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? on Kin. friction/no friction and mag. of acceleration intuition

  1. Jul 14, 2012 #1
    I was working on a problem with an incline plane and two masses connected by a pulley. One mass on the plane and the other hanging down the side. We had to first calculate the acceleration ignoring friction and then we were give a coefficient of kinetic friction and asked to recalculate acceleration accordingly.

    When I did the second part the magnitude of my acceleration was greater than when there was no friction. I'm wondering if this makes sense. Thinking solely in terms of F=ma it makes sense that if the force is greater but the mass stays the same the magnitude of the acceleration will be greater than with smaller forces. I am thinking that with regard to a problem as this with an incline plane and kinetic friction the tension (the force upward) in the pulley is directed along the x axis (up the plane) and the forces opposing this are the force of friction downward (negative x axis) and the sine of the angle times the mass x g of the object on the plane. Therefore, the force up the plane (the tension) is greater with friction involved than it is w/o friction because it must be greater than the two forces opposing it for any acceleration to happen. Therefore, it makes sense that the magnitude of acceleration is greater than w/o friction.

    However, intuitively, it feels strange. It seems odd that when there is friction involved the masses would have greater acceleration than if there was no friction opposing the acceleration.

    Any help explaining this to me? Am I right on my thoughts above and just need to "correct" my intuition or is my intuition correct and therefore, the magnitude of the acceleration should be less with kinetic friction than w/o friction and I need to rework my problem accordingly? Thanks!
  2. jcsd
  3. Jul 14, 2012 #2


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    I can't see how that can happen.

    Think of it from the point of view of energy. In the first case energy is transformed from PE to KE. In the second case the same PE is transformed into KE and heat (via friction). How can the KE in the second case be greater than the first?

    I suspect you have a sign wrong somewhere.
  4. Jul 14, 2012 #3
    Your intuitions are correct. I think you have the direction of your frictional force wrong. It's directions is always opposite to the velocity. If the block is accelerating up the plane, friction will be directed downward.
    The only way that the absolute value of acceleration can be larger with friction is in the case where you are starting with an initial velocity and friction is large enough that it eventually stops the masses (large negative acceleration).
  5. Jul 14, 2012 #4
    If my intuition is correct, then I certainly did the problem wrong. Hence, my red flag when I got the answer I did. I do have the frictional force opposing the tension, however, but my calculations are not working out so I must have a sign wrong somewhere.
    If the Sum of Fx is the two negative x axis forces plus the positive x axis force=ma then:
    neg. kinetic frictional force (coefficient of kf x FN) +
    neg. sine of the angle x's mg
    Plus Positive tension =ma and then I solve for T to get
    T=(ma) - (Fkinetic friction)- (sine angle x mg)

    I then plug in this expression for T into my sum Fy expression which is T-mg(of 2nd obj) =m(of 2nd obj) times acceleration. Then I solve for a, but it's not working out.

    What am I missing? Perhaps it is just my math but I've tried a few times now so I think I have something wrong in what I believe is the sum of Fx. I guess this has somewhat transformed to an intuition question into a homework problem, now.
  6. Jul 14, 2012 #5
    Are you sure that, without friction, the mass is not sliding *down* the ramp. This could be the case if the mass on the ramp is larger than that hanging mass.
  7. Jul 14, 2012 #6
    Now, that confuses me more. The mass on the incline is indeed larger than the other mass. However, because they specifically indicate the coefficient of kinetic friction and the mass is moving up the incline, I thought the kinetic friction would certainly be in the direction opposite, or down the incline, if the mass is moving up the incline regardless of whether it is bigger or smaller than the other object.
    Last edited: Jul 14, 2012
  8. Jul 14, 2012 #7

    Doc Al

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    Yes, you have a few signs wrong:
    ƩF = ma
    T - (Fkinetic friction) - (sine angle x mg) = ma

    Try that. (Be sure to distinguish the two masses.)
  9. Jul 14, 2012 #8


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    I haven't followed your last post but..

    It is not possible to tell which way the mass on the slope will go without working the numbers. If the incline is steep it might go down. If the incline is shallow it might go up.

    It's worth remembering that friction cannot make it go in the oposite direction to the frictionless case. So work out which direction it goes without friction first. Then redraw the problem showing the friction force in the correct direction whichever that is. This is probably why it's been set as two part question.

    Just remember to stick rigorously to the signing convention and you should get the right answer.
  10. Jul 14, 2012 #9
    I got it! I wasn't being careful enough with the directions designated as positive/negative. I forgot to denote that if the direction up the incline is positive then this also means the force downward on the object hanging off the edge is positive also as the object moving up the incline would eventually come down the other side. Changed everything! So, the initial negative value of acceleration I got was not the object moving up the incline but rather the object moving backwards down the incline.
    While I'm putting this problem to bed for a bit, I am sure when I take these values into consideration when I work on the second half involving friction I will see things even clearer.
  11. Jul 14, 2012 #10
    Kudos for engaging your brain and recognizing that your initial answer did not make sense intuitively. You would be surprised how many students work a problem out, get an answer that cannot possibly be correct, then go on to the next problem.
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