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Finding acceleration of a block on an incline without friction, then with friction!

  1. Oct 1, 2012 #1
    7. A block of mass m = 5.5 kg is pulled up a θ = 22° incline as in the figure with a force of magnitude F = 38 N.

    4-p-030.gif

    (a) Find the acceleration of the block if the incline is frictionless

    So I got this one right, and here is what I did...

    From the free body diagram I drew:

    Fnet = (38 N) + (-mg sin 22)
    ma = 38 - mg sin 22
    a = (38 - mg sin 22)/m
    a = [ 38 - (5.5)(9.81)(sin 22) ] / (5.5)
    a = (38 - 20.211) / 5.5
    a = 3.24 m/s2

    (b) Find the acceleration of the block if the coefficient of kinetic friction between the block and incline is 0.12.

    So...I know that

    fk = μkn
    fk = 0.12(Fappliedsin θ - mg)

    QUESTION 1: So this is where I'm a little confused...Normal force should be UPWARDS, right? then would that mean that n = Fappliedsin θ + (- mg) after rotating my free body diagram so that I can see the axis better??? Because I almost got the answer...

    fk = 0.12[38 sin 22 - (5.5)(9.81)]
    fk = -4.767 (the negative number makes sense since kinetic friction is OPPOSING the motion of the block which is moving up the incline.

    So then I add it to the equation for acceleration at the top

    ma = (38 N) + (-mg sin 22) + (-4.767)
    a = [ 38 - (5.5)(9.81)(sin 22) - 4.767 ] / (5.5)
    a = 13.022 / 5.5
    a = 2.36 m/s2

    This answer is wrong...Webassign says the answer is actually a = 2.15 m/s2

    QUESTION 2: Where did I go wrong? Was it the normal force equation part?
     
  2. jcsd
  3. Oct 1, 2012 #2

    Doc Al

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    Staff: Mentor

    Re: Finding acceleration of a block on an incline without friction, then with frictio

    Right.
    Not right.
    The normal force is 'normal'--perpendicular--to the surface. Figure out the normal force by analyzing force components perpendicular to the incline. They must add to zero.
     
  4. Oct 1, 2012 #3
    Re: Finding acceleration of a block on an incline without friction, then with frictio

    No wait...
    it would be

    -mg + (-mg sin 22)?
     
  5. Oct 1, 2012 #4
    Re: Finding acceleration of a block on an incline without friction, then with frictio

    It's just F cos θ, which is 38 cos 22...

    But I still don't get the right answer when I multiply 0.12 by 38 cos 22, and then add 4.22 to this equation...

    ma = 38 - 20.11

    a = (38 - 20.11 + 4.22) / 5.5 doesn't give me 2.15 m/s2

    Something else is wrong
     
    Last edited: Oct 1, 2012
  6. Oct 1, 2012 #5

    Doc Al

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    Staff: Mentor

    Re: Finding acceleration of a block on an incline without friction, then with frictio

    The applied force F is parallel to the incline. It has no normal component.

    The weight of the block, being vertical, will have a normal component.
     
  7. Oct 1, 2012 #6
    Re: Finding acceleration of a block on an incline without friction, then with frictio

    So it's -mg cos 22?
    Which is basically -(5.5)(9.81)(cos 22)...

    fk = 0.12[-(5.5)(9.81)(cos 22)]
    fk = -6.003

    So,

    a = [ 38 - 20.211 + (-6.003) ] / 5.5
    a = 2.159638636

    :)

    Thanks!
     
  8. Oct 1, 2012 #7

    Doc Al

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    Staff: Mentor

    Re: Finding acceleration of a block on an incline without friction, then with frictio

    Almost. What's the weight of the block?
     
  9. Oct 1, 2012 #8
    Re: Finding acceleration of a block on an incline without friction, then with frictio

    It's just 5.5 kg isn't it?
     
  10. Oct 1, 2012 #9

    Doc Al

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    Staff: Mentor

    Re: Finding acceleration of a block on an incline without friction, then with frictio

    No, that's the mass.
     
  11. Oct 1, 2012 #10
    Re: Finding acceleration of a block on an incline without friction, then with frictio

    oh...Weight = mg
    Weight = -(5.5)(9.81) = -53.955 N
     
  12. Oct 1, 2012 #11

    Doc Al

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    Staff: Mentor

    Re: Finding acceleration of a block on an incline without friction, then with frictio

    Right. The weight = mg and acts downward.
     
  13. Oct 1, 2012 #12
    Re: Finding acceleration of a block on an incline without friction, then with frictio

    Ohh ok!
    Thanks a lot!!!!
     
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