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A spring of unstretched length l has a mass m with one end fixed to a rigid support .Assuming spring to be made of a uniform wire,find the kinetic energy possessed by it if its free end is pulled with uniform velocity v .

7 years ago
whenever u find such questions replace m of spring by m/3 ..now see how to do it.
k.e=1/2mv^2
the velocity of a point dx at a distance x from the rigid support will be vx/l.
let w=m/l(linear mass density)
so k.e of particle at x distance of dx thickness=1/2* w*dx*(vx/l)^2
int we get
k.e=1/2 *(m/3)*v^2
5 years ago
fucking hate the way indians answer questions.... “replace m of spring by m/3” -like its sorcery
quote: “
whenever u find such questions replace m of spring by m/3 ..now see how to do it.
k.e=1/2mv^2
the velocity of a point dx at a distance x from the rigid support will be vx/l.
let w=m/l(linear mass density)
so k.e of particle at x distance of dx thickness=1/2* w*dx*(vx/l)^2
int we get
k.e=1/2 *(m/3)*v^2”
4 years ago

We can find the effective mass of the spring by finding its kinetic energy. This requires adding all the length elements' kinetic energy, and requires the following integral: Since the spring is uniform, , where is the length of the spring. Hence,  The velocity of each mass element of the spring is directly proportional to its length, i.e. , from which it follows:   hence the answer 3 years ago

We can find the effective mass of the spring by finding its kinetic energy. This requires adding all the length elements' kinetic energy, and requires the following integral: Since the spring is uniform, , where is the length of the spring. Hence,  The velocity of each mass element of the spring is directly proportional to its length, i.e. , from which it follows:   hence the answer 3 years ago
This is a very important concept of mass spring otherwise all the things done in our early classes of 11th is of mass Le spring but this is a very good question there is a very yes or no explanation of IT in mini box as this concept is widely used in olympiads level hope you understand about it