Stopping Of Block Due To Friction

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

Friction is the opposing force to the motion of one body over the surface of another body. As in the case of a ball rolling freely on the ground, the ball ultimately comes to rest, due to the frictional force that exists between the ball and the ground. Friction is a force that is around us all of the time, and it opposes relative motion between systems in contact and also allows us to move. It is parallel to the surface and opposite to the direction of the intended motion.

This Story also Contains

On the Horizontal Road
On the Inclined Road
Solved Examples Based on Stopping of Block Due to Friction
Summary

Stopping Of Block Due To Friction

In this article, we will cover the concept of stopping Block Due To Friction. This concept falls under the broader category of law of motion which is a crucial chapter in Class 11 physics. It is not only essential for board exams but also for competitive exams like the Joint Entrance Examination (JEE Main), National Eligibility Entrance Test (NEET), and other entrance exams such as SRMJEE, BITSAT, WBJEE, BCECE and more. Over the last ten years of the JEE Main exam (from 2013 to 2023), a total of three questions have been asked on this concept and no direct question was asked in NEET.

On the Horizontal Road

A block of mass m is moving initially with velocity u on a rough surface and due to friction, it comes to rest after covering a distance S.

Distance travelled before coming to rest (S):

F=ma=μRma=μmga=μgV2=u2−2asS=u22μg=P22μm2g

Where:

a= acceleration μ= coefficient of friction S= distance travelled g= gravity u= initial velocity V= finally velocity P= initial mometum=mu

Time taken to come to rest:

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From equation, v=u−at⇒0=u−μgt[ As v=0,a=μg]
∴t=uμg

The force of friction acting on the body:

F=maF=m(v−u)tF=mut[ As v=0]F=μmg[ As t=uμg]

On the Inclined Road

a=g[sin⁡θ+μcos⁡θ]V2=u2−2aS0=u2−2g[sin⁡θ+μcos⁡θ]SS=u22g(sin⁡θ+μcos⁡θ)

Where:

S= distance travelled μ= coefficient of friction V= Final velocity u= Initial velocity

Solved Examples Based on Stopping of Block Due to Friction

Example 1: A 2 kg mass starts from rest on an inclined smooth surface with an inclination 30∘ and a length 2 m. How much will it travel (in meters) before coming to rest on a surface with a coefficient of friction of 0.25?

1) 4

2)6

3)8

4)2

Solution:

v2=u2+2as=0+2×gsin⁡30×2

Let it travel a distance ' S ' before coming to rest on a horizontal surface
S=v22μg=202×0.25×10=4 m

Hence, the answer is option (1).

Example 2: A body is moving with a speed of 12m/s and the coefficient of friction between the ground and the body is 0.4. The distance travelled by the body (in meters) before coming to rest is.

1) 18

2)10

3)15

4)20

Solution:

f=μmg
due to retardation
μmg=ma⇒a=μg=0.4∗10=4 m/s2
now for V=0
V2=u2−2as⇒0=u2−2asS=u22×a⇒12∗122∗4=18 m

Hence, the answer is option (1).

Example 3: A block of mass 10 kg starts sliding on a surface with an initial velocity of 9.8 ms−1. The coefficient of friction between the surface and block is 0.5. The distance covered by the block before coming to rest is:
[ use g=9.8 ms−2]

1) 4.9 m
2) 9.8 m
3) 12.5 m
4) 19.6 m

Solution:

f=μN=μmga=μg=4.9 m/s2V2=u2+2as0=(9.8)2+2(−4.9)ss=9.8 m
The distance covered by the block before coming to rest is $\mathrm{ 9.8\, m}$

Hence, the correct option is (2)

Example 4: A bag is gently dropped on a conveyor belt moving at a speed of 2 m/s. The coefficient of friction between the conveyor belt and bag Initially, the bag slips on the belt before it stops due to friction. The distance travelled by the bag on the belt during the slipping motion, is : [Take g=10 m/s−2 ]

1) 2 m
2) 0.5 m
3) 3.2 m
4) 0.8 ms

Solution:

f=μmga=fm=μg

The bag comes to rest when the speed of the bag is the same as the conveyor belt ie., 4 m/s
v2=u2+2 as (4)2=0+2(0.4×10)sS=2 m

The distance travelled by the bag on the belt during slipping motion is 2 m

Hence 1 is the correct option.

