# What is the spring constant for this spring?

• jannx3
In summary, a 50.0 g mass is hung from a spring, elongated to a total length of 40 cm. When an additional 20g mass is added, the new reading is 45cm. Using the equation k=mg/x, the spring constant is calculated to be 3.92 N/m. Adding another mass of 30g causes the spring to stretch an additional 7.5cm.
jannx3

## Homework Statement

A mass of 50.0 g mass is hung from a spring, spring is elongated to 40 cm, an additional mass of 20g is added, with a new reading of 45cm

a) what is the spring constant for this spring?
b) another mass of 30g is added to the spring, what is the new reading?

k= mg/x

## The Attempt at a Solution

not sure if this is the right approach
a)
k= change in mass x g / change in height
0.020x9.8/0.05 =3.92n/m
b)mg=kx
0.03x9.8=3.92x
x=0.075 so it extend another 7.5cm?

jannx3 said:
not sure if this is the right approach
a)
k= change in mass x g / change in height
0.020x9.8/0.05 =3.92n/m
b)mg=kx
0.03x9.8=3.92x
x=0.075 so it extend another 7.5cm?
Use a capital "N" for Newtons.

1 person
The numbers in your solution don't seem to match the numbers in the problem statement.

Chet

why not just set up a N2L equation for this? If the spring stretches an amount x with a mass m attached to it and comes to rest again, then that means that net force is zero, and mg = kx, you only need 1 weight and 1 distance.

Chestermiller said:
The numbers in your solution don't seem to match the numbers in the problem statement.
They look fine to me.

jannx3 said:
A mass of 50.0 g mass is hung from a spring, spring is elongated to 40 cm,
I interpret the 40 cm as the total length of the spring, including its unstretched length.

Ahhh, I see what you're saying, so you do actually need two masses. Good call Doc.
elongated to 40 cm

Last edited:

## 1. What is the definition of spring constant?

The spring constant, also known as the force constant, is a measure of the stiffness of a spring. It represents the amount of force required to stretch or compress a spring by a certain distance.

## 2. How is spring constant calculated?

The spring constant can be calculated by dividing the force applied to the spring by the resulting displacement. This can be expressed as k = F/x, where k is the spring constant, F is the applied force, and x is the displacement.

## 3. What factors affect the spring constant?

The spring constant is affected by several factors, including the material and diameter of the spring, the number of coils, and the length and cross-sectional area of the spring. It is also affected by the temperature and the amount of stress placed on the spring.

## 4. How does spring constant affect the behavior of a spring?

The spring constant determines how much force is required to stretch or compress a spring. A higher spring constant means that the spring is stiffer and requires more force to change its length, while a lower spring constant means that the spring is more flexible and requires less force to change its length.

## 5. How is spring constant used in real-world applications?

The spring constant is an important factor in many real-world applications, such as in mechanical engineering, where it is used to design and control the movement of springs in various devices. It is also used in physics experiments to study the properties of springs and their relationship with force and displacement.

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