A body of mass m rests on horizontal surface. The...

A body of mass $m$ rests on horizontal surface. The coefficient of friction between the body and the surface is $\mu$. If the mass is pulled by a force $P$ as shown in the figure, the limiting friction between the body and surface will be (a) $\mu \mathrm{mg}$ (b) $\mu\left[m g+\left(\frac{P}{2}\right)\right]$ (c) $\mu\left[m g-\left(\frac{P}{2}\right)\right]$ (d) $\mu\left[m g-\left(\frac{\sqrt{3} P}{2}\right)\right]$

A body of mass $m$ rests on horizontal surface. The coefficient of friction between the body and the surface is $\mu$. If the mass is pulled by a force $P$ as shown in the figure, the limiting friction between the body and surface will be
(a) $\mu \mathrm{mg}$
(b) $\mu\left[m g+\left(\frac{P}{2}\right)\right]$
(c) $\mu\left[m g-\left(\frac{P}{2}\right)\right]$
(d) $\mu\left[m g-\left(\frac{\sqrt{3} P}{2}\right)\right]$

Key Concepts

Equilibrium Conditions

Equilibrium conditions imply that the sum of forces in both the vertical and horizontal dimensions must balance to zero when a body is at rest or on the verge of motion (limiting equilibrium). This principle is critical when assessing how the applied force alters the normal reaction force and determining the correct expression for the limiting friction.

Force Decomposition

When a force is applied at an angle, it is necessary to resolve it into its horizontal and vertical components using trigonometric functions. The horizontal component influences the motion along the surface, while the vertical component modifies the effective weight and hence the normal reaction force. Understanding this decomposition is key to analyzing how applied forces affect friction.

Normal Reaction Force

The normal reaction force is the force exerted by a surface that supports the weight of an object resting on it. It is typically equal to the weight (mg) of the object. However, when an additional force is applied at an angle, its vertical component alters the normal force—reducing it if directed upward or increasing it if directed downward—which in turn affects the frictional force.

Friction

Friction refers to the resistive force that prevents two surfaces from sliding past one another. In this context, the maximum or 'limiting' frictional force is given by f_max = ?N, where ? is the coefficient of friction and N is the normal reaction force between the surfaces.

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