Considering Friction is here.. How can a body move with uniform velocity, to move with uniform velocity it should have acceleration equal to zero, for this suppose a body on which a force F is acting on right then the F(k) {Kinetic friction} will be on left (all this happening in x-axis). To have zero acceleration F=F(k), then how can a body even move having zero Force on it along with uniform velocity… I didn't get this theoretical concept.
[Physics] How to a body have constant velocity when net force on it is zero
friction
Related Solutions
Consider the diagram below of a ball on a horizontal surface:
Newton's Laws tell us that if no net force acts on the ball it will remain in a constant state of motion ($v=0$ or $v=\text{constant}$). Consequently, if no net torque acts on the ball its state of rotation will also remain constant ($\omega=0$ or $\omega=\text{constant}$).
Where friction does play a part, it is usually somewhat simplistically modelled as $F_f=\mu F_n$ with $\mu$ some friction coefficient and $F_n$ the normal force (here simply $mg$). But in the case of a ball rolling with constant $v$ and constant $\omega$ and no external force (say $F$) acting on it, this would lead to deceleration according to :
$$ma=-F_f$$
But then $F_f$ would also provide torque leading to angular acceleration according to:
$$I\dot{\omega}=F_f R,$$
with $I$ the inertial moment, $R$ the radius and $\dot{\omega}=\frac{d\omega}{dt}$ the angular acceleration.
This would be the case where you launch a ball with initial speed $v$ but no angular momentum ($\omega=0$) onto a surface that provides much friction: the ball would start spinning ($\dot{\omega} > 0$ but also start decelerating ($a < 0$) and translational kinetic energy would be converted to rotational kinetic energy. If the surface can provide enough friction that process would continue until $v=\omega R$: rolling without slipping.
To keep the ball moving without any deceleration we would have to supply an external force, so that:
$$F_f=F,$$
and $a=0$.
Critical coefficient of friction $\mu_c$:
Assume a ball with $v=0, \omega=0$ at $t=0$. We now apply a horizontal force $F$, so that $a>0$.
$$F_f=\mu F_n=\mu mg$$
$$I\dot{\omega}=F_fR=\mu mgR$$
After integration we get:
$$\omega=\mu\frac{mgR}{I}t$$
In that same amount of time the ball has also acquired translational speed:
$$F-F_f=ma$$
After integration we get:
$$v=\frac{F-\mu mg}{m}t$$
Without slipping we have:
$$v=\omega R$$
$$\frac{F-\mu mg}{m}t=\mu\frac{mgR^2}{I}t$$
Reworking and isolating $\mu$ we get:
$${\mu_c=\frac{FI}{mg(I+mR^2)}}$$
This is the minimum value for the coefficient of friction in order to achieve rolling without slipping when a horizontal force $F$ is applied.
I see three crucial misunderstandings that I would like to point out:
Correction 1
- A spaceship is moving with engines off, drifting through space. There are no forces.
- A spaceship is staying still, hanging in space. No speed. Also no forces.
Conclusion? Forces have got nothing to do with speed. No forces (no net force) means no change in speed. Not no speed. Your statement:
until the friction and force are the same magnitude, stopping the movement
is false. Balancing forces won't stop a motion.
This is from Newton's 2nd law:
$$\sum F=ma$$
A net force doesn't cause speed, it causes changes in speed (acceleration). No net force causes no change in speed.
Correction 2
- A spaceship is hit by a comet. A wing breaks off from enormous impact force. The wing flies away. But doesn't speed up. Nothing slows it down (no friction in space) - and nothing speeds it up. It drifts off at constant speed forever until it reaches and interacts with somethings new.
Conclusion? The force that gave it the speed, doesn't work on it anymore. Your statement:
Because since there is a starting push, that force would be acting on the person all through the 75m
is false. A force only works while being exerted by something. As soon as the cause of the force disappears, the force disappears.
This also answers your title question:
How can net force equal to friction?
It can, since the other force you thought was there isn't there. The force diagram should horizontally show only friction.
Correction 3
Kinetic friction follows Amontons law in everyday cases:
$$f_k=\mu_kn$$
No mention of speed, distance, time or similar here. Experiments show that friction is proportional to normal force, only. It will not grow or reduce along the way. Kinetic friction is constant while the sliding takes place.
Your statement:
until the friction and force are the same magnitude
is impossible since none of those two forces change during the motion. They never grow or reduce to become equal.
Best Answer
Frictional forces works in two different regimes; static and dynamic.
Immagine a solid resting on a table. When you pull from it with a force (we call that force in this context the acting force) the frictional force apears. It was not there before. This is the static friction force. It increases in magnitude at the same pace that you increase the acting force, thus is always perfectly counteracting your pull and therefore the object doesn't move. Or more precisely the object doesn't change its state of motion (which is a specific case of uniform rectilinear motion where velocity is zero).
If you keep increasing the pull, then the static friction would keep increasing to counterbalance it, until it reaches a critical threshold (a maximum force) where the frictional regime transforms to the so called dynamical. Above this force (this pull / acting force) the table can no longer resist your attempts to move the object and friction stops increasing as a response to your acting force. Then your acting force is greater than friction (since it can't keep increasing the bet) so the net force (the total sum of forces) is non zero, A.k.a. you start to accellerate the object.
You can see the response of the frictional force with respect to the acting force you are pulling the object with in this diagram:
THEORETICAL INTENSITY OF THE FRICTIONAL FORCE VS THE ACTING FORCE
EXPERIMENTAL DATA SHOWING INTENSITY OF THE FRICTIONAL FORCE VS THE ACTING FORCE
So, to finally answer your question. Can a body have constant velocity when net force on it is zero? Yes, and not only that. It will ALWAYS have constant velocity when the net force (the sum of all the forces acting on an object: in this case pulling and frictional forces response) is zero. This is the statement of Newton's 1st law of motion. It doesn't matter if there is friction or not, the statement is always valid. In the static regime, when you are not pulling very hard from the object and the frictional response is counteracting your pull the net force is zero and in fact the object mantains a constant velocity (zero velocity in this particular case). When you pull harder than a certain threshold force the friction is not completely counteracting your pull and thus there is a net force in the direction of the pull slowly accellerating the object (Newton's 2nd Law). This means that the object would change its state of motion from been at rest to start to move.