Question

A uniform horizontal strut weighs 400.0 N. One end of the strut is attached to a hinged support at the wall, and the other end of the strut is attached to a sign that weighs 200.0 N. The strut is also supported by a cable attached between the end of the strut and the wall. Assuming that the entire weight of the sign is attached at the very end of the strut, find the tension in the cable and the force at the hinge of the strut.

Answer 1

Answer:

Explanation:

Given

Weight of strut $W_1=400 N$

Weight of sign Board $W_2=200 N$

In this question angle which cable makes with horizontal is not given so

assuming $\theta =30^{\circ}$

From Diagram

Moment about hinge point

$T\sin 30\times L=W_1\times \frac{L}{2}+W_2\times L$

$T\sin 30=\frac{W_1}{2}+W_2$

$T\sin 30=\frac{400}{2}+200$

$T=800 N$

$\sum F$ in x direction is zero

$F_x=T\cos 30$

$F_x=800\cos 30=346.41 N$

$\sum F$ in Y direction is zero therefore

$F_y+T\sin 30=W_1+W_2$

$F_y=400+200-800\cdot \sin 30$

$F_y=200 N$

$F_{net}\ at\ hinge=\sqrt{F_x^2+F_y^2}$

$F_{net}=399.99\approx 400 N$