# Limiting Angle of Friction Theory Notes | Question Banks

The limiting angle of friction, also known as the angle of repose, is the maximum angle at which an object can rest on an inclined surface.

## LIMITING ANGLE OF FRICTION

Limiting Angle of Friction is defined as the angle which the resultant reaction (R) makes with the normal reaction (RN).

Consider a body A of weight W resting on a horizontal plane B as shown in Fig. 1.17. If a horizontal force P is applied to the body, no relative motion takes place until the applied force P is equal to the force of friction F, acting opposite to the direction of motion. The magnitude of this force of friction is
F = µ W = µ.RN, where RN is the normal reaction.

In the limiting case, when the body just begins to move, it is in equilibrium under the action of the following three forces :

1. Weight of the body (W),
2. Applied horizontal force (P), and
3. Reaction (R) between the body A and the plane B.

The reaction R must, therefore,be equal and opposite to the resultant of W and P and will be inclined at an angle (ϕ) to the normal reaction (RN). This angle ϕ is called the limiting angle of friction or simply angle of friction. From Fig. 1.17, we find that

## Q. What is limiting angle of friction

The limiting angle of friction, also known as the angle of repose, is the maximum angle at which an object can rest on an inclined surface without sliding due to gravity. It is a fundamental concept in physics and mechanics related to the frictional forces acting between the object and the surface.

# Q: How is the limiting angle of friction determined?

Ans: The limiting angle of friction can be determined experimentally by gradually increasing the angle of inclination of a surface until the object on it starts to move. At this point, the angle of inclination is equal to the limiting angle of friction.

## Q: What factors affect the limiting angle of friction?

Ans: Several factors can influence the limiting angle of friction, including the nature of the surfaces in contact, the type of materials involved, the roughness of the surfaces, and the presence of any lubricants or contaminants.

## Q: How does the coefficient of friction relate to the limiting angle of friction?

A4: The coefficient of friction (both static and kinetic) is directly related to the limiting angle of friction. The tangent of the limiting angle of friction is equal to the coefficient of static friction between the two surfaces. In mathematical terms, tan(θ) = μs, where θ is the limiting angle and μs is the coefficient of static friction.

## Q: Why is the limiting angle of friction important in engineering and everyday life?

Ans: Understanding the limiting angle of friction is crucial in various fields, including engineering, construction, and transportation. It helps determine the stability of objects on inclined surfaces and is important for designing structures, ensuring vehicle safety, and preventing accidents involving sliding or tipping.

Q: Can you provide an example of how the limiting angle of friction is used in practice?

Ans: Sure! Imagine you’re an engineer designing a ramp for a wheelchair-accessible entrance. You need to calculate the maximum allowable incline of the ramp to ensure it’s safe for wheelchair users. By considering the weight of the wheelchair and the coefficient of static friction between the ramp surface and the wheelchair’s wheels, you can determine the limiting angle of friction to design a safe and accessible ramp.

Q: What happens if an object exceeds its limiting angle of friction on an incline?

Ans: If an object on an incline exceeds its limiting angle of friction, it will start to slide or move downhill due to the force of gravity. This can lead to instability, loss of control, and potentially dangerous situations, which is why it’s essential to consider the limiting angle of friction in various applications.

Q: Can the limiting angle of friction change over time?

Ans: Yes, the limiting angle of friction can change over time, especially in dynamic situations where factors like temperature, humidity, or the presence of contaminants on the surfaces can alter the coefficient of friction. It’s important to consider these variables in real-world applications.

Q: Are there different types of limiting angles of friction for different materials?

Ans: Yes, different materials and surface combinations can have varying limiting angles of friction. For example, the limiting angle of friction for rubber on concrete will be different from that of metal on ice due to differences in material properties and surface characteristics.

## Q: How can one reduce the risk of exceeding the limiting angle of friction in practical situations?

Ans: To reduce the risk of exceeding the limiting angle of friction, you can use materials with higher friction coefficients, employ anti-slip coatings or treatments on surfaces, or decrease the angle of inclination if possible. Additionally, maintaining clean and dry surfaces can help maintain friction and prevent sliding.

Q: Is the limiting angle of friction always the same for a given material combination?

