Tension Forces are just forces that compensate for other forces. For instance, when a ball is hanging motionless on a wire, the net force on the ball must be zero. The gravity of the Earth is pulling it down, therefore there must be another force in the opposite direction compensating for this.
The force exerted by an object such as a wire or string is called a tension.$$\Delta \vec{p} = \vec{F}_{net}\Delta t$$$$0 = (\vec{F}_T - \vec{F}_{ext})\Delta t$$
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