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Coefficient Of Friction Between A Body And Wedge

Coefficient Of Friction Between A Body And Wedge

Vishal kumarUpdated on 02 Jul 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

  1. Case 1- A body Slides on a Smooth Wedge of Angle θ and its Time of Descent is t.
  2. For smooth wedge
  3. 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)
  4. Solved Example Based on Coefficient Of Friction Between A Body And Wedge
  5. Summary
Coefficient Of Friction Between A Body And Wedge
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

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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)

Q: How does the distribution of pressure between a body and a wedge affect the friction force?
A:
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.
Q: What is the relationship between friction and the concept of "self-locking" in wedge mechanisms?
A:
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.
Q: How does friction affect the motion of a body transitioning from a horizontal surface to an inclined plane?
A:
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.
Q: How does the coefficient of friction affect the force required to hold a body stationary on a wedge?
A:
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.
Q: What is the effect of friction on the period of oscillation of a body sliding back and forth on a wedge?
A:
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.
Q: How does the concept of friction apply to the phenomenon of "wedging" in mechanical systems?
A:
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.
Q: What is the role of friction in determining whether a body will tip or slide on a wedge?
A:
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.
Q: How does the presence of friction affect the path of a projectile launched from a wedge?
A:
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.
Q: What is meant by "stick-slip" motion, and how does it relate to friction on a wedge?
A:
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.
Q: What is the relationship between friction and the normal force for a body on a curved surface?
A:
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.
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