A block of mass 1 kg is at rest on a horizontal table. The...

A block of mass $1 \mathrm{~kg}$ is at rest on a horizontal table. The coefficient of static friction between the block and the table is $0.5$. If $g=10 \mathrm{~ms}^{-2}$, then the magnitude of the force acting upwards at an angle of $60^{\circ}$ from the horizontal that will just start the block moving is (a) $5 \mathrm{~N}$ (b) $5.36 \mathrm{~N}$ (c) $74.6 \mathrm{~N}$ (d) $10 \mathrm{~N}$

A block of mass $1 \mathrm{~kg}$ is at rest on a horizontal table. The coefficient of static friction between the block and the table is $0.5$. If $g=10 \mathrm{~ms}^{-2}$, then the magnitude of the force acting upwards at an angle of $60^{\circ}$ from the horizontal that will just start the block moving is
(a) $5 \mathrm{~N}$
(b) $5.36 \mathrm{~N}$
(c) $74.6 \mathrm{~N}$
(d) $10 \mathrm{~N}$

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Key Concepts

Static Friction

Static friction is the force that resists the initiation of sliding motion between two surfaces in contact. It is characterized by a coefficient of static friction multiplied by the normal force, and it adjusts up to a maximum value to counteract applied forces until motion begins.

Force Decomposition

Force decomposition involves breaking a force vector into its horizontal and vertical components when acting at an angle. This allows for the analysis of the individual contributions of a force in each direction, which is essential when forces impact both motion and normal contact forces.

Normal Force Adjustment

The normal force is the perpendicular force exerted by a surface in response to an object's weight and any additional vertical forces. When a force has a vertical component, it can either increase or decrease the normal force, thus affecting the maximum static friction available.

Equilibrium and Net Force Analysis

In problems involving motion initiation, equilibrium conditions are used to determine the balance of forces. Analyzing the net force in both horizontal and vertical directions allows for the determination of the threshold at which applied forces overcome static friction, causing motion to begin.

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