# Does the tension of a rope/cable change if acceleration/velocity changes?

For example, imagine an object of a certain mass which is attached to a rope and is dangling in the air. The rope needs to have a certain tension to be able to hold the object up, that is, negate the effects of gravity pulling it down. I'm wondering, if you took the other end of the rope and started pulling it upwards, would the tension need to be higher to still keep the object from falling? For example if a helicopter is carrying an object attached to a rope under it, would the tension of the rope need to be different for when the helicopter is hovering in the air and when it's flying upwards?

I'm wondering this because it feels like that should be the case, especially when I think about how swinging the rope rapidly in circles might make the object detach and fly off, even if it would've stayed on had the rope not been in motion.

• If the helicopter is accelerating upwards, the tension will increase. If it is flying upwards at a constant speed, then the tension will remain the same as before. – Rations Sep 4 '15 at 1:12

Yes, you are correct in stating that the tension will be higher. In fact, it is simply: $$T=mg+ma$$ It is important however, to make the distinction between tension and the maximum tensile strength. Tension, by definition is only as large as it needs to be (just like the normal force), because it is a reaction force. If it was any larger the body would undergo acceleration.