Why is tension in a rope constant despite increasing speed on a rough surface?

[phys_student1]

Hello again,

Sorry for posting two threads in one day. This is a general question.

Suppose we have a box on a rough surface (f_k). The box is being pulled by a

horizontal rope(T₁), and is moving with a constant speed v=0.5 m/s.

Now suppose there's exactly similar situation but with v=1 m/s.

According to the 2^nd law, T₁=T₂

I wonder why isn't T₂ larger since it's causing a speeder motion ??

(In Serway/Jewett book it's stated that coefficient of friction can vary with
but they approximate this and treat it as if it does not vary)

 

[Doc Al]

I wonder why isn't T₂ larger since it's causing a speeder motion ??

That tension didn't create the motion, it just maintains it.

To get the box moving at a greater speed requires some net work to be done. The greater the speed, the more work needs to be done. But once the box is moving the only force you need to maintain that speed is just that needed to overcome friction. It doesn't depend on the speed.

 

[phys_student1]

So, there's a transition period, where the speed is increased from, say, 0.5 m/s to 1 m/s,
then the same rope tension maintains the motion.

Well, I think this is clearer now...

Thanks you !