# Spring Question -- A mass falls onto a spring compressing it....

• smartdude00111
In summary, an object with a mass of 6kg falls 1.8m onto a spring with a spring constant of 2x10^3 N/m. At that instant, the velocity of the object is 4m/s. The compression of the spring is 0.219m. The other possible reference point is the top of the spring, where the gravitational potential is 0 and the only energy present is the kinetic and elastic potential when the spring is fully compressed.
smartdude00111

## Homework Statement

An object with a mass of 6kg falls 1.8m onto a spring with a spring constant of 2x10^3 N/m. At that instant, the velocity of the object is 4m/s. What is the compression of the spring and the max displacements of the spring.
m = 6kg
v = 4m/s
h = 1.8m
k = 2x10^3N/m

## Homework Equations

Gravitational potential = mgh
Elastic potential = (1/2)kx^2
Kinetic energy = (1/2)mv^2[/B]

## The Attempt at a Solution

(1/2)kx^2 = (1/2)mv^2
x = √((mv^2)/k)
x = √(((6)(4)^2)/2x10^3)
x = 0.219
This is my answer to a test question but many other people did it in different ways. Some used the floor as the reference point for y=0 where as I used the top of the spring at equilibrium.

The gravitational PE changes as the mass falls. You cannot ignore it.

Doc Al said:
The gravitational PE changes as the mass falls. You cannot ignore it.
We’re using the law school of conservation of energy. So if the reference point is at the top of the spring, the gravitational potential is 0, so the only energy there is the kinetic which is equal to the elastic potential when the spring is fully compressed

smartdude00111 said:
So if the reference point is at the top of the spring, the gravitational potential is 0, so the only energy there is the kinetic which is equal to the elastic potential when the spring is fully compressed
If the gravitational PE at the top is 0 (a perfectly OK reference point), what will it be when the spring is compressed? It changes.

## 1. What is the relationship between the mass and the compression of the spring?

The compression of a spring is directly proportional to the mass placed on it. This means that the greater the mass, the greater the compression of the spring.

## 2. How does the spring affect the motion of the mass?

The spring provides a restoring force that acts in the opposite direction of the compression. This force causes the mass to move upwards, resulting in a back-and-forth motion until the spring reaches its equilibrium position.

## 3. What factors affect the frequency of the spring-mass system?

The frequency of the spring-mass system is affected by the stiffness of the spring (measured by the spring constant), the mass of the object, and the amplitude of the oscillation (maximum displacement from the equilibrium position).

## 4. Can the spring-mass system experience damping?

Yes, the spring-mass system can experience damping, which is the gradual loss of energy due to external forces such as friction. This results in a decrease in the amplitude of the oscillation over time.

## 5. What is the formula for the potential energy of a compressed spring?

The formula for the potential energy of a compressed spring is PE = 1/2kx2, where k is the spring constant and x is the displacement from the equilibrium position. This formula shows that the potential energy of the spring-mass system increases as the spring is compressed further.

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