A system consists of two masses masses. Mass 1 oscillates around the origin alon

Question

A system consists of two masses masses. Mass 1 oscillates around the origin along the x-axis with amplitude 1.20 cm. Mass 2 oscillates around the origin with the same frequency along the y-axis. The two masses never hit each other: mi 0.0100 kg : m2 = 0.0300 kg : A2 r1 = Ai cos(at)i r2 = A2 cos(wt + 0.830 cm )j A1-1.250 cm 7.35 rad/s w Let the velocity of the centre of mass be vcmVcm,2 1+Vcm.yj a) Give the x coordinate of the centre of mass of the system at time t- 1s (in b) Give the y coordinate of the centre of mass of the system at time t 1s (in c) Give the x component of the velocity of the centre of mass of the system at d) Give the y component of the velocity of the centre of mass of the system at e) Now assume mass 2 is not known. The centre of mass movies in a circle cm cm) ime t = is(in m/s) ime t = is(in ms) around the origin. Calculate the value of mass 2.

Explanation / Answer

Here is

from the given data
m1 = 0.01 kg
m2 = ?
r1 = 1.25*cos(7.35t)i
r2 = 0.83*cos(7.35t + pi/2)j

hence at any time t, the location of center of mass is
r = (m1*r1 + m2*r2)/(m1 + m2) = (0.0125cos(7.35t)i - m2*0.83*sin(7.35t)j)/(0.01 + m2)
as r is always radius of a circle
hence
r(t = 0) = r(t = pi/7.35 s)
hence
0.0125 = sqroot(0.0125^2*cos^2(7.35t) + m2^2*0.83^2*sin^2(7.35t))
hence
m2*0.83 = 0.0125
hence
m2 = 0.01506 kg

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