# Calculate Coefficient of Kinetic Friction for Sliding Block - Spring Problem

• cd80187
In summary, the potential energy of the compressed spring is 11.154 J and the kinetic energy of the block is equal to this when it is released. Using the equation for work, the frictional force can be calculated by dividing the change in kinetic energy by the distance. This can then be used to find the coefficient of kinetic friction between the block and the table.
cd80187
You push a 4.6 kg block against a horizontal spring, compressing the spring by 26 cm. Then you release the block, and the spring sends it sliding across a tabletop. It stops 83 cm from where you released it. The spring constant is 330 N/m. What is the coefficient of kinetic friction between the block and the table?

So to start, I have figured out the potential energy of the spring when it is compressed, and it is .5 (330 N/m)(.26 m) squared = 11.154 J But after that, I am not really sure what to do. I tried something with force x distance, but I cannot remember what I did. But I am just unsure where to start on this one. Help would be great

HINT: Think about conservation of energy.

I know, but I'm trying to figure out what is actually there. I know that there is the max kinetic energy when the block hits the spring, but no potential energy (I'm taking the uncompressed spring to be height 0), and when the spring compresses, it is the gravitational potential energy and spring potential energy that are not 0, right?? so in the end, it should be (1/2)(m)(v)squared = 1/2 (k)(x)squared plus (m)x(g)x (y) where y and x are the distance compressed by the spring?

Your almost correct there, but since the spring and table are horizontal the gravitational potential of the block is constant, so now you have;

$$\frac{1}{2}mv^2=\frac{1}{2}kx^2$$

Edit: well it seems latex is down at the moment, so: 1/2mv2=1/2kx2

Do you follow?

Not really. So I have the maximum potential energy when the spring is compressed, which is all converted to kinetic energy when it is moved, right? So then because F x distance = Change in KE, can i simply sum of the forces work (Work of Block + Work of friction opposing it = 0?)

cd80187 said:
Not really. So I have the maximum potential energy when the spring is compressed, which is all converted to kinetic energy when it is moved, right? So then because F x distance = Change in KE, can i simply sum of the forces work (Work of Block + Work of friction opposing it = 0?)
Yes, so you can calculate the frictional force by dividing the change in kinetic energy by the distance.

So I find the force and then divide by force normal and that gives me the answer?

I actually got it, thank you very much for the help

## 1. What is the coefficient of kinetic friction?

The coefficient of kinetic friction is a unitless value that represents the amount of friction between two surfaces when one is in motion. It is denoted by the symbol μ (mu) and is typically a decimal value between 0 and 1.

## 2. How is the coefficient of kinetic friction calculated?

The coefficient of kinetic friction can be calculated by dividing the force of kinetic friction by the normal force between the two surfaces. This can be expressed in the equation μ= Fk/N, where Fk is the force of kinetic friction and N is the normal force.

## 3. What is the significance of the coefficient of kinetic friction in a sliding block - spring problem?

In a sliding block - spring problem, the coefficient of kinetic friction is an important factor in determining the acceleration of the block. It represents the resistance of the surface to the motion of the block and can affect the final position and velocity of the block.

## 4. How does the coefficient of kinetic friction affect the motion of the sliding block in a spring problem?

The coefficient of kinetic friction affects the motion of the sliding block by creating a force that opposes the motion of the block. This force will cause the block to decelerate and eventually come to a stop if the spring force is not strong enough to overcome it.

## 5. What factors can affect the coefficient of kinetic friction in a sliding block - spring problem?

Several factors can affect the coefficient of kinetic friction in a sliding block - spring problem, such as the type of surfaces in contact, the roughness of the surfaces, and the presence of any lubricants. Additionally, the normal force and the applied force can also impact the coefficient of kinetic friction.

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