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All surfaces are smooth. Find the horizo...

All surfaces are smooth. Find the horizontal displacements of the block and wedge when the block slides down from top to bottom.

Text Solution

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When the block slides down on the smooth wedge, the wedge moves backwards. In the horizontal direction there is no external force. `vecF_(x)=0` , `therefore vecP_(x)` = constant
`vecP_(f) = vecP_(i)` (along x-axis) `mvecu + MvecV =0`
`x_(1)` = forward distance moved by the block along x-axis.
`x_2` = backward distance moved by the wedge along x-axis.
`mvecu=-MvecV, m(x_(1)/t) =Mx_(2)/t`
`mx_(1) =Mx_(2).x_(1) =(ML)/(M+m) =(Ml cos theta)/(M+m)`
`x_(2) =(mL)/(M+m) =(mlcos theta)/(M+m)`
L can also be written as `l cos theta`
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