The vector position of a 3.60 g particle moving in the xy plane varies in time a
ID: 1435174 • Letter: T
Question
The vector position of a 3.60 g particle moving in the xy plane varies in time according to r with arrow1 = 3i + 3j t + 2jt2 where t is in seconds and r with arrow is in centimeters. At the same time, the vector position of a 5.25 g particle varies as r with arrow2 = 3i 2it2 6jt. (a) Determine the vector position of the center of mass at t = 2.70. r with arrowcm = 5.6497i.3844j Incorrect: Your answer is incorrect. cm (b) Determine the linear momentum of the system at t = 2.70. p with arrow = g · cm/s (c) Determine the velocity of the center of mass at t = 2.70. v with arrowcm = cm/s (d) Determine the acceleration of the center of mass at t = 2.70. a with arrowcm = cm/s2 (e) Determine the net force exerted on the two-particle system at t = 2.70. F with arrownet = µN
Explanation / Answer
a) Rcm = [3.15[(3i + 3j)t + 2jt^2] + 5.45[3i - 2jt^2 - 6jt] ]/[3.15+5.45] = 3it - 2.7jt - 0.534 j t^2
Rcm (t = 2.7) = 8.1i - 11.18j in cm
Rcm' = 3i - 2.7j - 1.068jt
Rcm' (t = 2.7) = 3i - 5.58j cm/s
b) P = (3.15+5.45)Rcm' = 8.6Rcm' = 118.73 g cm/s
c) Vcm (t = 2.7) = 3i - 5.58j cm/s
4) acm = -1.068j (constant)
5) F = ma = -9.1848N
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