0

In the book, “MECHANICS I” by BM Sharma (Cengage publications), I found following statement on page 6.9

Tension in a string remains same throughout if it is assumed to be massless and is equal to applied force on string. However if a string has mass, the tension at different points will be different being maximum to the applied force at the end through which force is applied and minimum at other end connected to body.

I really can't understand what this statement wants to convey. Why would the tension be maximum on the direction along which the force is applied and minimum on the other end?

Natru
  • 309
Lalit Tolani
  • 892

1 Answers1

1

Let's suppose your string has $\lambda$ mass per unit length and the total length of the string to be $l$ so that the total mass of the string is $\lambda l$. Let's hang this string on a branch of a tree and ask what's the tension at any point at a distance $x$ from below.

We will concentrate ourselves to a small element of length $dx$. There is an upward tension of $T(x)$ and downward force due to the weight of the lower part that is equal to $\lambda x$, Equating these two equations as the string is at equilibrium, We get

$$T(x)=\lambda xg$$ This is clearly as you can see is maximum at the top (equals to $\lambda l$) and minimum (equals to $0$) at the bottom.

Himanshu
  • 12,211