Answer:
∑
F
x
=
T
−
F
x
=
m
a
x
=
0
As stated in the question, it would mean that
T
=
F
x
(so
T
−
F
x
=
0
). Thus, if
F
x
=
10 N
,
T
=
10 N
.
(Additionally, even if
m
is small,
a
x
must therefore be
0 m/s
2
.)
Step-by-step explanation:
While many people would like to simply add the forces from each end to get a total force, this is fundamentally incorrect.
This is an application of Newton's Third Law: "For every action there is an equal and opposite reaction." The only way someone on one end of the string can exert a force of 10 N on the other end of the string is of the other end of the string exerts a 10 N force in the opposite direction.
Suppose I hang a 1 kg mass from a spring scale. This pulls with a force of approximately 10 N. Next, remove the weight and attach the spring scale to a wall. Pull on the scale until it reads 1 kg. That's the same 10 N force that the weight (and gravity) exerted downward when it was hanging. Lastly, consider what would happen if you attached a second spring scale to the wall and the end of the string to that spring scale. When you pull one hard enough to make it read 1 kg, the spring scale on the opposite end will also show 1 kg. They are indicating equal forces in opposite directions.