Problem 54 The vector position of a 3.50-g particle moving in the xy plane varie

Question

Problem 54 The vector position of a 3.50-g particle moving in the xy plane varies in time according to r,-(31+ 3j): + 2jl2, where t is in seconds and T is in centimeters. At the same time, the vector position of a 5.50 g particle varies as= 3-2 it 2-6% At 1 = 2.50 s, determine (a) the vector position of the center of mass, (b) the lin- ear momentum of the system, (c) the velocity of the cen- ter of mass, (d) the acceleration of the center of mass, and (e) the net force exerted on the two-particle system. , CENGAGE 'Learning Notes

Explanation / Answer

given m = 3.5 g

r1 = (3i + 3j)t + 2jt^2

r is in cm

M = 5.5g

r2 = 3i -2it^2 - 6jt

at t = 2.5 s

a. rcom = (mr1 + Mr2)/(m + M)

r1 = 7.5i + 20j cm

r2 = -9.5i - 15j cm

hence

rcom = -2.888i - 1.388 j cm

b. v1 = 3i + 3j + 4jt

v2 = -4it - 6j

at t = 2.5 s

v1 = 3i + 13j cm/s

v2 = -10i - 6j cm/s

hence

linear momentum = mv1 + Mv2 = -44.5i + 12.5j g cm/s

c. Vcom = (mv1 + Mv2)/(m + M) = -4.9444i + 1.3888j cm/s

d. a1 = 4j

a2 = -4i

hence

acom = (ma1 + Ma2)/(m + M) = -2.444i + 1.5556 j cm/s/s

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