1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Direction of normal acceleration problems

  1. Sep 18, 2014 #1
    1. The problem statement, all variables and given/known data


    2. Relevant equations

    An = mv^2 / r

    3. The attempt at a solution

    I get the 2D free body diagram, and how the vertical components are resolved, but how is Nc sin θ = mv^2 / r when they both are in the same direction?

    Also another related problem is this diagram here:


    The equation for the mass at B is,

    mg = Fc + N

    How is this so when both Mg and Fc are directed downwards (Fc being the centripetal force mv^2 / ρ). Shouldn't it be mg + Fc = N?

    I guess I don't understand the direction of Fc due to the normal acceleration. in either of these problems.
  2. jcsd
  3. Sep 18, 2014 #2


    User Avatar
    Science Advisor
    Homework Helper
    2017 Award

    "when they both are in the same direction?" is not all that clear to me. Who is in which direction, and who else ?

    In your second problem, a conceptual dwelling becomes a bit clearer.
    Basically, there is no Fc. For an object to execute a circular motion, some force has to play that role.

    In the first problem, the horizontal component of the normal force plays that role. Hence also the equality Nc sin θ = mv^2 / r.

    In the second problem, the vertical component of the gravitational force plays that role. Not all of it, so there remains some normal force. (**)

    A "much better" (ahem) way to write this would be mg - N = the force to cause a circular motion.

    Since we generally like short notation, we often use Fc for "the force to cause a circular motion", so now that name is back again. But remember it is shorthand for "the force to cause a circular motion" (or the force that changes the direction of the velocity vector...)

    (**) Well, if v is big enough, all of mg is needed to keep the object on the circular trajectory. Increasing v beyond that, the car will loose contact with the hill, since there are no other contribuant forces that might keep it on there.

    [edit] Ah, I see it's not a car but an unspecified "mass". Story doesn't change.
  4. Sep 18, 2014 #3

    Doc Al

    User Avatar

    Staff: Mentor

    Both what? I only see one force here: Nc. It has a component in the n direction. The rest is Newton's 2nd law.

    The way to understand it is to think of the net force at B: ∑F = mg - N. (mg is downward, N is upward) That net force is the Fc, so Fc = mg - N. Note that Fc acts downward.
  5. Sep 18, 2014 #4


    User Avatar
    Science Advisor
    Homework Helper
    2017 Award

    Because it's so important, I throw in another reply:

    In the top problem, there are only two forces working on the car: gravity and normal force. The (vector) sum of those is not zero due to the incline.

    We have learned F = ma (but actually it is ##\vec F = m \vec a##). Where F is the net sum of all forces.

    Furthermore, we have learned that for uniform circular motion an acceleration towards the center is needed with a magnitude mv2/r

    So if we want the object (car, block, ..) to execute a uniform circular motion, we must ensure that the net sum of forces is pointing the right way (exactly towards the center) and has the magnitude mv2/r.

    If you look upon Fc as something that is a resultant instead of one of the forces present, you almost can't go wrong.
  6. Sep 18, 2014 #5
    I see. I thought of Fc as another independent force. It makes sense now. Thanks for all of the replies.
  7. Sep 18, 2014 #6

    Doc Al

    User Avatar

    Staff: Mentor

    This is an important point. Fc is a resultant (or net) force, not a separate force of its own. Fc should never appear in a free body diagram.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted