = sqrt(K/(m1+m2)) =2.390 rad/s/s
omega =2*pi*F
F =0.380 Hz
speed after collision comes from conservation of liniar momentum
m1*Vi =(m1+m2)*Vf
Vf = m1*Vi/(m1+m2) =0.5*2.5 =1.25 m/s
energy of moving masses is
E = (m1+m2)*Vf^2/2 =21*1.25^2/2 =16.40625 Joule
KA^2/2 = E
Amplitude A is
A =sqrt(2*E/K) =0.5229 = 0.523 m
Period is
T=1/F =1/0.380 =2.6316 =2.632 seconds
t = T/2 = 1.31578 =1.316 seconds
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