# Finding the speed of the block for one and two springs

• miyayeah
In summary: When potential energy is doubled, k ⋅ Δx2 = mv2, so v= √[(k ⋅ Δx2)/m]This is the same velocity as when there is only one spring. So would the speed for both situation be the same?Yes, the speed would be the same.
miyayeah

## Homework Statement

The spring in the figure (Figure 1) is compressed by length Δx. It launches the block across a frictionless surface with speed v0. The two springs in the figure (Figure 2) are identical to the spring of figure 1. They are compressed by the same length Δx and used to launch the same block. What is the block's speed now (for figure 2)?

Figure 1:

Figure 2:

## Homework Equations

Ui = Kf
Esp = ½ k ⋅ Δx2
Esp = K = ½ mv2
(as it launches off)

## The Attempt at a Solution

I am not sure how having double the spring would affect the block's speed. I assumed it would increase (double) the spring potential energy because two of the same spring from Figure 1 are present for the situation in Figure 2. Would the speed for Figure 2, then, be simply 2V0?

v/v0 is also in front of the answer box, and I am not sure why.

Any help would be much appreciated!

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Is the potential energy doubled?
Is the kinetic energy doubled?
If the answer to both questions above is "yes", is the speed doubled?

Write a few equations down.

Hello
miyayeah said:

## The Attempt at a Solution

I am not sure how having double the spring would affect the block's speed. I assumed it would increase (double) the spring potential energy because two of the same spring from Figure 1 are present for the situation in Figure 2.
Yes, that's right.

Would the speed for Figure 2, then, be simply 2V0?
Why would that be? Hint: Think about how the final kinetic energies of the two cases compare.

v/v0 is also in front of the answer box, and I am not sure why.
Maybe they are asking you to give the ratio of the velocity with two springs to the velocity with one spring. So, the answer will just be a number with no units.

kuruman said:
Is the potential energy doubled?
Is the kinetic energy doubled?
If the answer to both questions above is "yes", is the speed doubled?

Write a few equations down.
TSny said:
Hello
Yes, that's right.

Why would that be? Hint: Think about how the final kinetic energies of the two cases compare.

Maybe they are asking you to give the ratio of the velocity with two springs to the velocity with one spring. So, the answer will just be a number with no units.

½ k ⋅ Δx2 = ½ mv2

When potential energy is doubled, k ⋅ Δx2 = mv2, so
v= √[(k ⋅ Δx2)/m]

This is the same velocity as when there is only one spring. So would the speed for both situation be the same?

U1=K1
U2=K2
You have U2=2U1 because you have two springs compressed by the same amount Δx. OK so far.
Now an expression for K1 is ½mv12. What do you think should be an analogous expression for K2?

kuruman said:
U1=K1
U2=K2
You have U2=2U1 because you have two springs compressed by the same amount Δx. OK so far.
Now an expression for K1 is ½mv12. What do you think should be an analogous expression for K2?

That helped a lot, I realized I have to use some kind of formula for that relationship between the two situations. I was able to get the answer to the question.
Thank you!

## What is the purpose of finding the speed of the block for one and two springs?

The purpose of finding the speed of the block for one and two springs is to understand the motion of the block in a spring system. This information can also help in determining the energy and forces involved in the system.

## How is the speed of the block calculated for one spring?

The speed of the block for one spring can be calculated using the equation v = √(2kx/m), where v is the speed, k is the spring constant, x is the displacement of the block from its equilibrium position, and m is the mass of the block.

## What is the formula for finding the speed of the block for two springs?

The formula for finding the speed of the block for two springs is v = √(k/m) * √(2 * (k/m + k/M) * x), where v is the speed, k is the spring constant, m is the mass of the block, and M is the mass of the second spring.

## How does the speed of the block change when the number of springs is increased?

When the number of springs is increased, the speed of the block will also increase. This is because more springs will provide a greater force on the block, resulting in a higher velocity.

## What are some factors that can affect the speed of the block in a spring system?

The speed of the block in a spring system can be affected by factors such as the mass of the block, the spring constant, the displacement of the block, and the number of springs in the system. Other external factors such as friction and air resistance can also play a role in determining the speed of the block.

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