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Atwood machine Atwood used the sy...

Atwood machine

Atwood used the system to prove Netwons laws of motion. Atowood machine consists of two loads of mases `m _(1) and m _(2)` attached to the ends of a limp of inextensible string as shown in tghe figure 11. The string runs over a pully. FInd the acceleration of each load and tension in the string `(m _(1) gt m _(2))`

Text Solution

Verified by Experts

we know that tension of string always tries to pull te bodies up.

From the FBD of the mass `m _(1),` there exist two forces on the load of mass `m _(1),` one is tension of the string acting in upward direction and weight of the load `(m_(1) g)` acting in downward direction.
The net force on `m _(1) F _(n et) = m_(1) a`
`implies m _(1) g -T =m_(1) a ---------------(1)`
Thus the net force `(F_(n et))` acting on mass `m _(1)` produces an acceleration .a. in it.
When `m _(1)` moves down, `m _(2)` moves up. So the magnitudes of acceleration are same.

From the FBD of mass `m _(2)`
`F _(n et) =T - m _(2) g =m_(2)a ----------------(2)`
Solving (1) and (2) equations, we get
`a = ((m _(1) - m _(2) g)/( m _(1) + m _(2))`
` T = ( 2m _(1) m _(2) g)/( m _(1) +m_(2))`
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Knowledge Check

  • Two bodies of masses 1 kg and 2 kg are connected by a very light string passed over a clamped light smooth pulley. If the system is released from rest, find the acceleration of two two masses and the tension in the string

    A
    `3.27m//s^2 , 13N`
    B
    `4.5m//s^2,26N`
    C
    `1.27m//s^2,13N`
    D
    `0.327m//s^2,13N`

  • Two bodies of masses 1 kg and 2 kg are connected by a very light string passed over a clamped light smooth pulley. If the system is released from rest, find the acceleration of the two masses and the tension in the string

    A
    3.27 `m//s^(2)` , 13 N
    B
    `4.5 m//s^(2)` , 26 N
    C
    `1.27 m//s^(2) , 13 N`
    D
    `0.327 m//s^(2)` ,13 N

  • Two bodies of masses 1 kg and 2 kg are connected by a very light string passed over a clamped light smooth pulley. If the system is released from rest, find the acceleration of the two masses and the tension in the string

    A
    `3.27 m//s^(2), 13 N`
    B
    `4.5 m//s^(2), 26 N`
    C
    `1.27 m//s^(2), 13 N`
    D
    `0.327 m//s^(2), 13 N`

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