Ans: No, the limiting angle of friction can vary depending on specific conditions. It can change due to factors like surface roughness, temperature, humidity, and the presence of contaminants. So, it’s essential to consider these variables when determining the limiting angle of friction for a particular situation.

Q: Can the limiting angle of friction be calculated theoretically, or is it primarily determined experimentally?

Ans: While the limiting angle of friction can be estimated theoretically using the coefficient of static friction (μs), it is often determined experimentally in practical applications. Theoretical calculations provide a starting point, but real-world conditions can influence the actual limiting angle, making experimentation necessary for precision.

Q: What is the difference between the limiting angle of friction and the angle of repose?

Ans: The limiting angle of friction and the angle of repose are essentially the same concepts. They both refer to the maximum angle at which an object can rest on an inclined surface without sliding due to the force of friction. The terminology can vary depending on the context, but the underlying principle is the same.

Qns: Can you provide an example of the limiting angle of friction in everyday life?

Ans: Certainly! Imagine you’re stacking firewood on a sloped surface. If the angle of the slope becomes too steep, the firewood may start sliding downhill due to gravity, exceeding its limiting angle of friction with the ground. This illustrates the importance of considering the limiting angle of friction when stacking objects on inclined surfaces to prevent accidents.

Q: How can engineers use the concept of the limiting angle of friction in designing structures?

Ans: Engineers can use the concept of the limiting angle of friction when designing structures to ensure stability and safety. For example, when designing retaining walls or embankments, engineers need to consider the angle of repose to prevent soil or materials from collapsing due to excessive incline. This helps in designing structurally sound and safe constructions.

Q: Is the limiting angle of friction the same for all materials?

Ans: No, the limiting angle of friction can vary significantly between different materials and surface combinations. For instance, smooth ice on ice might have a very low limiting angle of friction, while rough rubber on concrete can have a higher limiting angle due to differences in material properties and surface textures.

## Q: How does lubrication affect the limiting angle of friction?

Ans: Lubrication reduces the limiting angle of friction between two surfaces. When a lubricant is applied, it forms a thin layer between the surfaces, reducing the frictional resistance and allowing them to slide more easily. This is why lubricants are used in various applications, such as in machinery and engines, to reduce friction and improve efficiency.

## Q: Can the limiting angle of friction be exceeded in certain situations?

Ans: Yes, the limiting angle of friction can be exceeded in some situations, particularly when external forces, such as a strong push or pull, overcome the frictional force holding an object in place. This can result in sliding or movement even if the object was initially at rest within its limiting angle.

## Q: How can you measure the limiting angle of friction in a laboratory setting?

Ans: In a laboratory setting, you can measure the limiting angle of friction by setting up an inclined plane and gradually increasing the angle of inclination until the object on the plane starts to move. You can measure this angle using instruments like protractors. The angle at which movement begins is the limiting angle of friction.

## Q: Are there safety standards or guidelines related to the limiting angle of friction in specific industries?

Ans: Yes, various industries have safety standards and guidelines that take into account the limiting angle of friction. For example, in construction and workplace safety, regulations may specify maximum allowable slopes or inclines for walkways, ramps, or vehicle access points to ensure they are within safe limits regarding the limiting angle of friction. Compliance with these standards helps prevent accidents and injuries.

#### MCQ Questions based on Limiting Angle of Friction

1. What is the limiting angle of friction?

a) The angle at which an object will always slide on a surface
b) The maximum angle at which an object will not slide on a surface due to friction
c) The angle at which an object will remain in motion on a surface
d) The angle at which an object loses all contact with a surface

Answer: b) The maximum angle at which an object will not slide on a surface due to friction

2. Which factor does NOT influence the limiting angle of friction?

a) Nature of the materials in contact
b) Temperature
c) Surface roughness
d) Presence of lubricants

3. The tangent of the limiting angle of friction is equal to:

a) The coefficient of dynamic friction
b) The coefficient of rolling friction
c) The coefficient of static friction
d) The coefficient of kinetic friction

Answer: c) The coefficient of static friction

4. Why is the limiting angle of friction important in engineering and construction?

a) It determines the maximum speed of moving objects
b) It helps in designing more aerodynamic structures
c) It ensures the stability of objects on inclined surfaces
d) It affects the color of materials used in construction

