Question

In case 1, one end of a horizontal plank of mass M and length L is attached to a wall by a hinge and the other end is held up by a wire attached to the wall. In case 2 the plank is half the length but has the same mass as in case 1, and the wire makes the same angle with the plank. 1) In which case is the tension in the wire biggest?

Answer 1

Answer:

Same.

Explanation:

I made a diagram with the description that is given. So things to be able to perform. In this diagram I consider the recessed bar.

For the solution to this problem it is necessary to take into account the concepts of static force and torque.

For case 1,

We perform sum of moments in the embedded end,

$\sum T = 0$

$F(L)(sin\theta) -mg (\frac{L}{2})=0$

clearing F,

$F=\frac{mg}{2sin\theta}$

For case 2,

We perform sum of moments in the embedded end

$F(\frac{L}{2})sin\theta - mg \frac{L/2}{2}=0$

$F\frac{L}{2}sin\theta = mg \frac{L}{4}$

$F = \frac{mg}{2sin\theta}$

We can verify that the tension for both cases is same.