# Spring Constant Question Help

• dmolson
In summary, the problem asks for the calculation of the spring constant when given a spring hung from the ceiling, a 0.497 kg block attached to the free end of the spring, and the block dropping 0.12 m before momentarily coming to rest. The other force acting on the block is gravity (mg), and in order for the block to be in equilibrium, the relation between these two forces is F = kx - mg. However, if the block is at rest, the net force must equal zero, so kx = mg. The next part of the problem is to calculate the angular frequency, but the solution has not been found yet.

#### dmolson

I have a problem I cannot figure out. It asks to calculate the spring constant when given a spring hung from the ceiling, a 0.497 kg block attached to the free end of the spring. The block is released from rest, drops 0.12 m before coming momentarily to rest. How do I calculate the spring constant?? Please Help!

What does the force in a spring equal?

F = -kx I thought

Right. That's one of the forces acting on the block. Which is the other one? What is the relation between these two forces in order for the block to be in equilibrium?

Right. That's one of the forces acting on the block. Which is the other one? What is the relation between these two forces in order for the block to be in equilibrium?

The other one would be gravity (mg) acting on the block. I thought the relation was F = kx - mg. But I do not know for sure.

dmolson said:
The other one would be gravity (mg) acting on the block. I thought the relation was F = kx - mg. But I do not know for sure.

If there was a non-zero net force F, as you stated, the block wouldn't be at rest. The problem states that the block came to rest, after the spring extended for some amount x. So, if the block is at rest, the net force must equal zero. Hence, kx = mg.

I tried that solution and it did not work. Here is the original problem.

A spring is hung from the ceiling. A 0.497-kg block is then attached to the free end of the spring. When released from rest, the block drops 0.12 m before momentarily coming to rest. What is the spring constant?

Interesting, it should work, unless I'm missing something enormous here. Do you know the solution?

No, it is part of the e-homework I have. The next part says to calculate the angular frequency. I only have limited tries and I have tried the second part.

*have not tried

## 1. What is a spring constant?

The spring constant, also known as the force constant or stiffness, is a measure of how difficult it is to stretch or compress a spring. It is represented by the letter k and is measured in units of newtons per meter (N/m).

## 2. How is spring constant calculated?

The spring constant is calculated by dividing the force applied to the spring by the resulting displacement. This can be expressed with the equation 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 the material and shape of the spring, as well as its dimensions and the number of coils. The type and amount of load applied to the spring can also affect its spring constant.

## 4. How does the spring constant relate to Hooke's Law?

Hooke's Law states that the force exerted by a spring is directly proportional to the displacement of the spring from its equilibrium position. The spring constant is the proportionality constant in this equation, and it determines how much force is needed to stretch or compress the spring by a certain amount.

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

The spring constant is used in various fields such as engineering, physics, and biology. It is used to design and analyze structures that use springs, such as car suspensions, mattresses, and door hinges. It is also used in experiments and studies involving the behavior of materials under stress and strain.