As shown in figure a block of mass m is attached with a cart. If the coefficient of static frict

step 1 So in this problem block will not fall block will not fall when frictional force when frictional

As shown in figure a block of mass m is attached with a...

As shown in figure a block of mass $\mathrm{m}$ is attached with a cart. If the coefficient of static friction between the surface of cart and block is $\mu$ than what would be acceleration $\alpha$ of cart to prevent the falling of block? (A) $\alpha>(\mathrm{mg} / \mu)$ (B) $\alpha>(\mathrm{g} / \mathrm{m})$ (C) $\alpha \geq(\mathrm{g} / \mu)$ (D) $\alpha<(g / \mu)$

As shown in figure a block of mass $\mathrm{m}$ is attached with a cart. If the coefficient of static friction between the surface of cart and block is $\mu$ than what would be acceleration $\alpha$ of cart to prevent the falling of block?
(A) $\alpha>(\mathrm{mg} / \mu)$
(B) $\alpha>(\mathrm{g} / \mathrm{m})$
(C) $\alpha \geq(\mathrm{g} / \mu)$
(D) $\alpha<(g / \mu)$

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Key Concepts

Newton's Second Law

This principle states that the net force acting on an object is equal to the mass of the object multiplied by its acceleration. In problems involving dynamics, it forms the basis of relating the forces (like friction and inertial forces) to the acceleration, which is crucial for determining conditions such as when an object remains stationary relative to an accelerating frame.

Static Friction

Static friction is the force that resists the initiation of sliding motion between two surfaces in contact. It has an upper limit determined by the coefficient of static friction multiplied by the normal force. In this context, the static friction must be sufficient to counteract forces (generated by gravity and inertial effects) that would otherwise cause relative motion between the block and the cart.

Inertial Frames and Pseudoforces

When analyzing dynamics within a non-inertial (accelerating) frame, such as the cart, one must consider additional apparent forces called pseudoforces. These forces help account for the acceleration of the frame itself, allowing one to apply Newton’s laws as if the frame were inertial. This is crucial when determining how the acceleration of the cart affects the forces acting on the block.

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