Coefficient Of Friction Between A Body And Wedge

Edited By Vishal kumar | Updated on Jul 02, 2025 05:44 PM IST

The coefficient of friction between a body and a wedge plays a crucial role in determining the ease with which the body can slide over the wedge's surface. This fundamental concept in physics helps us understand the interaction between surfaces in contact. In real life, we encounter such interactions in various scenarios, from moving furniture across a floor to driving a car on a ramp. Understanding the coefficient of friction can aid in designing safer and more efficient systems in everyday applications, ensuring stability and preventing unwanted slippage. This article explains into the principles behind the coefficient of friction, its calculation, and its practical implications.

This Story also Contains

Case 1- A body Slides on a Smooth Wedge of Angle θ and its Time of Descent is t.
For smooth wedge
Case 2- If the Same Wedge is Made Rough Then the Time Taken by it to Come Down becomes n times more (i.e., nt)
Solved Example Based on Coefficient Of Friction Between A Body And Wedge
Summary

Coefficient Of Friction Between A Body And Wedge

Case 1- A body Slides on a Smooth Wedge of Angle θ and its Time of Descent is t.

For smooth wedge

S=u⋅t+12at2S=12(gsin⁡θ)t2....(i)u=0a=gsin⁡θ

Case 2- If the Same Wedge is Made Rough Then the Time Taken by it to Come Down becomes n times more (i.e., nt)

For Rough wedge

S=12g[sin⁡θ−μcos⁡θ](nt)2 (i) = (ii) μ=tan⁡θ[1−1n2]

μ= coefficient of friction θ= Angle of inclination n= an integer

Solved Example Based on Coefficient Of Friction Between A Body And Wedge

Example 1: A body takes just twice the time as long to slide down a plane inclined at 30⁰ to the horizontal as if the plane were frictionless. The coefficient of friction between the body and the plane is:

1) 34
2) 3
3) 43
4) 34

Solution:

Coefficient of Friction Between a Body and Wedge -

If the same wedge is made rough then the time taken by it to come down becomes n times more (nt)

Then find the Coefficient of Friction between the body and wedge in terms of n.

For this make 2 cases

Case 1- A body slides on a smooth wedge of angle θ and its time of descent is t.

Case 2- If the same wedge is made rough then the time taken by it to come down becomes n times more (i.e., nt)

(The length of the path in both cases are the same)

For smooth wedge

S=u⋅t+12at2S=12(gsin⁡θ)t2....(i)u=0a=gsin⁡θ

For Rough wedge

S=12g[sin⁡θ−μcos⁡θ](nt)2...(ii) (i) = (ii) μ=tan⁡θ[1−1n2]

μ= coefficient of friction θ= Angle of inclination n= an integer

By using this concept -

μ=tan⁡Θ(1−1n2)=tan⁡30(1−122)=34

Hence, the answer is option (1).

Example 2: In case (i) plane is smooth and in case (ii) plane is rough. If the time taken by the block in case (ii) to come down is 3 times to the time to come down in case (i) then the coefficient of friction of plane in case (ii) is?

1) 13
2) 23
3) 34
4) 12

Solution:

Length covered in both cases is same so for smooth wedge s=ut+12at2

s1=12at2s1=12gsin⁡θt2−(I)[a=gsin⁡θ]

For rough wedge
s2=12g(sin⁡θ−μcos⁡θ)(nt)2−(II)[a=g(sin⁡θ−μcos⁡θ)]

Now s1=s2
12gsin⁡θt2=12g(sin⁡θ−μcos⁡θ)(nt)2

Solving

μ=tan⁡θ[1−1n2]=34[1−132]=34×89⇒23

Hence, the answer is option (2).

Example 3: A sphere of radius R is in contact with a wedge. The point of R contact is R/3 from the ground as shown in the figure. Wedge is moving with a velocity 10 m/s, then the velocity of the sphere at this instant will be:

1) 10 m/s
2) 33 m/s
3) 55 m/s
4) 15 m/s

Solution:

By wedge constraint,

Relative velocity along the line perpendicular to the contact surface is zero.

10sin⁡θ=Vcos⁡θ10tan⁡θ=VV=10×52=55 m/s

Hence, the answer is option (3).

