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davedave
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Can someone tell me how to correct my solution to get the right answerÉ
A 1 kg pigeon sits on the middle of a clothesline whose supports are 10 m apart. The clothesline sags by 1 m. If the weight of the clothesline is negligible, find the tension in it.
Here is my solution.
let T1x, T2x, T1y and T2y be x and y components of tension of the left and right parts of the clothesline respectively when its middle sags by 1 m.
T1x+T2x=0
equivalently, we have -T1*cos u+T2*cosu=0
so, let T1=T2=T
next equation, T1y+T2y+w=0 where w is the weight of the pigeon
rewriting the equation gives
T1*sinu+T2*sinu+w=0
with T1=T2=T, 2T*sinu-mg=0
isolating T and solving gives T=mg/(2*sinu)
= (1 kg)(9.8 m/s squared)/(2*1/sqrt(26))
= 25 N
The answer in the book is 26 N.
How do you get 26 N.
A 1 kg pigeon sits on the middle of a clothesline whose supports are 10 m apart. The clothesline sags by 1 m. If the weight of the clothesline is negligible, find the tension in it.
Here is my solution.
let T1x, T2x, T1y and T2y be x and y components of tension of the left and right parts of the clothesline respectively when its middle sags by 1 m.
T1x+T2x=0
equivalently, we have -T1*cos u+T2*cosu=0
so, let T1=T2=T
next equation, T1y+T2y+w=0 where w is the weight of the pigeon
rewriting the equation gives
T1*sinu+T2*sinu+w=0
with T1=T2=T, 2T*sinu-mg=0
isolating T and solving gives T=mg/(2*sinu)
= (1 kg)(9.8 m/s squared)/(2*1/sqrt(26))
= 25 N
The answer in the book is 26 N.
How do you get 26 N.