A small sphere is given vertical velocity of magnitude hvnot=5m/s and it swings in vertical plane about end of massless string if max tension string can withstand is equal to twice the weight of sphere then angle theta with vertical at which string will break
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mass= m
length= l
weight= mg
max tension in string = T= 2W= 2mg
By the equation of motion:
T= mgcos 0
T= mgsin 0= mv²/l
from the above equations we get
tan0= mv²/l divide 2mg
= v²/ 2lg
0= tan⁻¹(v²/ 2lg)
= tan⁻¹(1.275/l)
this angle is on vertical at which tension is max
the string will break when the angle with the vertical is greater than 0
length= l
weight= mg
max tension in string = T= 2W= 2mg
By the equation of motion:
T= mgcos 0
T= mgsin 0= mv²/l
from the above equations we get
tan0= mv²/l divide 2mg
= v²/ 2lg
0= tan⁻¹(v²/ 2lg)
= tan⁻¹(1.275/l)
this angle is on vertical at which tension is max
the string will break when the angle with the vertical is greater than 0
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