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Question

The natural length of a spring is 60cm and its spring constant is 4000Nm. A mass of 20kg is hung from it. The extension produced in the spring is (Take g = 9.8m/s2)


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Solution

Step 1: Given

Length of spring(l)=60cm=60×10-2m

Spring constant (k) = 4000Nm

Acceleration due to gravity (g) =9.8m/s2

Mass (m) = 20kg

Step 2: Formula used

The force on string Fk=-kx, where kis the spring constant and x is the elongation in the spring.

Step 3: Find the extension produced in the spring

Weight hung to spring

=mg=20kg×9.8m/s2=196N

The force of string Fk=-kx (negative sign only as per sign convention and not for calculation). On balancing the forces:

Force applied on string = Downward force on the string

kx=mg

4000x=196x=1964000=0.049m=4.9cm

The extension produced in the string is equal to 0.049m or 4.9cm.


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