# Find launch speed given spring constant and compressed distance

• Chica1975
In summary, the spring constant of a potato gun is 41N/m and when compressed a distance of 7.30cm, it can launch a .00321kg piece of potato at a speed of 8.3m/s.
Chica1975

## Homework Statement

A potato gun contains a spring which is compressed a distance of 7.30cm (0.073m) when it is loaded. If the spring's constant is 41N/m, what is the launch speed of a .00321kg piece of potato when the gun is fired? Give the answer in m/s.

## Homework Equations

Power = W/T
V^2=Vi^@+2a(y-y0) (projectile motion)
I have no idea what else I need - am stuck.

## The Attempt at a Solution

I drew what it might look like and tried to work out mg (0.00321*9.8 = .31458) as the height but am really stuck.

the lecturer has given the answer as 8.3m/s

Help!

Equate the energy stored in the spring to the kinetic energy of the potato piece.
You should know a formula for the energy in the spring in terms of the spring constant and the compression.

## 1. How do you calculate the launch speed using the spring constant and compressed distance?

The launch speed can be calculated using the formula: v = √(kx²/m), where v is the launch speed, k is the spring constant, x is the compressed distance, and m is the mass of the object being launched.

## 2. What is the significance of the spring constant in this calculation?

The spring constant is a measure of the stiffness of the spring, and it determines how much force is required to compress the spring a certain distance. It is a crucial factor in calculating the launch speed as it directly affects the amount of potential energy stored in the spring.

## 3. Can this formula be used for any object launched with a spring?

Yes, this formula can be used for any object launched with a spring as long as the mass of the object is known and the compressed distance is measured from the equilibrium position of the spring.

## 4. How accurate is this method for calculating launch speed?

The accuracy of this method depends on the accuracy of the measurements of the spring constant and compressed distance. The more precise these values are, the more accurate the calculated launch speed will be.

## 5. Are there any limitations to this formula?

One limitation of this formula is that it assumes that all of the potential energy stored in the spring is converted into kinetic energy of the launched object. In reality, some energy may be lost due to friction and other factors. Additionally, this formula only applies to objects launched vertically with a spring.

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