In the figure below, two identical containers of sugar are connected by a cord t
ID: 1960900 • Letter: I
Question
In the figure below, two identical containers of sugar are connected by a cord that passes over a frictionless pulley. The cord and pulley have negligible mass, each container and its sugar together have a mass of 460 g, the centers of the containers are separated by 50 mm, and the containers are held fixed at the same height.
(a) What is the horizontal distance between the center of container 1 and the center of mass of the two-container system initially?
mm
(b) Now 27 g of sugar is transferred from container 1 to the container 2. What is the horizontal distance between the center of container 1 and the center of mass of the system?
mm
(c) What is its acceleration?
Explanation / Answer
Assume that the origion is situated aththe center of pully.a) m1 = m2 = M = 460 g, x1 = -25mm, x2 = 25 mm
xc = (m1x1 +m2x2)/(m1 + m2) = 0
Horizontal distance is xc - x1 = 25 mm
b) m1 = M - m = 460 - 27 = 433 g, m2 = M + m= 460 + 27 = 487 g,
x1 = -25 mm, x2 = 25 mm
xc = (m1x1 +m2x2)/(m1 + m2) = 1.467mm
answer of the question = xc - x1 = 26.467mm
d) m2g - T = m2a
T - m1g = m1a
a = (m2 - m1)g/(m1 +m2) = 0.392 m/s2 , Acts downwards