Question

hey friends

plz, solve this question...

Answer 1

Assuming the string to have a uniform mass distribution and the external force to act along the length of a string, following procedure can be adopted.......

Due to applied force, the rope will accelerate over the smooth horizontal surface at the rate of given by
a=F/M

If we further assume that the rope is almost inextensible or non-deformable, it is obvious that acceleration of each small constituiting parts of the rope would be same and equal to a=F/M

Lets think by dividing the rope into two sections 1 and 2 as depicted in the picture above.Let T be the tension at the junction.We have now to analyse the dynamics of one of the two sections Consider the section 2

Mass of section 2 is
m2=(M/L)*(L-l)

Applying newton 's second law of motion on section 2,

T=m2a
or,T=(M/L)*(L-l)*(F/M)
or,T=(F/L)*(L-l)

In this way, we get tension as a function of l.

Also on putting y= 0 in above expression, we get tension at right equal angle to F and similarly on putting y=L, we get tension at left and equal to zero which are quite obvious results.


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