# How does a sliding object stop moving by the effect of kinetic friction, if kinetic friction is constant and Fk can't be greater than Fapp on its own

The kinetic friction is constant. So if say, I apply a force of 20N on an object and the kinetic friction is 13N, then how does the object stop moving after some seconds. I believe that kinetic friction is constant, it cannot increase more than the applied force by changing its value on its own like static friction?

So does the object stop because the effect of applied force decreases over time? How does this happen due to kinetic friction (keeping in mind kinetic friction is constant - has a fixed value)? How does this work?

How does an object remain balanced on a frictionless surface and keep moving with a constant velocity without any friction to balance the forces (the resultant net force is equal to 0.)

Imagine you throw a ball vertically upward against the force of gravity , the ball would move some distance vertically and then stop due to force of gravity.

When you throw the ball , you exert force on the ball which is obviously greater than gravitational pull. But after throwing the ball the force applied by you become zero , so why does the ball travel some distance and then stop?

The answer: The instant you throw the ball , it gains some acceleration due to your applied force which is indeed greater than gravitational force. Suppose the initial velocity the ball will get due to applied force is 50m/s . It will take 5 seconds to gravitational force to stop the ball ( accelration due to gravity = 10 m/s²).

This is what happens in the case described by you. Kinetic friction will take some time to stop the object since the accelration provided by you was bigger than the accelration(retardation) of kinetic friction.

Hope this helps

• Your claim "suppose the accelration of the ball due to applied force is 50m/s² . It will take 5 seconds to gravitational force to stop the ball ( accelration due to gravity = 10 m/s²)" is wrong, the upward initial velocity needs to be 50m/s not a force of 50m/s² to stop after 5s. If you want that initial velocity with a specific force of 50m/s² you need to apply that force for 1.25s (since the net upward acceleration is only 40m/s²), which you didn't mention. May 25, 2022 at 21:13
• @Yukterez , Thanks for mentioning
– user329624
May 26, 2022 at 6:28

You're right that kinetic friction is constant, assuming the coefficient of friction and mass of the weight don't suddenly change. It seems like your confusion is how a mass would eventually come to rest if friction isn't greater than an applied force. Let's break this down with Newton's second law:

$$m\ddot{x}=\sum_iF_i=F_{applied}-F_{friction}$$

$$\ddot{x}$$ in this case refers to the acceleration of the mass. If $$F_{applied}>F_{friction}$$, then the mass will accelerate at a constant rate and will not come to rest.

Now, if suddenly $$F_{applied}$$ disappeared, or reduced in magnitude so that $$F_{friction}>F_{applied}$$, then the object will eventually come to rest because it would be constantly decelerating until it comes to a stop.

On a frictionless surface, there is no $$F_{friction}$$, so the motion of the object is completely described by:

$$m\ddot{x}=F_{applied}$$

So the mass would keep accelerating as long as the force is applied.

Hopefully that answers your question, let me know if that makes sense!

• So does the effect of friction on an object gradually decrease with time? Are the forces balanced on a frictionless surface as there is no friction? (I have learnt that only when a force is balanced with friction, then there is a uniform motion with constant velocity). May 25, 2022 at 16:04
• The force of friction on an object doesn't change with time based on the definition $F_{friction}=\mu F_{normal}$. On a frictionless surface, the force of friction is 0 $F_{friction}=0$, so for forces to be balanced, any applied force must also be 0, $F_{applied}=0$ May 25, 2022 at 16:10
• But if I apply a force on 5N on an object on a frictionless surface, (then the Fapplied ≠ 0). Then will the forces be balanced? I think no. But if no, then why do an object move with constant velocity on a frictionless surface (as I have learnt that balanced forces are required to keep a body moving with uniform velocity). May 25, 2022 at 16:13
• If you were to apply 5N to an object on a frictionless surface, then it wouldn't move with a uniform velocity, the forces would be unbalanced and it would accelerate, continuously increasing the velocity May 25, 2022 at 16:18
• There's an implicit assumption in what you're saying, that assumption is that the applied 5N force stops at some point after the object is in motion. If the force is constantly applied, it won't ever move with constant velocity May 25, 2022 at 16:29

If you continually apply a force of 20 newtons to an object, and there is a frictional force of 13 newtons on it, then there is a net force of 7 newtons in the direction you're applying the force. This means that the object will accelerate in the direction you're applying the force, and (assuming it starts from rest) it will not come to rest so long as you're applying the force.

Once you stop applying the force, then the only force on the object will be 13 newtons in the direction opposing the motion. This will bring the object to a rest after a certain distance.

• Does the impact of force on an object decrease over time if I don't exert a new force? May 25, 2022 at 16:07
• @TomHenderson: You seem to be conceiving of a force as something that happens at a brief moment in time, like a hammer blow. But when we say that we "apply a force of 20 newtons", we mean that this force is applied continually and continuously. So by definition, its "impact" is constant over time unless otherwise specified, and if it is unbalanced it leads to a constant acceleration (not a constant velocity) over that time. May 25, 2022 at 16:33

Simple. Your initial force only acts for some finite duration, over which body will get final momentum due to second Newton law : $$p= p_{_0} + F\tau$$,

Where $$\tau$$ is pushing force duration, time window when you actually apply your force.

Afterwards, over small duration of time, kinetic friction will do a negative work towards body,- decreasing your initial given kinetic energy by some fixed amount, repeatedly, until body will finally stop after traveling distance $$d$$.

What distance $$d$$ it will travel, can be find out, by equating friction total work done until it stops body to the kinetic energy body had at first moments due to your pushing force :

$$\frac {p^2}{2m} = \mu Nd$$,

where $$N$$ is normal force, and $$\mu$$ is coefficient of kinetic friction.

The only question remains is that, why friction can stop any object with arbitrary huge kinetic energies, given enough time ? Answer is that no matter your force magnitude,- you can only act for a reasonable period of time. But friction force is proportional to normal force which is proportional to body weight :

$$F_{fr} \propto N \propto mg$$

And gravity never sleeps, and will continue to act over all bodies until gravity source exists, so it will stop anything sooner or later. Unless you give so much kinetic energy, that body escapes Earth at all and becomes it's satellite, that's how rocket's do. Or you may constantly re-supply kinetic energy what's lost due to friction (i.e., rolling resistance + air drag),- that's how cars do it, by burning fuel.

There are very tiny bumps and ridges along the surfaces of contact.

What we call "Force of friction" is a sort of overall estimate on a large-scale of how all these bumps colliding with other surface bumps are causing deceleration.

The coefficient of friction of surfaces has been proven experimentally.

But what's going on are really tiny bumps on the surface are colliding with each other which slowly decelerate the object and this deceleration decreases.

So you're losing momentum overtime.