A uniform plank of mass 10kg and length 10m rests on two supports, A and B as shown. A boy of weight 500N stands at a distance of 2m from A. Find the reaction forces U¹ and U² at the supports A and B respectively
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Answer:
U² = 142.86 N
U¹ = 357.14 N
Explanation:
Taking summation of the moment about point A, we get the following equilibrium equation: (taking clockwise direction as positive)
[tex]W(2\ m) - U^2(7\ m) = 0[/tex]
where,
W = weight of boy = 500 N
U² = reaction ay B = ?
Therefore,
[tex](500\ N)(2\ m)-(U^2)(7\ m)=0\\U^2=\frac{1000\ Nm}{7\ m}\\[/tex]
U² = 142.86 N
Now, taking summation of forces on the plank. Taking upward direction as positive, for equilibrium position:
[tex]W-U^1-U^2=0\\500\ N - 142.86\ N = U^1\\[/tex]
U¹ = 357.14 N