Example 5: A block of mass M slides down on a rough inclined plane with constant velocity. The angle made by the inclined plane with horizontal is θ. The magnitude of the contact force will be:

1) Mg
2) Mgcos⁡θ
3) Mgsin⁡θ+Mgcos⁡θ
4) Mgsin⁡θ1+μ

Solution:

For block moving at constant velocity

∑Fx=0−mgsin⁡Θ+μMgcos⁡Θ=0tan⁡Θ=μf=Mgsin⁡Θ=μMgcos⁡Θ→(1) Contact force =f2+N2(Mgsin⁡Θ)2+(Mgcos⁡Θ)2 Contact force =Mg

Hence, the answer is option (1).

Summary

When a moving block encounters friction, the force of friction opposes its motion, gradually reducing its speed until it comes to a complete stop. The stopping distance depends on the initial speed of the block and the coefficient of friction between the block and the surface. Understanding this interaction is crucial for applications requiring precise control of motion and stopping.

Frequently Asked Questions (FAQs)

1. What causes a moving block to eventually stop on a horizontal surface?

Friction between the block and the surface causes the block to stop. As the block slides, the friction force opposes its motion, gradually reducing its speed until it comes to rest.

2. Why doesn't a block keep moving forever on a frictionless surface?

In an ideal frictionless environment, a block would continue moving indefinitely at constant velocity. This is an application of Newton's First Law of Motion. In reality, some friction always exists, causing objects to eventually stop.

3. How does the surface area of a block affect its stopping distance due to friction?

For most macroscopic objects, the surface area doesn't affect the stopping distance. This is because while a larger area increases the number of contact points, it also distributes the weight over a larger area, keeping the pressure and thus the friction force constant.

4. What happens to the kinetic energy of a block as it slides to a stop?

The kinetic energy of the block is converted to thermal energy (heat) as it slides to a stop. The work done by friction against the motion of the block results in an increase in temperature of both the block and the surface.

5. How does the concept of work relate to a block stopping due to friction?

The work done by friction is equal to the change in the block's kinetic energy. As the block slides, friction does negative work, reducing the block's kinetic energy until it reaches zero and the block stops.

6. Why does a block slide farther on ice than on concrete?

Ice has a lower coefficient of friction compared to concrete. This means the frictional force between the block and ice is smaller, resulting in less deceleration and a longer sliding distance before coming to a stop.

7. How does the initial velocity of a block affect its stopping distance due to friction?

A higher initial velocity results in a longer stopping distance. This is because the block has more kinetic energy to dissipate through friction. The work done by friction to bring the block to rest must equal the initial kinetic energy, which increases with the square of velocity.

8. What role does the normal force play in stopping a block due to friction?

The normal force is crucial in determining the strength of the friction force. The friction force is proportional to the normal force (F = μN, where μ is the coefficient of friction and N is the normal force). On a horizontal surface, the normal force equals the weight of the block.

9. How does the mass of a block affect its stopping distance due to friction?

A block with greater mass will have a longer stopping distance. This is because a more massive object has more inertia, requiring more force to change its motion. The friction force, which depends on the normal force, increases proportionally with mass, but so does the object's resistance to changes in motion.

10. How does the coefficient of friction affect a block's stopping distance?

A higher coefficient of friction results in a shorter stopping distance. The coefficient of friction determines the strength of the frictional force relative to the normal force. A larger coefficient means a stronger frictional force, which more quickly reduces the block's velocity to zero.

11. What's the difference between static and kinetic friction in stopping a block?

Static friction prevents the block from starting to move when at rest, while kinetic friction acts to slow the block once it's in motion. Kinetic friction is typically less than static friction, which is why it's easier to keep an object moving than to start it moving.

12. Why doesn't doubling the mass of a block double its stopping distance?

Doubling the mass doesn't double the stopping distance because both the friction force and the block's inertia increase proportionally. The increased mass leads to more friction (due to increased normal force) but also more resistance to changes in motion, resulting in the same stopping distance.

13. How does the stopping distance of a block relate to its initial kinetic energy?

The stopping distance is directly proportional to the block's initial kinetic energy. Since kinetic energy is given by 1/2mv², doubling the velocity quadruples the stopping distance, assuming constant friction.

14. What's the relationship between a block's deceleration and the coefficient of friction?

The block's deceleration is directly proportional to the coefficient of friction. A higher coefficient results in stronger friction, causing greater deceleration. The relationship is given by a = μg, where a is the deceleration, μ is the coefficient of friction, and g is the acceleration due to gravity.

15. What would happen if you applied an external force equal to the friction force on a sliding block?

If you applied an external force equal and opposite to the friction force, the block would continue moving at a constant velocity. The applied force would exactly balance the friction force, resulting in no net force and thus no acceleration or deceleration.

16. How would the stopping distance of a block change if gravity suddenly doubled?

If gravity doubled, the stopping distance would decrease. This is because the normal force would double, leading to a doubling of the friction force. The increased friction would bring the block to a stop more quickly.

