# Problem in understanding Newtonian 2nd law

In Resnick, Halliday, Walker s' Principle of Physics , I found this question :

Two forces are acting on a block on a frictionless floor. On the left of the block $3~\text{N}$ & on the right of the block $5~\text{N}$ are acting. If a third horizontal force $\vec{F_3}$ also acts on the block, what are the magnitude and direction of $\vec{F_3}$ when the block is a)stationary and b)moving to the left with a constant speed of $5~\text{m/s}$ ?

What I have done: For being stationary, $2~\text{N}$ must be applied on the leftside of the block so as to make the net external force zero. In order to move with $5~\text{m/s}$ to the left, first we have to apply force greater than $5~\text{N}$ to the left side so as to accelerate it to the left. When the velocity reaches $5~\text{m/s}$,then we will weaken the force on the left to match the force on right ie. $5~\text{N}$ so that block moves at that required velocity.

My book's answer: Without explaining much, they wrote that in both the cases the force will be $2~\text{N}$ .

So, why did they tell that it was $2~\text{N}$ in the second case? What is the problem with my analysis? If it were $2~\text{N}$ , then the block will not move;at first I have to exert a greater force, then can only I reduce the force to let it move at that constant rate. So why am I wrong??

• The wording asks about two cases: stationary and moving. It is silent about how they got to those states. You are told the block is moving. It's already reached it's speed an leveled off. – garyp Oct 31 '14 at 16:40

Remember that a force causes acceleration. If you pull the block to the left with $5\mbox{N}$ when the velocity reaches $5\mbox{m/s}$, then the net force will be $2\mbox{N}$ towards the left. And the block will experience acceleration.
If you want steady speed, you need $0$ acceleration, and this is achieved by setting the net force to $0$.
This is a common trip-up for first year physics students. Both part a) and part b) of your problem describe situations with no acceleration. A stationary object is not accelerating, but a moving object at constant velocity is not accelerating either. Therefore, Newton's Second Law tells us that in both situations, there is no net force on the block. $$\Sigma F=ma$$ and then $$\Sigma F=0$$ because $a=0$.