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    A sledge of mass 25 kg is on a plane inclined at 30° to the horizontal. The coefficient of friction between the sledge and the plane is 0.2.
    On a subsequent occasion the cable is not in use and two people of total mass 150 kg are seated in the sledge. The sledge is held at rest by a horizontal force of magnitude P newtons. Find the least value of P which will prevent the sledge from sliding down the plane.

    Completely stuck and this is the only question I don't understand the full concept. Please could someone explain and show the answer?
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    draw a diagram of the plane and the block (including the block's total mass [25+2*150]). Resolve parallel to the plane since P acts parallel to the plane (ie do F=ma parallel to the plane [taking up or down as +ve and the other as -ve]):

    ie F=ma (on sledge, taking up slope as the +ve direction)

    Pcos(30) - {[25+2*150]*9.8}sin(30) +0.2*[25+2*150]cos(30) = [25+2*150]*a

    1st term on LHS = horizontal force component, 2nd on LHS = gravity component parallel to slope and 3rd on LHS = friction (acts up slope because it opposes motion)
    P is horizontal, NOT parallel to the slope.
    Where a is acceleration, which is zero since the question says it doesn't move.
    This is my method, I have a slightly different method to the book.

    Good luck.
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    I'm still lost
    oh and the total mass is 150, not each person's mass
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    (Original post by JChoudhry)
    I'm still lost
    oh and the total mass is 150, not each person's mass
    Oh I see, you'll have to forgive me.

    OK basically you draw a diagram with all of the forces and angles on it etc, resolve the forces so that you have the component of each force parallel to the slope (remember that P is horizontal not parallel to the slope). Then do F=ma on the sledge, this will give you an equation involving P, which you then make the subject and find the value of it.

    Sorry if that doesn't help, but there is only so much I can do over the internet, if not go and ask a teacher to go through it with you, but don't panic over it, it isn't worth it OK.
 
 
 
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