A coil spring stretches by 2.50 cm when a mass of 750 g is suspended from it. (a) Find the force constant of the spring. (b) How much will the spring stretch if 800 g is suspended from it

(a) 294 N/m

(b) 0.027 m or 2.7 cm

Explanation:

(a) From Hook's law,

F = ke Equation 1.

make k the subject of the equation

k = F/e Equation 2

Where F = force applied on the spring, k = spring constant, e = extension.

From the question, the force applied to the spring is the weight of the mass.

F = mg = 0.75(9.8) = 7.35 N

Also, e = 2.5 cm = 0.025 m

Substitute these values into equation 2

k = 7.35/0.025

k = 294 N/m.

(b) If a mass of 800 g is suspended,

F = ke

e = F/k Equation 3

F = mg = 0.8(9.8) = 7.84 N,

k = 294 N/m.

Substitute these values into equation 3

e = 7.84/294

e = 0.027 m

e = 2.7 cm

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