Question

A 11-cm-long spring is attached to the ceiling. When a 2.4kg mass is hung from it, the spring stretches to a length of 18cm .

Part A What is the spring constant k?
Part B How long is the spring when a 3.0 kg mass is suspended from it?

Answer 1

Part A : 336 N/m

Part B: 19.75 cm

Step-by-step explanation:

Part A: Using hooks law,

F = ke................... Equation 1

Where F = Force applied to the spring, k = spring constant, e = extension.

Note: From the question, the force applied to the spring is the weight of the mass hung on it.

Hence,

F = mg............... Equation 2

Substitute equation 2 into equation 1.

mg = ke

make k the subject of the equation

k = mg/e.............. Equation 3

Given: m = 2.4 kg, e = 18-11 = 7 cm = 0.07 m

Constant: g = 9.8 m/s²

Substitute these value into equation 3

k = 2.4(9.8)/(0.07)

k = 336 N/m.

Part B,

Similarly,

mg = ke.

make e the subject of the equation

e = mg/k................ Equation 4

Given: m = 3.0 kg, k = 336 N/m, g = 9.8 m/s²

Substitute into equation 4

e = 3.0(9.8)/336

e = 0.0875 m

e = 8.75 cm

Length of the spring = original length+ extension

Length of the spring = 11+8.75

Length of the spring = 19.75 cm.