Chapter 3: Dynamics

Solve · page 78: 3.5. Describe the motion of a block on a table taking into account the friction between the two surfaces. What is the static friction and kinetic friction?

When a block resting on a table is pulled by a horizontal force, friction (رگڑ) opposes its motion until the pulling force exceeds the maximum static friction, after which the block accelerates forward against a smaller kinetic friction force.

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1. Motion of a Block on a Table with Friction

• Rest State: A block of mass $m$ rests on a horizontal table. Its weight $W = mg$ acts vertically downwards, balanced by the normal reaction (عمودی ردعمل) $R = mg$ of the table acting vertically upwards.
• Small Applied Force: When a small horizontal force $F$ is applied to pull the block, the microscopic cold welds between the surface of the block and table resist the movement. An equal and opposite force of friction arises, keeping the block at rest.
• Increasing Force: As you gradually increase the pulling force $F$, the friction force increases equally to keep the net horizontal force zero ($F_{\text{net}} = 0$).
• Point of Motion: When the applied force exceeds the maximum limit of static friction (limiting friction), the cold welds break, and the block begins to slide across the table.
• In Motion: Once the block starts moving, the opposing friction force drops slightly to a constant value called kinetic friction. The net force producing acceleration $a$ is:

$$F_{\text{net}} = F - F_k = m a$$

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2. Static Friction and Kinetic Friction

• Static Friction (سکونی رگڑ):

The force of friction that acts between two surfaces in contact when there is no relative motion between them is called static friction ($F_s$).

• Its maximum value is called limiting friction ($F_s$), given by the formula:

$$F_s = \mu_s R = \mu_s m g$$ (where $\mu_s$ is the coefficient of static friction).

• Kinetic Friction (حرکی رگڑ):

The opposing force that acts between two surfaces when one surface slides over the other is called kinetic friction ($F_k$).

• It is generally smaller than static friction ($\mu_k < \mu_s$) and is given by:

$$F_k = \mu_k R = \mu_k m g$$ (where $\mu_k$ is the coefficient of kinetic friction).

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3. Labelled Diagram Description

• Block on Table: A rectangular block resting horizontally on a surface.
• Vertical Forces: Weight vector $W = mg$ directed vertically downwards; Normal reaction vector $R$ directed vertically upwards from the table surface ($R = W$).
• Horizontal Forces: Applied pulling force $F$ directed to the right; Friction force $F_s$ or $F_k$ acting at the contact boundary directed to the left.