# Doubt on a question from Newton's laws of motion

We(me and my classmates) had completed a chapter on Newton's Laws of Motion. Now this question pops up:

A cricket ball of mass $70\,\mathrm{g}$ moving with a velocity of $0.5\,\mathrm{m/s}$ is stopped by a player in $0.5\,\mathrm{s}$ . What is the force applied by the player to stop the ball?

My answer is $0.07\,\mathrm{N}$ while the answer of the majority of the class is $-0.07\,\mathrm{N}$. I even asked our Physics teacher he says their answer is correct i.e, $-0.07\,\mathrm{N}$.

My solution is:

$$m = 70\,\mathrm{g} = 0.07\,\mathrm{kg}$$ $$u = 0.5\,\mathrm{m/s}$$ $$v = 0$$ $$t = 0.5s$$

$$F = ma = \frac{m(v-u)}{t}= 0.07( \frac{-0.5}{0.5}) = -0.07\,\mathrm{N}$$

The force exerted by the player will be the reaction force of the action force exerted by the ball. Thus, $0.07\,\mathrm{N}$

So, which one is correct?

• Think about how you've defined the reference frame. If the ball is initially moving with a velocity of +0.5m/s, what must be the sign of F in order to stop it? – sxwzd Sep 19 '15 at 11:21

Perhaps this whole question is just a matter of semantics, but I am inclined to agree with your classmates and teacher that the force exerted by the player is negative. Here's why:

Whether unknowingly or not, you have chosen (or whoever wrote the problem has chosen) for the direction of the ball's initial motion to be positive. For the sake of clarity in this answer, let's say that direction is to the right. This is because you're representing the initial velocity of the ball as positive, ie $0.5 \mathrm {m/s}$. Because you've chosen the direction to the right to be positive, and because the ball eventually comes to rest, it must experience an acceleration in the opposite direction, that is, to the left.

Newton's Second Law of Motion states in part that the net force acting on an object is in the same direction as the object's acceleration. Therefore the net force action on the object must also be negative. Since we're ignoring the effects of other forces such as air resistance, that entire force must have been provided by the cricket player. Because the force exerted by the cricket player acts to the left, it is negative. In these sorts of problems I'd recommend you always draw a picture including your forces and chosen coordinate axes!

See if you consider that the ball is moving in the +ve X-direction , then to stop the ball , the ball must decelerate,i.e, an acceleration must be applied on the ball in the opposite direction. The force by the player will be in the -ve X-direction. That is what your friends and your teacher are calling their answer.

As for your calculation, you are putting a "-" sign before the expression claiming it to be the reaction force by the player. But the $F$ in your equation is neccesarily the net force in the system and that indicates that the motion of the ball and that of the force are in opposite direction. So, force being a vector quantity, answer should be $-0.07\,\mathrm{N}$.

• So the final answer is -0.07N ? – Deepam Sarmah Sep 19 '15 at 11:39
• Yes. Sorry for messing it up initially. I have edited my answer and now it is fine. – SchrodingersCat Sep 19 '15 at 11:40
• Woah, you totally changed your answer (and now it's pretty similar to mine) – Sean Sep 19 '15 at 11:45
• @DeepamSarmah If you like any answer, you have the option to upvote, or better still, accept it. Just for your information. – SchrodingersCat Sep 19 '15 at 12:18

the differences in sign of the answers (your '+' and your teacher's '-') just lies in the fact that the way in which you see who applies the force and in which direction you see the force acting upon the ball. Or you can see the direction of force applied by the player. It doesn't mean that your answer is wrong... It's just about the fact that Force being a vector quantity should be handled while taking its direction in consideration.