Question

You need to make a spring scale to measure the mass of objects hung from it. You want each 2.3 cm length along the scale to correspond to a mass difference of 0.10 kg.

What should be the value of the spring constant?

Answer 1

Answer: The value of spring constant is 42.6 N/m

Step-by-step explanation:

Force is defined as the mass multiplied by the acceleration of the object.

`F=m* g`

where,

F = force exerted on the spring

m = mass = 0.10 kg

g = acceleration due to gravity =
`9.8m/s^2`

Putting values in above equation, we get:

`F=0.10kg* 9.8m/s^2\\\\F=0.98N`

To calculate the spring constant, we use the equation:

`F=k* x`

where,

F = force exerted on the spring = 0.98 N

k = spring constant = ?

x = length of the spring = 2.3 cm = 0.023 m (Conversion factor: 1 m = 100 cm)

Putting values in equation 1, we get:

`0.98N=k* 0.023m\\\\k=(0.98N)/(0.023m)=42.6N/m`

Hence, the value of spring constant is 42.6 N/m

Answer 2

42.6 N/m

Step-by-step explanation:

The spring constant can be found by using Hooke's law:

F = kx

where

F is the force applied

k is the spring constant

x is the stretching/compression of the spring

In this problem, the mass applied is

m = 0.10 kg

so the force applied is the weight of the mass:

`F=mg=(0.10 kg)(9.8 m/s^2)=0.98 N`

The stretching of the spring is

x = 2.3 cm = 0.023 m

So the spring constant is

`k=(F)/(x)=(0.98 N)/(0.023 m)=42.6 N/m`