Understanding Sliding on an Inclined Plane

When an object is placed on an inclined plane, two main forces act on it along the plane: the component of gravity pulling it down the plane and the force of static friction opposing this motion. As the angle of inclination increases, the component of gravity down the plane increases, while the maximum possible static friction force remains constant (depending on the normal force and coefficient of static friction). There is a specific angle at which the component of gravity becomes just equal to the maximum static friction. If the angle is increased even slightly beyond this, the object will begin to slide down the plane.

The question asks for the minimum angle with the horizontal at which an object on the inclined surface just begins to slide. This specific angle has a widely recognized term in physics.

Identifying the Minimum Sliding Angle

Let's consider the forces acting on an object of mass \(m\) on an inclined plane with inclination angle \(\theta\):

• Weight (\(mg\)): Acts vertically downwards.
• Normal Force (\(N\)): Acts perpendicular to the inclined plane, pushing upwards.
• Static Friction Force (\(f_s\)): Acts parallel to the inclined plane, opposing the tendency to slide downwards.

We can resolve the weight into components:

• Component parallel to the plane: \(mg \sin\theta\)
• Component perpendicular to the plane: \(mg \cos\theta\)

The normal force is equal to the component of weight perpendicular to the plane:

\(N = mg \cos\theta\)

The static friction force opposes the component of weight pulling the object down the plane. The maximum static friction force is given by:

\(f_{s,max} = \mu_s N = \mu_s mg \cos\theta\)

Sliding just begins when the component of gravity down the plane equals the maximum static friction force:

\(mg \sin\theta = \mu_s mg \cos\theta\)

Dividing both sides by \(mg \cos\theta\) (assuming \(\cos\theta \neq 0\)):

\(\frac{\sin\theta}{\cos\theta} = \mu_s\)

\(\tan\theta = \mu_s\)

The angle \(\theta\) at which this condition is met, and the object just begins to slide, is known as the Angle of Repose.

What is the Angle of Repose?

The Angle of Repose is defined as the steepest angle of descent relative to the horizontal plane to which a material can be piled without slumping. For a single object on an inclined plane, it is the minimum angle of inclination at which the object starts to slide due to gravity overcoming static friction. This angle is equal to the angle of friction, whose tangent is the coefficient of static friction (\(\mu_s\)).

Analyzing the Given Options

Let's look at the provided options in the context of our understanding:

• Angle of friction: This is the angle whose tangent is the coefficient of static friction. The Angle of Repose is numerically equal to the angle of friction for an object just about to slide. While related, the question asks for the name of the angle of the inclined plane itself.
• Angle of Repose: This is precisely the definition we derived and discussed — the minimum angle of the inclined plane with the horizontal where sliding begins.
• Angle of latitude: This is a geographical coordinate, irrelevant to this physics concept.
• Angle of elevation: This refers to the angle upwards from a horizontal line to a point above, irrelevant to the context of an object sliding on a surface.

Based on the definition and the physics involved, the correct term for the minimum angle made by an inclined plane with the horizontal such that an object placed on the inclined surface just begins to slide is the Angle of Repose.

Conclusion on Sliding Angle

The phenomenon where an object just begins to slide on an inclined plane as the angle increases is crucial in understanding friction. The critical angle at which this motion initiates is specifically named the Angle of Repose.

Revision Table: Angle of Repose and Friction

Additional Information: Factors Affecting Angle of Repose

The Angle of Repose is a property dependent on the surfaces in contact. Key factors include:

• Material Properties: The type of materials in contact (e.g., wood on wood, metal on ice) determines the coefficient of static friction.
• Surface Roughness: Rougher surfaces generally have higher coefficients of friction and thus larger angles of repose.
• Presence of Lubricants: Lubricants reduce friction, decreasing the angle of repose.

Note that for a simple block on a plane, the Angle of Repose is independent of the mass of the object or the surface area of contact, as long as the material properties and roughness remain consistent.