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:

42.6 N/m

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

$k=\frac{F}{x}=\frac{0.98 N}{0.023 m}=42.6 N/m$

Answer 2

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

Explanation:

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

$F=m\times g$

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:

$F=0.10kg\times 9.8m/s^2\\\\F=0.98N$

To calculate the spring constant, we use the equation:

$F=k\times x$

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:

$0.98N=k\times 0.023m\\\\k=\frac{0.98N}{0.023m}=42.6N/m$

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