# Homework Help: Absurdly easy tension problem

1. Dec 15, 2003

### StephenPrivitera

The book and I aren't getting along tonight. Maybe you can help.
A rope of length L has a tension T. Someone pushes on the rope with a force F at its midpoint and deflects the rope by a distance d. What is T is terms of L,d and F.
This is so simple I won't even explain my work.
2Tsin&theta;=F
sin&theta;=d/(L/2)=2d/L (approx)
so
$$T=\frac{FL}{4d}$$
Right?
The prob. in the book had numbers, but in the end I was off by a factor of 2.

2. Dec 16, 2003

### ShawnD

Ok well this is what I'm getting. instead of using some greek letter for the angle, i'll use H.

forces balancing:
F = 2Tsin(H)
T = F/2sin(H)

length of rope used by the angle is L/2.
since L is the hypotinuse, sin(H) = d/(L/2)
sin(H) = 2d/L

sub that into the first equation:
T = F/2(2d/L)
T = F/(4d/L)
T = FL/4d

I get the same thing.

3. Dec 16, 2003

### himanshu121

I too got the same value i.e. t=FL/4d

4. Dec 16, 2003

### StephenPrivitera

BOOK's WRONG AHAHAHAHA!

5. Dec 16, 2003

### Staff: Mentor

What book are you using? Seems like it has quite a few mistakes.

6. Dec 16, 2003

### StephenPrivitera

I know. I've found at least four in the last two chapters, and I've verified these with my professor, so it's not just stupid Stephen being less smart than the author. The book is PHYSICS by Ohanian 2ed.