Question

equilibrium practice
draw a freebody diagram with appropriate vectors. show all work

1. hanging sign: a shop sign weighing 200 n hangs vertically from a string attached to the ceiling. if the sign is in static equilibrium, what is the tension in the string?

free body diagram
show work

Explanation:

Step1: Identify forces acting on sign

The sign has its weight $W = 200\ N$ acting downwards and the tension $T$ in the string acting upwards.

Step2: Apply equilibrium condition

In static equilibrium, the net force $\sum F = 0$. In the vertical direction, $\sum F_y=T - W=0$.

Step3: Solve for tension

Since $T - W = 0$, then $T=W$. Substituting $W = 200\ N$, we get $T = 200\ N$.

Answer:

The tension in the string is $200\ N$.

For the free - body diagram: Draw a dot to represent the sign. Draw a downward - pointing arrow labeled $W = 200\ N$ to represent the weight of the sign. Draw an upward - pointing arrow of the same length labeled $T$ to represent the tension in the string.