Summary

This article explores the concept of the coefficient of friction between a body and a wedge, examining its impact on the interaction between surfaces and motion. The coefficient of friction, which depends on the materials in contact, represents the portion of the force of friction holding between surfaces. The article elaborates on how this coefficient significantly influences the stability and ease of movement on inclined planes.

Frequently Asked Questions (FAQs)

1. How does surface roughness affect the coefficient of friction on a wedge?

Increased surface roughness generally leads to a higher coefficient of friction. Rougher surfaces have more microscopic irregularities that interlock, increasing resistance to motion. However, extremely rough surfaces can sometimes reduce contact area and lower friction.

2. How does the angle of the wedge affect the friction between the body and the wedge?

As the angle of the wedge increases, the normal force between the body and the wedge decreases, which in turn reduces the friction force. This is because the component of the body's weight perpendicular to the wedge surface becomes smaller as the angle increases.

3. What happens when the angle of the wedge exceeds the angle of repose?

When the wedge angle exceeds the angle of repose, the body will begin to slide down the wedge. This occurs because the component of the body's weight parallel to the wedge surface becomes greater than the maximum static friction force.

4. What is the role of friction in determining whether a body will slide or roll down a wedge?

Friction plays a crucial role in determining whether a body will slide or roll. If the static friction is sufficient to prevent slipping at the point of contact, the body will roll. If the static friction is overcome, the body will slide. The shape of the body and the coefficient of friction both influence this behavior.

5. Can the coefficient of friction ever be greater than 1?

Yes, the coefficient of friction can be greater than 1, although it's uncommon. This can occur with very sticky or interlocking surfaces. However, in most practical situations involving a body on a wedge, the coefficient of friction is typically less than 1.

6. How does the mass of the body affect its motion on a frictionless wedge?

On a frictionless wedge, the mass of the body does not affect its acceleration down the wedge. This is because the increased gravitational force on a more massive object is exactly balanced by its increased inertia, resulting in the same acceleration for all masses.

7. How does lubrication affect the coefficient of friction on a wedge?

Lubrication generally reduces the coefficient of friction by creating a thin film between the body and the wedge. This film reduces direct contact between the surfaces, lowering the resistance to motion. The extent of reduction depends on the type and amount of lubricant used.

8. How does the shape of a body affect its friction with a wedge?

The shape of a body influences the contact area and pressure distribution with the wedge surface. A flat surface may have more contact area and thus more friction, while a spherical body may have less contact area but higher pressure at the point of contact. The shape also affects whether the body is more likely to slide or roll.

9. What is the difference between Coulomb friction and viscous friction on a wedge?

Coulomb friction is independent of the relative velocity between surfaces and is proportional to the normal force. It's the type of friction typically considered for solid bodies on a wedge. Viscous friction, more relevant to fluids, is proportional to the relative velocity between surfaces and is generally not significant for solid bodies on a wedge.

10. How does the concept of friction affect the design of ramps and inclined surfaces in real-world applications?

In real-world applications, the coefficient of friction is crucial in designing safe and effective ramps and inclined surfaces. Engineers must consider the balance between providing enough friction for safety (preventing slipping) and minimizing friction for ease of use (e.g., in conveyor systems or wheelchair ramps).

11. What is the coefficient of friction between a body and a wedge?

The coefficient of friction between a body and a wedge is a measure of the resistance to motion between the two surfaces when they are in contact. It is a dimensionless quantity that depends on the materials and surface characteristics of both the body and the wedge.

12. How does the coefficient of friction affect energy dissipation when a body slides down a wedge?

A higher coefficient of friction leads to greater energy dissipation as the body slides down the wedge. This is because more work is done against the friction force, converting mechanical energy into heat. With a lower coefficient of friction, more of the body's potential energy is converted to kinetic energy.

13. What forces act on a body resting on a wedge?

The forces acting on a body resting on a wedge are: the body's weight (acting downward), the normal force from the wedge (perpendicular to the wedge surface), and the friction force (parallel to the wedge surface, opposing potential motion).

14. What is the relationship between friction and the normal force on a wedge?

The friction force is directly proportional to the normal force according to the equation F = μN, where F is the friction force, μ is the coefficient of friction, and N is the normal force. On a wedge, as the angle increases, the normal force decreases, reducing the friction force.

