In Fig. 5-34, A is a 4.4-kg block and B is a 2.6 -kg block....

In Fig. 5-34, $A$ is a $4.4-\mathrm{kg}$ block and $B$ is a $2.6$ -kg block. The coefficients of static and kinetic friction between $A$ and the table are $0.18$ and 0.15. (a) Determine the minimum mass of the block $C$ that must be placed on $A$ to keep it from sliding. (b) Block $C$ is suddenly lifted off $A$. What is the acceleration of block $A$ ?

Key Concepts

Static Friction

Static friction is the force that resists the initiation of motion between two surfaces in contact. It acts up to a maximum value determined by the product of the coefficient of static friction and the normal force. When additional weight is applied to an object, the normal force increases, thereby increasing the maximum available static friction force, which is crucial in determining whether or not an object will move.

Kinetic Friction

Kinetic friction is the force that opposes the relative motion of two surfaces that are already sliding past each other. Unlike static friction, it has a constant value defined by the coefficient of kinetic friction multiplied by the normal force. Kinetic friction is typically less than the maximum static friction, impacting the acceleration of objects once motion has begun.

Newton's Second Law

Newton's second law explains that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass, summarized by the equation F=ma. This principle is used to relate the forces, friction, and masses involved in the system, helping determine conditions for equilibrium or acceleration.

Normal Force and Its Relation to Friction

The normal force is the force perpendicular to the contact surface, usually equal to the weight of the object or sum of weights acting downward. It plays a critical role in friction, as both static and kinetic frictional forces are proportional to the normal force. An increase in the normal force, such as from an additional weight, directly increases the frictional force between the surfaces.

Free-Body Diagram Analysis

Free-body diagram analysis involves drawing all the forces acting on an object to visualize and apply Newton's laws effectively. This technique is essential for setting up and solving equations related to force balance, frictional forces, and acceleration, making it a vital tool in mechanics problems like the one presented.

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