# Does applying a force to keep a body in uniform motion not considered as a force because there is no acceleration. (Friction included) [closed]

Because I have studied that if there is no acceleration then there is no force.

• "Because I have studied that if there is no acceleration then there is no force." ------> actually we call it as a case of no net force. Feb 12, 2021 at 7:15

It is still a force.
Just because there is no acceleration doesn't make it any less of a force. The force just gets balanced out by a force in the opposite direction. The net force on the body is 0 though and hence no net acceleration.
So if you are doing a problem where the forces are balancing out, then (Most probably) taking the net force as 0 should do it.

• So if the net force is zero, does it also imply that the work done is also zero? But we are definitely doing some work to keep the body moving.
– Shiv
Feb 19, 2021 at 3:32

If a body with mass $$m\neq 0$$ has not acceleration then the total acting force is null: $$\vec{a}=\vec{0} \iff \vec{F_{tot}}=m\vec{a}=\vec{0}$$. It means that a force applied to keep a body in uniform motion, say $$\vec{F_1} \neq \vec{0}$$ has to be considered. In particular if the body moves in uniform motion it means that there has to be an other force acting to it, say $$\vec{F_2} \neq \vec{0}$$ and this other force has to be opposite to the fist: $$\vec{F_2}=- \vec{F_1}$$ such that $$\vec{F_{tot}}= \vec{F_1} + \vec{F_2}= \vec{F_1}-\vec{F_1} =\vec{0} =m\vec{a} \iff \vec{a} =\vec{0}$$. For example, if there is a friction force on a table and you want to move a book on it in horizontal direction in uniform motion, you have to act a force such that her sum with the friction has to be $$\vec{0}$$.

There is a net force. Suppose the body has speed $$v$$ and undergoes uniform circular motion in a circle of radius $$r$$. Then the net force is the centripetal force, namely $$\Sigma F=\dfrac{mv^2}{r}$$

The acceleration is therefore $$a=v^2/r$$. This acceleration is radial, and only changes the direction of velocity, and not the speed. Remember that if velocity (which is speed+direction) changes, then there is a net force. In uniform circular motion, speed does not change, but the velocity's direction definitely does.

Second, there can be a zero net force, but there are still forces applied. Consider a stationary block on a table. Of course gravity is acting on it, but so is the table's normal force. The reason the block does not move is because the force of gravity equals in magnitude the normal force such that the (vector sum) net force is zero.