15. What is the difference between microscopic and macroscopic friction on a wedge?

Microscopic friction arises from molecular interactions and surface irregularities at the atomic level. Macroscopic friction is the observable resistance to motion we experience. Both contribute to the overall coefficient of friction between a body and a wedge, but macroscopic effects usually dominate.

16. What's the difference between static and kinetic friction on a wedge?

Static friction acts when the body is at rest relative to the wedge, preventing motion from starting. Kinetic friction acts when the body is already moving along the wedge surface. Generally, the coefficient of static friction is greater than the coefficient of kinetic friction.

17. How does the coefficient of friction relate to the angle of repose?

The angle of repose is the maximum angle at which a body can rest on a wedge without sliding. It is directly related to the coefficient of static friction. The tangent of the angle of repose is equal to the coefficient of static friction between the body and the wedge.

18. How does humidity affect the coefficient of friction on a wedge?

Humidity can significantly impact the coefficient of friction. In some cases, it may increase friction by creating adhesion through capillary action. In others, it may decrease friction by acting as a lubricant. The effect depends on the materials involved and the amount of moisture present.

19. How does temperature affect the coefficient of friction between a body and a wedge?

Temperature changes can alter the coefficient of friction by affecting material properties. Higher temperatures often lead to softer materials, which can increase the contact area and friction. However, some materials may become more slippery at higher temperatures. The specific effect depends on the materials involved.

20. What is meant by the coefficient of restitution, and how does it relate to friction on a wedge?

The coefficient of restitution measures the elasticity of a collision between two objects. While not directly related to friction, it affects how a body bounces after colliding with a wedge. A higher coefficient of restitution results in a more elastic collision, while friction during the collision reduces the coefficient of restitution.

21. What is the significance of the "angle of friction" in determining the behavior of granular materials on an inclined surface?

The angle of friction is crucial in determining how granular materials behave on an inclined surface. It represents the maximum angle at which a pile of the material can remain stable. Beyond this angle, the material will begin to flow. This concept is important in geotechnical engineering and the design of storage systems for granular materials.

22. What is meant by the term "limiting friction" in the context of a body on a wedge?

Limiting friction refers to the maximum static friction force that can exist between the body and the wedge before motion begins. It's equal to the coefficient of static friction multiplied by the normal force. Once this limit is exceeded, the body begins to slide down the wedge.

23. How does the distribution of mass within a body affect its motion on a wedge with friction?

The distribution of mass within a body affects its moment of inertia, which influences how easily it can rotate. On a wedge with friction, a body with mass concentrated at its center may be more likely to slide, while a body with mass distributed towards its edges may be more likely to roll, assuming sufficient friction.

24. What is meant by the term "angle of friction" in the context of a body on a wedge?

The angle of friction is the angle whose tangent is equal to the coefficient of friction. It represents the minimum angle of inclination at which a body will start to slide down a wedge. If the wedge angle is less than the angle of friction, the body will remain at rest without external forces.

25. What is the difference between rolling friction and sliding friction on a wedge?

Rolling friction occurs when an object rolls along the wedge surface, while sliding friction occurs when an object slides without rolling. Rolling friction is generally much lower than sliding friction because it involves less deformation of surfaces and less relative motion between the body and the wedge at the point of contact.

26. How does the presence of friction on a wedge affect the principle of mechanical advantage?

Friction reduces the mechanical advantage of a wedge by requiring additional force to overcome it. In an ideal, frictionless wedge, the mechanical advantage is determined solely by the wedge angle. With friction, some of the input force is used to overcome friction, reducing the effective force available for the intended task.

27. What is the role of friction in determining the efficiency of a wedge as a simple machine?

Friction reduces the efficiency of a wedge as a simple machine. It causes energy loss, converting some of the input work into heat rather than useful output work. The efficiency of a wedge is the ratio of output work to input work, and friction decreases this ratio by increasing the required input work.

28. How does the coefficient of friction affect the acceleration of a body sliding down a wedge?

A higher coefficient of friction results in lower acceleration for a body sliding down a wedge. This is because the friction force opposes the motion, reducing the net force acting down the incline. The acceleration can be calculated using a = g(sin θ - μ cos θ), where θ is the wedge angle and μ is the coefficient of friction.

