Friction question, maximum incline

AI Thread Summary
To determine the maximum incline angle (alpha) for a 50kg object on a rough plane, the forces acting on the object must be analyzed. The tension in the string, which has a breaking strain of 200N, must balance the gravitational component and frictional force. The equation derived is 50g sin(alpha) = 200 + 10g cos(alpha). To solve for the maximum alpha, a substitution using trigonometric identities is suggested, where sin(alpha) is represented as x and cos(alpha) as √(1-x²). This approach allows for the expression of the left-hand side as a single trigonometric function, facilitating the determination of the largest angle before the string breaks.
Kinhew93
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Homework Statement



An object of mass 50kg rests on a rough plane incline at an angle alpha to the horizontal. It is supported in this position by a light string parallel to the plane. The string has a breaking strain of 200N and the coefficient of friction between the object and the plane is 0.2. Find the largest value of alpha for the string to remain intact.

The Attempt at a Solution



Resolving parallel to the plane:

50gsin(alp) = 200 + (0.2x50gcos(alp))
= 200 + 10gcos(alp)

So it seems that I have to find the maximum value of alpha for which the above equation is true, but I have no idea how to do that.

Any help would be much appreciated. Thanks :)
 
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why not take sin(α)=x and cos(α)=√(1-x2)
 
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You can rewrite as $$50g \sin \alpha - 10 g \cos \alpha = 200$$ and express the LHS as one trig function and a corresponding phase.
 

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