A block of mass M lies on a plane inclined at an angle `alpha` to the horizontal. A wieght a mass m is connected to the block by a thread slung over a pulley (Fig.).

Find the acceleration of the weight and the tension of the thread. Friction, the mass of the pulley and of the thread are to be neglected.

Answer

`a="g"(m-M sin alpha)/(m+M), F=(mMg(1+sin alpha))/(m+M)`.

Explanation

The forces acting on the weight are the gravitational force mg and the tension of the thread F (Fig.). The equation of motion is
`mg-F=ma`
Three forces act on the block: the gravitational force Mg, the reaction of the inclined plane Q and the tension of the thread F. The equation of motion is
`F-mg sin alpha = Ma`
Hence the answer given follows.
It many be seen that for `mgt M sin alpha` the system will be accelerated in the direction shown in Fig. For `m lt M sin alpha` the acceleration will be reversed, and for `m-M sin alpha` the system will move at the constant speed impurled to it initiully, or remain at rest.