A person places a hand on a closed book resting on a table, and then presses downward while pushing outward. Either the book slides across the table or the hand slides across the book. What determines which of these happens? Which type(s) of friction is (are) involved?

Short Answer

Expert verified
How do static and kinetic friction play a role in this scenario? Answer: The event that occurs depends on the static friction coefficients between the book and the table (μ_sb) and between the book and the hand (μ_sh). If μ_sb is greater than or equal to μ_sh, the hand is more likely to slip on the book. If μ_sh is greater than μ_sb, it is more likely that the book slides across the table. Both static and kinetic friction are involved in this scenario. Static friction is initially present between the book and the table and the book and the hand. When either the book starts sliding across the table or the hand starts sliding across the book, kinetic friction replaces static friction at the interface where the sliding is occurring.

Step by step solution

01

Understand static and kinetic friction

Static friction is the friction present when two objects are in contact but not in relative motion to each other, while kinetic friction is the friction between two objects when they are in relative motion. In this scenario, the interaction between the book and the hand or the book and the table involves friction.
02

Identify the forces at play

When a person presses down on the book and pushes outward, there are two main forces at play. The normal force, which acts perpendicular to the table's surface, and the applied force, which is the force that the person exerts on the book in an outward direction.
03

Analyze the downward force

When the person presses down on the book, the normal force increases. This increases the maximum force of static friction available between the book and the table as well as the book and the hand, because the maximum static friction force is proportional to the normal force (f_s = μ_s*F_N, where μ_s is the static friction coefficient and F_N is the normal force).
04

Analyze the outward force

When the person pushes the book outward, they increase the applied force parallel to the table's surface. This applied force attempts to overcome the static friction force between the book and the table or the book and the hand.
05

Determine which event happens

The event that occurs depends on the static friction coefficients between the book and the table (μ_sb) and between the book and the hand (μ_sh). If μ_sb is greater than or equal to μ_sh, the hand is more likely to slip on the book, as the friction force between the book and the table is stronger and harder to overcome. On the other hand, if μ_sh is greater than μ_sb, it is more likely that the book slides across the table, as the static friction between the book and the hand is harder to overcome.
06

Identify the types of friction involved

Both static friction and kinetic friction are involved in this scenario. Static friction is initially present between the book and the table and the book and the hand. When either the book starts sliding across the table or the hand starts sliding across the book, kinetic friction replaces static friction at the interface where the sliding is occurring.

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