Question

A block of mass $10kg$ placed on a frictionless, inclined plane of angle $\theta$ , as shown in the figure. Determine the acceleration of the block after it is released. What is force exerted by the incline on the block?

Answer 1

The acceleration of the block released at an inclination of angle$\theta$is

We know that in case of the absence of frictional force the acceleration of the object is calculated by using the net force that is parallel component of the force acting on the object.

$N=mg\sin \theta$

$ma=mg\sin \theta$

$a=g\sin \theta$

The net force is force acting in the parallel direction of the inclined plane is given as.

$F=10\times 10\sin \theta$

$F=100\sin \theta N$

The perpendicular force and the normal will cancel out each other and the parallel forces and frictional force will be the force acting. Since it given that there is no frictional force. Hence the net force acting will be parallel only.