equilibrium practice\ndraw a freebody diagram with appropriate vectors. show all work\n1. hanging sign: a…
equilibrium practice\ndraw a freebody diagram with appropriate vectors. show all work\n1. 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?\nfree body diagram\nshow work
Answer
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.