In the figure below, two identical containers of sugar are connected by a cord t
ID: 2004268 • 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 620 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 29 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) The two containers are now released. In what direction does the center of mass move?
(d) What is its acceleration?
Magnitude m/s2
Direction
Explanation / Answer
let the two containers be at co ordinates -13mm and 13mm respectively centre of mass =(680x13-680x13)/(680+680) =0mm ANS: therefore it is at a distance of 13mm from centre of container 1 After the mass transfer container 1 =653g container 2=707g centre of mass=(-653x13+707x13)/(653+707) =0.51mm ANS :therefore at a distance of 13.51mm from container 1 Now the system is released acceleration =(707 -653)*g/(707+653) =0.39 m/s^2 for container 1 this acceleration is in the opposite direction =-0.39m/s^2 acceleration of centre of mass=(707x0.39-653x0.39)/(707+653) ANS=0.015m/s^2 downwards .