Introduction

This article delves into the physics of a 5kg block placed on a smooth inclined plane at a 30-degree angle. We'll analyze the forces acting on the block, determine the gravitational components, and ultimately ascertain the acceleration of the block in various directions.

The Problem at Hand

The question revolves around the motion of a 5kg block on a plane inclined at 30°. Specifically, we aim to find the acceleration perpendicular to this inclined plane.

Forces Acting on the Block

To begin, let's consider the forces acting on our 5kg block:

Gravitational Force (Weight)

The weight ( W ) of the block can be easily calculated:

W mg 5 , text{kg} times 9.81 , text{m/s}^2 49.05 , text{N}

Components of the Weight

The weight can be broken down into two components:

Parallel to the Incline: This component of the weight forces the block to slide down the plane. It is calculated as: ( W_{text{parallel}} W sin theta 49.05 , text{N} times sin 30^circ 49.05 , text{N} times 0.5 24.525 , text{N} ) Perpendicular to the Incline: This component of the weight is what we're interested in when determining the acceleration perpendicular to the plane. It is given by: ( W_{text{perpendicular}} W cos theta 49.05 , text{N} times cos 30^circ approx 49.05 , text{N} times 0.866 approx 42.43 , text{N} )

Acceleration Perpendicular to the Inclined Plane

Since the plane is smooth, there is no friction. Therefore, the only force acting perpendicular to the inclined plane is ( W_{text{perpendicular}} ). However, this force is balanced by the normal force exerted by the plane, which means there is no net force and no acceleration in this direction.

Thus, the acceleration of the block perpendicular to the plane is:

( text{Acceleration perpendicular to the plane} 0 , text{m/s}^2 )

Conclusion

The key takeaways from this analysis are that the block does not accelerate in the direction perpendicular to the inclined plane. While there is a gravitational component ( W cos theta ), it is counterbalanced by the normal force exerted by the plane, resulting in a net acceleration of zero in that direction.

Understanding these concepts is crucial for anyone studying mechanics and inclined plane problems. Whether you're a student, a teacher, or someone with a general interest in physics, this analysis provides a solid foundation for further exploration.