Question

the pygmy shrew has an average mass of 2.0 g if 49 of these shrew are placed on a spring scale with a spring constant of 24 N/m , what is the springs displacement

Answer 1

Spring's displacement, x = -0.04 meters.

Step-by-step explanation:

Let the spring's displacement be x.

Given the following data;

Mass of each shrew, m = 2.0 g to kilograms = 2/1000 = 0.002 kg

Number of shrews, n = 49

Spring constant, k = 24 N/m

We know that acceleration due to gravity, g is equal to 9.8 m/s².

To find the spring's displacement;

At equilibrium position:

Fnet = Felastic + Fg = 0

But, Felastic = -kx

Total mass, Mt = nm

Fg = -Mt = -nmg

-kx -nmg = 0

Rearranging, we have;

kx = -nmg

Making x the subject of formula, we have;

`x = \frac {-nmg}{k}`

Substituting into the formula, we have;

`x = \frac {-49*0.002*9.8}{24}`

`x = \frac {-0.9604}{24}`

x = -0.04 m

Therefore, the spring's displacement is -0.04 meters.