Must the tension in a string be uniform?

[jeremy22511]

Homework Statement

Must the tension in a string be uniform? If so, why is that? Thanks!

Homework Equations

The Attempt at a Solution

 

[Tzim]

I believe that when a string has no mass at every point of it the net force is equal to zero from the equation F=ma(when m=0 ,F=0).For example imagine a pulley and a string holding two masses.The force from the first mass to the string is T and from the second T'.the net force on the string is T-T'=ma because m=0 we have T=T'.

 

[Tzim]

i hope i helped

 

[stewartcs]

Homework Statement

Must the tension in a string be uniform? If so, why is that? Thanks!

Homework Equations

The Attempt at a Solution

The tension in a string is typically assumed to be constant due to another assumption...i.e. the string is massless (or negligible). If the string has mass then the tension may not be constant.

CS

 

[jeremy22511]

But is there an explanation for that? Why is the tension in the string constant if it is massless? And how come it is not when the string has mass?
Thanks!~

J.

 

[ideasrule]

Take a section of the rope; suppose the tension pulling it to the left is T1, the tension pulling it to the right is T2, and T1 doesn't equal T2. The section will have an infinite acceleration since it has a mass of 0. This is clearly impossible, so T1 has to equal T2.

 

[stewartcs]

But is there an explanation for that? Why is the tension in the string constant if it is massless? And how come it is not when the string has mass?
Thanks!~

J.

Take an infinitely small element of a massless string. Call its length dx. Since the element's mass is zero there is no gravitational force acting on the element. The two forces acting are T1 (up) and T2 (down). Since the net force must be zero due to the zero mass of the element (F = ma), T1 must equal T2.

Drawing a FBD of the problem we find that:

T1 - T2 = ma

Since it is massless, m = 0 and thus ma = 0

Hence, T1 - T2 = 0 which gives T1 = T2.

CS

 

[jeremy22511]

Thanks everyone!
J.