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Thread: Mechanics - Friction and acceleration on a slope

  1. #1
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    Mechanics - Friction and acceleration on a slope

    A tree trunk, of mass 250kg, is pulled up a slope by a chain attached to a tractor.
    The chain is at an angle of 10 degrees to the slope. The slope itself is at 8 degrees to the horizontal.
    The tree trunk initially accelerates at 0.2 ms-2. A friction force, of magnitude 2000N, acts on the tree trunk.

    (a) Modelling the tree trunk as a particle, find the initial tension in the chain.
    (b) Explain why the tension in the chain will probably decrease.


    I have answered part (a) correctly by using Newton's 2nd law parallel to the slope (Tension = 2428 N) but I am struggling with part (b).
    The answer at the back of the book states "The resistance force will increase and it will stop accelerating".

    The questions I have are:
    1. Why will the resistance force increase? (Maybe due to air resistance?)
    2. Why, if it stops accelerating, will the tension in the chain decrease?


    Any help would be gratefully appreciated!
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  2. #2
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    Re: Mechanics - Friction and acceleration on a slope

    Hey rubikwizard.

    You have either two reasons for this - mathematical or physical and this is a physical problem and not so much a mathematical one.

    The physical context includes friction, momentum, and other factors that change how the force acts over time - something a simple force calculation may not reveal.

    The trunk will also get to a point where it is on the slope completely instead of on the ground and things like that can impact this.

    What ideas do you have regarding this problem?
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  3. #3
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    Re: Mechanics - Friction and acceleration on a slope

    There are two reasons i can think of why tension will decrease:

    1. The 2000N initial friction force may be a measure of static friction, meaning the force that needs to be overcome to get the tree to start moving. In most cases the value of static friction is greater than the value if dynamic friction, so once the tree starts moving the friction force would decrease.

    2. The second reason is more practical: if the the initial tension results in constant acceleration of 0.2m/s^2, what velocity do you get after 10 seconds? 100 seconds? 20 minutes? Clearly when you're dragging something there must be a maximum velocity, so you can't have constant acceleration forever and at some point the tension must be reduced so that acceleration = 0.
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