Question

In a supermarket, you place a 22.3-N (around 5 lb) bag of oranges on a scale, and the scale starts to oscillate at 2.7 Hz. What is the force constant (spring constant) of the spring of the scale?

Answer 1

Force constant, k = 653.3 N/m

Step-by-step explanation:

It is given that,

Weight of the bag of oranges on a scale, W = 22.3 N

Let m is the mass of the bag of oranges,

`m=(W)/(g)`

`m=(22.3)/(9.8)`

m = 2.27 kg

Frequency of the oscillation of the scale, f = 2.7 Hz

We need to find the force constant (spring constant) of the spring of the scale. We know that the formula of the frequency of oscillation of the spring is given by :

`f=(1)/(2\pi)\sqrt{(k)/(m)}`

`k=4\pi^2 f^2m`

`k=4\pi^2 * (2.7)^2* 2.27`

k = 653.3 N/m

So, the force constant of the spring of the scale is 653.3 N/m. Hence, this is the required solution.