Answer: c) It ensures the stability of objects on inclined surfaces

5. Which term is synonymous with the limiting angle of friction?

a) Angle of inclination
b) Angle of resistance
c) Angle of departure
d) Angle of descent

#### Quiz based on Limiting Angle of Friction

6. If an object exceeds its limiting angle of friction on an incline, what will happen?

a) It will accelerate uphill
b) It will remain stationary
c) It will start sliding downhill
d) It will rotate

Answer: c) It will start sliding downhill

7. In a laboratory setting, how is the limiting angle of friction typically determined?

a) By conducting surveys and field tests
b) By using computer simulations
c) By mathematical calculations
d) By gradually increasing the angle of inclination until the object starts to move

Answer: d) By gradually increasing the angle of inclination until the object starts to move

8. What does the tangent of the limiting angle of friction represent?

a) The angle at which an object starts to roll
b) The angle at which an object becomes weightless
c) The angle at which an object starts to slide
d) The angle at which an object becomes transparent

Answer: c) The angle at which an object starts to slide

9. Which of the following statements is true regarding the limiting angle of friction?

a) It is a constant value for all materials.
b) It decreases with increasing surface roughness.
c) It can change due to factors like temperature and contaminants.
d) It is always greater than 90 degrees.

Answer: c) It can change due to factors like temperature and contaminants.

10. What is the practical significance of knowing the limiting angle of friction in everyday life?

a) It helps determine the melting point of materials.
b) It aids in designing safer vehicle tires.
c) It influences the taste of food.
d) It determines the color of objects.

Answer: b) It aids in designing safer vehicle tires.

#### Exam Questions based on Limiting Angle of Friction

11. Which term is often used interchangeably with the limiting angle of friction?

a) Angle of reflection
b) Angle of refraction
c) Angle of incidence
d) Angle of repose

12. In engineering, what is the primary reason for considering the limiting angle of friction when designing structures?

a) To determine the structure’s color
b) To calculate the speed of sound within the structure
c) To ensure structural stability on inclined surfaces
d) To estimate the structure’s thermal conductivity

Answer: c) To ensure structural stability on inclined surfaces

13. If the coefficient of static friction between two surfaces decreases, what happens to the limiting angle of friction?

a) It increases.
b) It remains the same.
c) It decreases.
d) It becomes irrelevant.

14. What is the primary difference between the coefficient of friction and the limiting angle of friction?

a) The coefficient of friction is measured in degrees, while the limiting angle is dimensionless.
b) The coefficient of friction is a ratio, while the limiting angle is a force.
c) The coefficient of friction relates to a specific object, while the limiting angle is a general property of surfaces.
d) There is no significant difference between the two terms.

Answer: c) The coefficient of friction relates to a specific object, while the limiting angle is a general property of surfaces.

15. Which of the following is an example of a situation where knowledge of the limiting angle of friction is essential for safety?

a) Determining the cooking time for a recipe
b) Designing a new smartphone
c) Calculating the volume of a water tank
d) Designing a highway curve

Answer: d) Designing a highway curve

#### Exam Questions Paper based on Limiting Angle of Friction

16. If the limiting angle of friction between two surfaces is 30 degrees, what is the tangent of this angle?

a) 0.577
b) 1.732
c) 0.866
d) 0.5

17. Which type of friction is primarily associated with the limiting angle of friction?

a) Static friction
b) Kinetic friction
c) Rolling friction
d) Fluid friction

18. What is the primary reason for using lubricants between moving parts in machinery and engines?

a) To increase the limiting angle of friction
b) To reduce the coefficient of friction
c) To make the parts more colorful
d) To increase the melting point of the parts

Answer: b) To reduce the coefficient of friction

19. In construction, why is it important to consider the limiting angle of friction when designing slopes and ramps?

a) To make the structures look more appealing
b) To minimize the use of construction materials
c) To ensure the safety and stability of the structures
d) To maximize the speed of vehicles on the slopes

Answer: c) To ensure the safety and stability of the structures

20. If an object has a higher coefficient of static friction with a surface, what can be said about its limiting angle of friction on that surface?

a) The limiting angle is lower.
b) The limiting angle is higher.
c) The limiting angle remains the same.
d) There is no relationship between the coefficient and the angle.

Answer: b) The limiting angle is higher.