- #1

decentfellow

- 130

- 1

## Homework Statement

In the figure shown, friction force between the bead and the light string is ##\dfrac{mg}{4}##. Find the time in which the bead looses contact with the string after the system is released from rest.

## Homework Equations

Weight of the bead ##(m_1)=mg##

Friction acting on the bead=##\dfrac{mg}{4}##

Relation between the acceleration of the block ##(m_2)## and the string going over the non-movable pulley

$$2a_2=a_{string}$$

## The Attempt at a Solution

FBD of ##m_2##

From the above FBD we get the following equation:-

$$mg-2T=ma_2$$

FBD of the bead

I was having trouble figuring out whether tension would be acting or not on the bead, so I thought about the need for the string to be taught(as the dtring is ideal) hence there should be tension acting on the bead.

From the above FBD of the bead we get the following equation:-

$$ma_{string}+mg-\dfrac{mg}{4}-T=ma_{1/string}$$

We, see that there are only two equations and there are ##3## variables, so the equations are not solvable. What is wrong with the solution above, if there is anything please point out.

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