29. What is meant by "stick-slip" motion, and how does it relate to friction on a wedge?

Stick-slip motion is a jerky motion that can occur when an object moves along a surface with friction. On a wedge, it can happen when the static friction is overcome, causing the body to "slip," but then friction increases as it moves, causing it to "stick" again. This can result in a series of stops and starts rather than smooth motion.

30. How does the concept of friction apply to the stability of a stack of blocks on an inclined plane?

Friction is crucial for the stability of a stack of blocks on an inclined plane. It prevents both sliding between the blocks and sliding of the entire stack down the incline. The stability depends on the coefficients of friction between the blocks and between the bottom block and the incline, as well as the incline angle.

31. What is the significance of the "critical angle" in problems involving friction on a wedge?

The critical angle is the maximum angle at which a body can rest on a wedge without sliding. It's determined by the coefficient of static friction. When the wedge angle equals the critical angle, the body is on the verge of sliding. At angles greater than the critical angle, the body will slide down the wedge.

32. How does friction affect the motion of a body that is initially at rest on a wedge and then set into motion?

When a body at rest on a wedge is set into motion, it must first overcome static friction. Once motion begins, kinetic friction (usually lower than static friction) opposes the motion. If moving uphill, friction adds to the resistive force. If moving downhill, friction reduces the accelerating force.

33. What is the relationship between friction and the normal force for a body on a curved surface?

On a curved surface, the relationship between friction and the normal force remains F = μN, but the normal force varies with position. At each point, the normal force is perpendicular to the surface. The friction force is tangent to the surface and opposes motion. This variation can lead to complex motion patterns.

34. How does the presence of friction affect the path of a projectile launched from a wedge?

Friction affects the initial velocity of a projectile launched from a wedge by reducing the energy available for launch. It also influences the launch angle if the projectile slides before launch. During the launch itself, friction with the wedge can impart spin to the projectile, potentially affecting its trajectory through the air.

35. What is the role of friction in determining whether a body will tip or slide on a wedge?

Friction plays a crucial role in determining whether a body will tip or slide on a wedge. High friction can cause a tall, narrow object to tip rather than slide as the wedge angle increases. The outcome depends on the object's height, base width, center of mass location, and the coefficient of friction with the wedge.

36. How does the concept of friction apply to the phenomenon of "wedging" in mechanical systems?

In mechanical systems, "wedging" occurs when friction causes components to bind or lock together. This can happen when forces and friction combine to create a self-reinforcing jam. Understanding the role of friction in wedging is crucial for designing systems that avoid unintended locking or for creating intentional locking mechanisms.

37. What is the effect of friction on the period of oscillation of a body sliding back and forth on a wedge?

Friction decreases the amplitude and increases the period of oscillation for a body sliding back and forth on a wedge. It causes energy loss with each oscillation, gradually reducing the amplitude. The increased period is due to the friction force opposing motion in both directions, slowing the body throughout its path.

38. How does the coefficient of friction affect the force required to hold a body stationary on a wedge?

A higher coefficient of friction reduces the force required to hold a body stationary on a wedge. This is because friction provides a force opposing the body's tendency to slide down. The minimum force required is F = mg(sin θ - μ cos θ), where θ is the wedge angle and μ is the coefficient of friction.

39. How does friction affect the motion of a body transitioning from a horizontal surface to an inclined plane?

As a body transitions from a horizontal surface to an inclined plane, friction plays a changing role. Initially, it may provide the force necessary to begin upward motion. On the incline, it opposes motion up the plane but assists in preventing sliding down. The changing normal force as the body moves onto the incline also affects the available friction force.

40. What is the relationship between friction and the concept of "self-locking" in wedge mechanisms?

Self-locking in wedge mechanisms occurs when friction prevents the wedge from sliding back under load. This happens when the friction angle is greater than the wedge angle. The relationship is expressed as μ > tan θ, where μ is the coefficient of friction and θ is the wedge angle. Self-locking is used in many tools and fasteners.

41. How does the distribution of pressure between a body and a wedge affect the friction force?

The distribution of pressure between a body and a wedge can affect the friction force even if the total normal force remains constant. Areas of higher pressure may experience more friction due to increased surface interaction or deformation. This can lead to non-uniform friction across the contact surface, potentially affecting the body's motion.