# Homework Help: Net force acting on a car

1. Jan 21, 2016

### Thewindyfan

1. The problem statement, all variables and given/known data
A car is going around a circular track at constant velocity. What direction is the net force acting on the car pointing to?

2. Relevant equations
Fnet = ma

Fnet = m(v^2/r) --> don't really know if this will help me understand it, but if this will help me understand what's going on then that'll be great to keep in mind.
Newton's 1st law
3. The attempt at a solution
I'm unsure about what direction exactly the net force would be acting in.
We know the car is going at constant velocity, so Newton's first law should be applicable since we're only considering inertial reference frames in my physics class.
But at the same time, there is centripetal acceleration in this scenario, where the acceleration vector is always pointed towards the center of the circular path
The confusing thing for me is that I'm unsure of whether it's correct to say that the net force is also pointing in the direction of the acceleration vector for this case, since I'm unsure of what happens if the force in the opposite direction of the acceleration vector is greater than the force acting in the same direction as the acceleration.

I feel like the answer should be my 2nd guess, but I'd like someone to clarify with me on this; if the force acting on the car in the opposite direction of the acceleration is greater than the force acting on the car in the same direction (and thus I would assume the net force is pointing in the opposite direction), does that mean the acceleration vector just becomes smaller overall or am I actually making sense with this assumption?

2. Jan 21, 2016

### Simon Bridge

... velocity is a vector, to be a constant the magnitude and direction must remain the same. Going in a circle, the direction of the velocity vector is constantly changing, therefore the velocity cannot be constant. So there is a typo in the problem statement. What should it say?

... that is the magnitude equation for centripetal force ... the question is asking about direction. This should help...

Do you know the equation for centripetal acceleration?
Can you relate that equation to the one for Fnet you have above?

Do you know a vector equation that relates net force vector to acceleration vector? (Hint: Newton's Laws). What does that say about the direction of the force and acceleration?

You are clearly doing a section on circular motion in class ... your text book and/or class notes should have some diagrams which show you the direction of the force, probably close to where they also give you the equation for Fnet you wrote out above. If not, you can google "circular motion" and read.

If an object has two forces on it, and the forces act in opposite directions, how is the direction of the accekleration determined?
If we start with an object mass $m$ accelerating to the left with acceleration $a_1$ then we can deduce that the net force is $\vec F_1=m a_1 \hat\imath$... if we then introduce another force $\vec F_2 = -k\vec F_1 : k>1$ i.e. it acts opposite F1 and is bigger ... then you can work out $\vec a_2$ to see what happens.

3. Jan 21, 2016

### Thewindyfan

Ah my mistake! I meant constant speed, so the magnitude of the velocity remains constant the entire time. I may have also improperly used the term "centripetal acceleration" to refer to the idea that in uniform circular motion, the acceleration vector always points to the center of the circular path. Sorry for making that mistake, since it seems you answered a question that would be a bit more involved.

4. Jan 21, 2016

### Simon Bridge

Well done.
No - that is the correct terminology.
No - I answered the question assuming you meant "speed" rather than velocity ... so the reply stands.
You didn't get the simple answer you were expecting because you are better served using your understanding to figure it out for yourself.

5. Jan 21, 2016

### Thewindyfan

Upon re-reading what you said in the last part of your reply, I think I understood the point you made with the idea of the acceleration happening to the left and the force opposite of that acceleration being > the force in the direction of the acceleration, which you would then end up finding a2 to be < a1 because while it's still accelerating to the left, the force opposing the acceleration is affecting the magnitude of that acceleration. Am I understanding that correctly?

If so, that means that the net force vector is pointing radially inwards to the center of the circular path then.

6. Jan 21, 2016

### Simon Bridge

No. You apparently did not understand that I intended for you to do the math. $\sum \vec F = m\vec a \implies m\vec a_2 = \vec F_1 + \vec F_2$

7. Jan 22, 2016

### haruspex

Yes, though I did not follow the a1, a2 discussion.

8. Jan 22, 2016

### Simon Bridge

... it's off the detailed question earlier.

Of course the acceleration always points in the same direction as the net (resultant) force. That is what Newton's law says.

9. Jan 23, 2016

### Thewindyfan

Sorry guys, this question was pretty straightforward but I must've been really overthinking simple things the last couple of days. I think I'm going to take another look at how I'm managing my time. Thank you for the help!

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