# Force of spring constant

• soul5
In summary, a 1.8kg block with a speed of 2.0m/s hits a spring and compresses it 0.11m before stopping. The coefficient of friction between the block and the surface is 0.560. To find the force constant of the spring, you can use the equations Ek=1/2mv^2 and Ff=uFn, where Fn is equal to the force of gravity on the horizontal surface.

## Homework Statement

A 1.8kg block slides on a rough, horizontal surface. The block hits a spring with a speed of 2.0m/s and compresses it a distance of 0.11m before coming to rest. The coefficent of friction between the block and the surface is 0.560. What is the force constant of the spring?

Ep=1/2kx^2
Ek=1/2mv^2

## The Attempt at a Solution

I used Ek=1/2mv^2 to find Ek and I got 3.6J. I can use Ff=uFn to find force friction, but I don't know what to do? help.

Since you know the mass of the object you would also know the Force of Gravity. Since force of gravity = Normal Force whenever its perfectly horizontal, then you could use that number you got times mew to get your frictional force

First, we need to find the work done by the block on the spring. This can be calculated as the change in kinetic energy of the block:

W = Ek final - Ek initial
W = 0 - 3.6J
W = -3.6J

Next, we can use the work-energy theorem to relate the work done by the block on the spring to the potential energy stored in the spring:

W = Ep final - Ep initial
-3.6J = 1/2kx^2 - 0
1/2kx^2 = -3.6J

Solving for k, we get:

k = 2(-3.6J) / (0.11m)^2
k = 2936.4 N/m

Therefore, the force constant of the spring is 2936.4 N/m.

## 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 is the amount of force required to stretch or compress a spring by a certain distance.

## 2. How is spring constant calculated?

The spring constant is calculated by dividing the force applied to a spring by the displacement of the spring. This can be represented by the equation k = F/x, where k is the spring constant, F is the force applied, and x is the displacement.

## 3. Does the spring constant change for different types of springs?

Yes, the spring constant can vary depending on the type of spring. For example, a stiffer spring will have a higher spring constant than a more flexible spring.

## 4. What are the units of spring constant?

The units of spring constant are typically represented in newtons per meter (N/m) in the metric system, or pounds per inch (lb/in) in the imperial system.

## 5. Can the spring constant be affected by external factors?

Yes, the spring constant can be affected by external factors such as temperature and material properties. Changes in these factors can alter the stiffness and thus the spring constant of a spring.