Question

When you place a heavy encyclopedia, of mass 8 kg, on a kitchen scale (a spring scale) you notice that before coming to equilibrium, the pointer of the scale oscillates back and forth around the equilibrium position a few times with a period of 0.4 s. What is the effective spring constant of the internal spring of the kitchen scale? (Neglect other masses in the scale.)

Answer 1

The effective spring constant of the internal spring of the kitchen scale is 2000 N/m

Explanation:

Mass of the book = 8 kg

Let the spring constant be k

Then the time period of the spring is given by

$\boxed{T=2\pi\sqrt{\frac{m}{k}}}$

Given Time period of te spring T = 0.4 s

Therefore,

$0.4=2\pi\sqrt{\frac{8}{k}}$

$\implies\frac{8}{k}=(\frac{0.4}{2\pi})^2$

$\implies \frac{8}{k}=(\frac{0.2}{3.14159})^2$

$\implies \frac{8}{k}=0.004$

$\implies k=\frac{8}{0.004}$

$\implies k=2000$ N/m

Hope this answer is helpful.

Know More:

Q: A body of mass M is oscillating harmonically suspended from a massless spring of spring constant K . what is a time period ?

Click Here: https://brainly.in/question/2799989

Q: Time period of a particle in SHM depends on the force constant K and mass m of the particle: $T= 2\pi \sqrt{\frac {m}{k}}$ . A simple pendulum executes SHM approximately. Why then is the time period of a pendulum independent of the mass of the pendulum?

Click Here: https://brainly.in/question/7382076

Q: If a body of mass 10 kg hanging from a spring)oscillate with your time period of a 6.28 seconds and the spring constant is:

Click Here: https://brainly.in/question/3091393