17. How does the temperature of the surface affect a block's stopping distance?

Temperature can affect stopping distance, but the effect is usually small in everyday scenarios. Higher temperatures can sometimes slightly reduce friction by causing minor expansion of materials and potentially altering surface properties. However, this effect is often negligible compared to other factors like the coefficient of friction.

18. How would the stopping distance of a block change in a stronger gravitational field, like on Jupiter?

In a stronger gravitational field like Jupiter's, the stopping distance would decrease. The stronger gravity would increase the normal force, leading to a stronger friction force. This increased friction would bring the block to a stop more quickly.

19. What role does the coefficient of restitution play in the stopping of a block due to friction?

The coefficient of restitution doesn't directly affect the stopping of a block due to friction on a flat surface. It becomes relevant only if the block collides with another object during its motion, determining how much kinetic energy is conserved in the collision.

20. How would the stopping distance of a block change in a reduced gravity environment, like on the Moon?

In a reduced gravity environment like the Moon, the stopping distance would increase. The lower gravity results in a smaller normal force, which leads to a weaker friction force. This reduced friction would take longer to bring the block to a stop.

21. Why does a block sliding on a banked curve without friction maintain a constant speed?

On a properly banked curve without friction, the normal force from the surface provides the centripetal force necessary for circular motion. There's no force opposing the motion in the direction of travel, so the block maintains a constant speed. This illustrates how friction isn't always necessary to change an object's direction.

22. How does the concept of friction challenge the idea of perpetual motion machines?

Friction is one of the main reasons why perpetual motion machines are impossible. In any real system, friction will eventually dissipate the energy of moving parts, bringing them to a stop unless energy is continuously supplied from an external source.

23. How does the angle of an inclined plane affect a block's stopping distance due to friction?

On an inclined plane, the stopping distance typically increases compared to a horizontal surface. This is because the normal force decreases (as it's now only a component of the weight), reducing the friction force. Additionally, gravity now has a component parallel to the surface, working against the friction.

24. Why does a heavier person typically slide down a slide more slowly than a lighter person?

This is a common misconception. In reality, neglecting air resistance, both would slide down at the same rate. The increased mass leads to both more gravitational force and more friction, which balance out. However, factors like body position and air resistance can cause differences in real-world scenarios.

25. What would happen if friction suddenly disappeared while a block was sliding?

If friction suddenly disappeared, the block would continue moving at a constant velocity indefinitely (assuming a flat surface). This illustrates Newton's First Law of Motion: an object in motion stays in motion unless acted upon by an external force.

26. Why does a block eventually stop even on a very slippery surface?

Even on very slippery surfaces, there is still some friction, albeit small. This small friction force, given enough time and distance, will eventually bring the block to a stop by continuously doing work against its motion.

27. How does the texture of a surface affect a block's stopping distance?

A rougher surface typically results in a shorter stopping distance. Rough surfaces generally have higher coefficients of friction, leading to stronger frictional forces that decelerate the block more quickly.

28. How does air resistance affect a block's stopping distance on a horizontal surface?

Air resistance typically has a minimal effect on a block's stopping distance on a horizontal surface, especially at low speeds. However, for very light objects or at high speeds, air resistance can contribute to stopping the block, slightly reducing the stopping distance.

29. Why does a block slide farther on a hot day compared to a cold day?

On a hot day, materials often expand slightly, which can reduce the microscopic interlocking between surfaces. This can lead to a slight decrease in the coefficient of friction, resulting in a longer sliding distance. However, this effect is usually small for most everyday situations.

30. How does the shape of a block affect its stopping distance due to friction?

The shape of the block generally doesn't significantly affect its stopping distance due to friction. What matters more is the nature of the contact between the block and the surface. However, shape can indirectly affect stopping distance if it influences factors like air resistance or the distribution of mass.

31. How does the concept of impulse relate to a block stopping due to friction?

Impulse, which is the change in momentum, is related to the friction force and the time it takes for the block to stop. The impulse provided by friction (force integrated over time) equals the block's initial momentum, bringing it to a stop.

32. Why does a block slide farther on a smooth, polished surface than on a rough one?

A smooth, polished surface has a lower coefficient of friction compared to a rough surface. This results in a weaker friction force, causing less deceleration and allowing the block to slide farther before coming to a stop.

33. How would the stopping distance change if a block were sliding on a surface in a vacuum?

In a vacuum, the stopping distance would be slightly longer compared to in air. This is because there would be no air resistance to contribute to slowing the block. However, for most everyday scenarios, this difference would be negligible as friction with the surface is the dominant factor in stopping the block.

