Two masses, 0.600 kg and 0.300 kg, begin uniform motion at the same speed, 0.790 m/s, from the origin at t = 0 and travel in the directions ?
Two masses, 0.600 kg and 0.300 kg, begin uniform motion at the same speed, 0.790 m/s, from the origin at t = 0 and travel in the directions shown in Figure P9.48.
(a) Find the velocity of the center of mass in unit-vector notation.
i m/s +
j m/s
(b) Find the magnitude and direction of the velocity of the center of mass.
m/s
° (counterclockwise from the +x-axis)
(c) Write the position vector of the center of mass as a function of time.
[ ____ i + ____ j] t m
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velocity = "weighted" velocity / weight
(a) v = [(-0.600 + 0.300)*cos45º i + (0.600 + 0.300)*sin45º j]kg *0.790m/s / 0.900kg
v = [-0.186 i + 0.559 j] m/s ◄
(b) |v| = √(0.186² + 0.559²) m/s = 0.589 m/s ◄
Θ = arctan(0.559/-0.186) = 108º ccw from +x axis ◄
(c) simply multiply the velocity vector by t:
s(t) = [-0.186 i + 0.559 j] m/s * t
(a) v = [(0.600 kg)(0.790 m/s)(j/sqrt(2) - i/sqrt(2)) +
+ (0.300 kg)(0.790 m/s)(j/sqrt(2) + i/sqrt(2))]/(0.900 kg)
= use calculator.
(b) Use arctan(vy/vx) to get the direction, which should be around 105 degrees; and use Pythagorean Theorem to find the magnitude
(c) Position is (vx)*i t + (vy)*j t