The angle between the resultant reaction and normal to the plane on which the motion of body is impending is known as-
Angle of limiting friction
Understanding Friction and Forces
When a body rests on a surface, several forces act upon it. These include the weight of the body acting downwards and the normal reaction from the surface acting perpendicular to the surface. If there is a force attempting to move the body along the surface, a friction force will oppose this motion. The maximum possible static friction force that can exist before motion begins is called limiting friction.
Resultant Reaction and Normal Reaction
The normal reaction is the component of the surface's reaction force that is perpendicular to the surface. The friction force is the component of the surface's reaction force that is parallel to the surface, opposing motion or impending motion. The resultant reaction is the single force that combines the normal reaction and the friction force.
Imagine the normal reaction vector pointing directly away from the surface and the friction force vector pointing along the surface, opposing motion. These two vectors are perpendicular to each other. The resultant reaction is the hypotenuse of the right triangle formed by the normal reaction and the friction force vectors.
Defining the Angle between Resultant Reaction and Normal
The question asks about the angle between the resultant reaction and the normal to the plane when the motion of the body is impending. When motion is impending, the friction force is at its maximum possible value, which is the limiting friction. The angle between the resultant reaction and the normal reaction at this point is a specific, important property related to the surface materials.
Analysis of Options
Let's look at the given options:
- Angle of zenith: This term is used in astronomy and relates to the angle between a vertical line and a direction to a celestial body. It has no connection to friction or forces on a surface.
- Angle of limiting friction: This is defined precisely as the angle between the normal reaction and the resultant reaction when the friction force is limiting (i.e., when motion is impending). This angle is typically denoted by $\lambda$ and is related to the coefficient of limiting friction ($\mu_s$) by the equation $\tan(\lambda) = \mu_s$.
- Angle of friction: This term can sometimes be used more broadly to refer to the angle between the resultant reaction and the normal reaction for *any* value of the friction force (static or kinetic), not just limiting friction. However, when motion is impending, the friction force is at its limiting value, making "angle of limiting friction" the most accurate and specific term for the angle at the point of impending motion.
- Angle of repose: This is the maximum angle of inclination of a plane at which a body placed on it will remain at rest due to static friction. While the angle of repose is numerically equal to the angle of limiting friction, it describes the angle of the *plane*, not the angle between the resultant reaction and the normal reaction.
Based on the definitions, the angle between the resultant reaction and the normal to the plane when the motion of the body is impending is specifically known as the angle of limiting friction.
Conclusion
The angle between the resultant reaction and the normal to the plane on which the motion of body is impending is called the angle of limiting friction.
| Term | Definition Relevant to Friction |
|---|---|
| Resultant Reaction | Vector sum of normal reaction and friction force. |
| Normal Reaction | Component of surface reaction perpendicular to the surface. |
| Friction Force | Component of surface reaction parallel to the surface, opposing motion. |
| Limiting Friction | Maximum static friction force just before motion begins. |
| Angle of Limiting Friction | Angle between the resultant reaction and the normal reaction when motion is impending. |
Revision Table: Key Concepts in Friction
| Concept | Description |
|---|---|
| Static Friction ($\text{f}_s$) | Force opposing impending motion, varies from 0 up to a maximum value. |
| Limiting Friction ($\text{f}_{s,max}$) | Maximum value of static friction, $\text{f}_{s,max} = \mu_s \text{N}$. |
| Kinetic Friction ($\text{f}_k$) | Force opposing motion when body is sliding, $\text{f}_k = \mu_k \text{N}$. |
| Coefficient of Static Friction ($\mu_s$) | Ratio of limiting friction to normal reaction. |
| Coefficient of Kinetic Friction ($\mu_k$) | Ratio of kinetic friction to normal reaction. |
| Normal Reaction ($\text{N}$) | Perpendicular force exerted by the surface. |
| Resultant Reaction ($\text{R}$) | Vector sum of N and f. $R = \sqrt{N^2 + f^2}$. |
| Angle of Limiting Friction ($\lambda$) | Angle between R and N when $f = f_{s,max}$. $\tan(\lambda) = \mu_s$. |
| Angle of Repose | Maximum incline angle where a body remains at rest. Equal to $\lambda$. |
Additional Information on Limiting Friction and Angle of Friction
While "angle of friction" is sometimes used loosely for the angle at any point, "angle of limiting friction" specifically refers to the maximum possible angle between the resultant reaction and the normal reaction. This occurs only when the friction force reaches its maximum static value, i.e., limiting friction, which is exactly when motion is impending. The tangent of the angle of limiting friction is equal to the coefficient of static friction ($\mu_s$). This relationship is fundamental in understanding the mechanics of friction.
The angle of limiting friction is a crucial parameter in engineering calculations involving the stability of objects on surfaces or the forces required to initiate motion.
Important Questions from Friction
The maximum static frictional force that an object experiences just before it begins to slide over a surface is commonly referred to as the:
Coefficient of friction depends upon
Limiting force of friction is the
Coulomb friction is the friction between
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 called-