34. What's the difference between sliding friction and rolling friction in terms of stopping a block?

Sliding friction is typically greater than rolling friction. If a block could roll instead of slide, it would generally travel farther before stopping. This is why wheels are used to reduce friction in many applications.

35. How does the distribution of mass within a block affect its stopping distance?

The distribution of mass within the block doesn't directly affect its stopping distance on a horizontal surface. What matters is the total mass and the nature of the contact with the surface. However, mass distribution could indirectly affect stopping if it changes how the block interacts with the surface or air.

36. Why doesn't friction bring a block to an immediate stop?

Friction doesn't bring a block to an immediate stop because it takes time to do the work necessary to reduce the block's kinetic energy to zero. The block's inertia resists the change in motion, and the friction force, while constant, gradually reduces the velocity over time and distance.

37. How does the concept of mechanical energy conservation apply to a block stopping due to friction?

Mechanical energy is not conserved when a block stops due to friction. The initial mechanical energy (kinetic energy) is converted to thermal energy (heat) due to friction. This illustrates that friction is a non-conservative force.

38. What would happen to a block's stopping distance if you could somehow increase gravity without changing mass?

If gravity increased without changing mass, the stopping distance would decrease. This is because the normal force would increase, leading to a stronger friction force. The increased friction would bring the block to a stop more quickly.

39. Why does a block eventually reach a terminal velocity when sliding down a very long incline?

On a long incline, a block reaches terminal velocity when the component of gravity parallel to the incline exactly balances the friction force. At this point, the net force becomes zero, and the block continues at a constant velocity.

40. How does the concept of work-energy theorem apply to a block stopping due to friction?

The work-energy theorem states that the work done on an object equals its change in kinetic energy. In the case of a block stopping due to friction, the negative work done by friction exactly equals the initial kinetic energy of the block, bringing it to rest.

41. Why does a block sliding on a surface that transitions from rough to smooth continue to slow down, but at a decreased rate?

When the block transitions to a smoother surface, it continues to slow down because friction is still present, just reduced. The smoother surface has a lower coefficient of friction, resulting in a weaker friction force and thus a lower rate of deceleration.

42. How would the stopping distance change if a block were sliding on a surface with periodically changing coefficients of friction?

On a surface with periodically changing coefficients of friction, the block's deceleration would vary. It would slow down more quickly on high-friction sections and less quickly on low-friction sections. The overall stopping distance would be an average effect of these varying friction forces.

43. What happens to the friction force as a block slows down due to friction?

The magnitude of the kinetic friction force remains constant as the block slows down, assuming the coefficient of friction and normal force don't change. However, the rate of kinetic energy loss decreases as the block slows because power (rate of energy loss) is force times velocity.

44. How does the concept of friction relate to the idea of energy dissipation in a sliding block?

Friction is a mechanism of energy dissipation. As the block slides, the friction force converts the block's kinetic energy into thermal energy (heat), dissipating the energy that was initially in the block's motion into the block and the surface.

45. Why does a block sliding on a surface that becomes progressively rougher stop more quickly than expected?

A block on a progressively rougher surface stops more quickly because the friction force increases as it moves. The increasing coefficient of friction leads to a stronger friction force, causing greater deceleration and a shorter overall stopping distance than if the surface had a uniform roughness.

46. What's the relationship between a block's stopping distance and the work done by friction?

The work done by friction is equal to the friction force multiplied by the stopping distance. This work is also equal to the initial kinetic energy of the block. Therefore, the stopping distance is directly related to the initial kinetic energy and inversely related to the friction force.

47. How does the concept of power apply to a block stopping due to friction?

Power is the rate at which work is done or energy is transferred. In the case of a block stopping due to friction, power represents the rate at which kinetic energy is being converted to thermal energy. The power decreases as the block slows because power is the product of force (constant) and velocity (decreasing).

48. How does the stopping distance of a block relate to the impulse provided by friction?

The impulse provided by friction (force integrated over time) is equal to the change in the block's momentum. The stopping distance is related to how long it takes for this impulse to reduce the block's momentum to zero. A larger friction force provides the necessary impulse over a shorter distance.

49. What would happen to a block's motion if the friction force suddenly increased halfway through its slide?

If the friction force suddenly increased halfway through the block's slide, its deceleration would increase. This would result in the block stopping more abruptly than expected. The second half of the slide would have a much shorter stopping distance compared to if the friction had remained constant.

50. Why does a block sliding down an incline eventually reach a point where it stops accelerating?

A block sliding down an incline reaches a point where it stops accelerating when the component of gravity parallel to the incline exactly balances the friction force. At this point, the net force becomes zero, and the block continues at a constant velocity (its terminal velocity for that incline).