An ice cart of mass 60 kg rests on a horizontal snow pateh...

An ice cart of mass $60 \mathrm{~kg}$ rests on a horizontal snow pateh with coefficient of statie friction $1 / 3$ Assuming that there is no vertical acceleration, find the magnitude of the maximum horizontal force required to move the ice cart. $\left(g=9.8 \mathrm{~ms}^{-2}\right)$ [BVP Engg, 2007] (a) $100 \mathrm{~N}$ (b) $110 \mathrm{~N}$ (c) $209 \mathrm{~N}$ (d) $196 \mathrm{~N}$

An ice cart of mass $60 \mathrm{~kg}$ rests on a horizontal snow pateh with coefficient of statie friction $1 / 3$ Assuming that there is no vertical acceleration, find the magnitude of the maximum horizontal force required to move the ice cart. $\left(g=9.8 \mathrm{~ms}^{-2}\right)$ [BVP Engg, 2007]
(a) $100 \mathrm{~N}$
(b) $110 \mathrm{~N}$
(c) $209 \mathrm{~N}$
(d) $196 \mathrm{~N}$

Key Concepts

Static Friction

Static friction is the force that resists the initiation of motion between two surfaces in contact. Its maximum value is proportional to the normal force and given by the product of the coefficient of static friction and the normal force. It is crucial for determining the minimum applied force required to overcome the resistance and initiate movement.

Normal Force

The normal force is the perpendicular force exerted by a surface on an object resting on it. In cases with no vertical acceleration, the normal force is equal in magnitude and opposite in direction to the gravitational force. It is fundamental for calculating frictional forces, as friction is proportional to the normal force.

Coefficient of Friction

The coefficient of friction is a dimensionless constant that characterizes the frictional properties of two surfaces in contact. It represents the ratio between the frictional force and the normal force. The coefficient is specific to the pair of materials in contact and is key to calculating the force needed to initiate or sustain motion.

Equilibrium in Forces

Equilibrium in forces refers to the condition where the sum of all forces acting on an object is zero, resulting in no net acceleration. In the context of horizontal surfaces, ensuring that vertical forces are balanced (i.e., gravitational force equals the normal force) is essential for correctly calculating the horizontal frictional force.

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