Question

A 7.30 kg sign hangs from two wires. The

first wire is attached to the left end, and
pulls 28.0 N directly left. What is the
x-component of the force of
the second
wire?

Answer 1

`28.0\; {\rm N}` to the right.

Step-by-step explanation:

Since the sign is not moving, the net force on this sign should be
`0\; {\rm N}`. For that, the horizontal component (
`x`-component) of external forces on this sign should be
`0\; {\rm N}`.

Sources of external forces on this sign include tension from the wires, as well as gravitational pull (weight) from the earth. The gravitational pull from the earth is entirely vertical (
`y`-component,) with a magnitude of
`0\; {\rm N}` in the horizontal direction. Thus, the only external forces on this sign in the
`x`-component would be from the two wires.

The question states that the
`x`-component of the force from the first wire is
`28.0\; {\rm N}` to the left. Thus, for the net force in the
`x`-direction to be
`0\; {\rm N}`, the force from the other wire in the
`x\!`-component needs to be
`28.0\; {\rm N}\!` to the right (same magnitude but opposite direction.)