String got heavy!

Classical Mechanics Level 2

A heavy string of mass m hangs between two fixed points A and B at an angle "a" with the horizontal as shown in figure.The tension at the lowest point in the string is:

mg/[2sec(a)] mg/[2tan(a)] mg/[2cosec(a)] mg/[2cot(a)]

Gautam Sharma by Gautam Sharma , 23, India

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1 solution

Gautam Sharma
Aug 4, 2014

oh! man i forgot to add level to the problem.

1 Helpful 0 Interesting 0 Brilliant 0 Confused

Let the mass of the string be m.

Visualize it like two blocks of mass m/2 attached together by a light in-extensible string and each of them attached to the wall by another strings .(total strings three).

Let the tension in the common string be T and other strings be t(tension will be same in other two strings ).

t s i n ( θ ) = T t sin(\theta)=T

t c o s ( θ ) = m g / 2 t cos(\theta)=mg/2

dividing both eq

we get
t a n ( θ ) = 2 T / ( m g ) tan(\theta)=2T/(mg)

so T= ( m g t a n ( θ ) ) 2 \dfrac{(mgtan(\theta))}{2}

This method cannot be executed if we have to calculate tension at any other point on string with these parameters only.

Gautam Sharma - 6 years, 10 months ago

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but the answer is mg/[2tan(a)] it should be as follows tsin@=mg/2 and tcos@=t

Utkarsh Singh - 3 years, 10 months ago

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