Spring Force Formula and Sample Sums

Spring Force Formula :

The spring force F(N/M) in newton per meter is equal to the product of the spring constant k(N/M) in newton  per meter is multiply by the displacement of the spring from its position at equilibrium x  is subtracted by the equilibrium position xo .hence the spring force formula has been written as,
F(N/M) = k(N/M) (x – x0)

Where,
F → spring force (N/M)
xo  → equilibrium position
x → displacement of the spring from its position at equilibrium
k → spring constant (N/M)
The negative sign tells that the visualized spring force is a restoring force and acts in the opposite direction.

Sample Sums :

Sum1 :

Calculate its spring constant? in a spring has length 20 cm/s. If it is loaded with 2 kg, it gets stretched by 10 cm/s.

Solution :

We have,

m = 2

x = 20

xo = 10

Calculate the spring force.

F = ma

= 2 (20 – 10)

= 2 (10)

= 20 N

Using the formula for spring constant we get,

k = – F/(x – xo)

= – 20/(20 – 10)

= – 20/10

= -2 N/m.

Sum2 :

Calculate its spring constant? If a body is stretched by 3m with force 300 N.

Solution:

Known:

(Displacement) x = 2m

(force) F = 100 N

The spring constant is articulated as,

K = – F /x

K = – 300 N/ 3m

K = -100 N/m.

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