A block is kept on a smooth inclined plane of angle of inclination 30^∘ that moves with a consta

step 1 In this question it is told that a block is kept on a smooth inclined plane of angle that is 30

A block is kept on a smooth inclined plane of angle of...

A block is kept on a smooth inclined plane of angle of inclination $30^{\circ}$ that moves with a constant acceleration so that the block does to slide relative to the inclined plane. Let $F_{1}$ be the contact force between the block and the plane. Now the inclined plane stops and let $F_{2}$ be the contact force between the two in this case. Then $\vec{F}_{1} / F_{2}$ is (a) 1 (b) $4 / 3$ (c) 2 (d) $3 / 2$

A block is kept on a smooth inclined plane of angle of inclination $30^{\circ}$ that moves with a constant acceleration so that the block does to slide relative to the inclined plane.
Let $F_{1}$ be the contact force between the block and the plane. Now the inclined plane stops and let $F_{2}$ be the contact force between the two in this case. Then $\vec{F}_{1} / F_{2}$ is
(a) 1
(b) $4 / 3$
(c) 2
(d) $3 / 2$

Key Concepts

Normal Force

The normal force is the component of the contact force exerted by a surface that acts perpendicular to the surface. It balances the perpendicular component of other forces (such as gravity and pseudo forces in accelerated systems) so that there is no acceleration into or away from the surface. In problems involving inclined planes, the normal force is key to understanding how the block is supported by the surface, and its magnitude can change depending on additional accelerations or forces acting perpendicular to the plane.

Non?Inertial Frame and Pseudo Force

When a system is accelerating, it is often convenient to consider the problem from the perspective of a non–inertial frame attached to the accelerating object. In such frames, additional fictitious forces, known as pseudo forces, must be introduced to account for the acceleration. These pseudo forces act opposite to the direction of the frame’s acceleration and modify the effective force balance. They are crucial for analyzing conditions such as when a block does not slide on an accelerating inclined plane.

Force Decomposition on an Inclined Plane

Decomposing forces into components that are parallel and perpendicular to an inclined plane is a fundamental technique when analyzing motion on slopes. This approach simplifies the problem by aligning one axis with the plane and allows for a clear separation of the gravitational, pseudo, and normal forces. Understanding these components is essential for determining conditions for equilibrium or for calculating normal forces when additional accelerations are present.

Effect of Acceleration on Apparent Weight

Acceleration affects the normal or contact force between objects by altering the effective force acting perpendicular to the surface, often described as a change in 'apparent weight.' In an accelerating frame, the combination of gravitational and pseudo forces changes the load on a surface. This change is reflected in the magnitude of the normal force. Comparing cases with and without acceleration can reveal differences in how forces are transmitted between contacting bodies.

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