# Solve Spring Gun Problem: Recoil Speed Calculation

• Raymond Huang
In summary, to calculate the recoil speed of a mechanical gun after firing a bullet using a compressed spring, you can use the conservation of momentum and conservation of energy equations. By isolating the recoil speed of the gun, you can solve for it using the given masses and initial velocity of the bullet.
Raymond Huang

## Homework Statement

A mechanical gun of mass M(g) uses a spring to shoot a bullet of mass M(b). The energy of the compressed spring before firing is E. Assuming the gun is at rest before firing, what is the recoil speed of the gun immediately after it shoots the bullet?

## Homework Equations

Conservation of momentum (M(g)+M(b)vi= M(g)vbf+M(g)vgf
Conservation of Energy

## The Attempt at a Solution

I first tried to isolate vgf(speed of gun after the bullet is fired), which gave me

-Vgf= M(b)vbf/M(g), I don't what to do after this...

Raymond Huang said:

## Homework Statement

A mechanical gun of mass M(g) uses a spring to shoot a bullet of mass M(b). The energy of the compressed spring before firing is E. Assuming the gun is at rest before firing, what is the recoil speed of the gun immediately after it shoots the bullet?

## Homework Equations

Conservation of momentum (M(g)+M(b)vi= M(g)vbf+M(g)vgf
Conservation of Energy

## The Attempt at a Solution

I first tried to isolate vgf(speed of gun after the bullet is fired), which gave me

-Vgf= M(b)vbf/M(g), I don't what to do after this...
On the relevant equations section, you wrote conservation of energy, yet you did not use it.

## 1. What is the formula for calculating recoil speed in a spring gun?

The formula for calculating recoil speed in a spring gun is v = √(2k/m), where v is the recoil speed, k is the spring constant, and m is the mass of the projectile.

## 2. How do you determine the spring constant of a spring gun?

The spring constant of a spring gun can be determined by measuring the displacement of the spring when a known force is applied. The spring constant can then be calculated using the formula k = F/x, where k is the spring constant, F is the applied force, and x is the displacement of the spring.

## 3. What units should be used when calculating recoil speed?

The units used when calculating recoil speed should be consistent with the units used for the spring constant and mass. For example, if the spring constant is measured in newtons per meter (N/m) and the mass is measured in kilograms (kg), then the recoil speed should be calculated in meters per second (m/s).

## 4. Can the recoil speed of a spring gun be increased or decreased?

Yes, the recoil speed of a spring gun can be increased or decreased by adjusting the spring constant or the mass of the projectile. Increasing the spring constant or decreasing the mass will result in a higher recoil speed, while decreasing the spring constant or increasing the mass will result in a lower recoil speed.

## 5. Are there any other factors that can affect the recoil speed of a spring gun?

Yes, there are other factors that can affect the recoil speed of a spring gun, such as air resistance, friction, and the angle at which the gun is fired. These factors may cause the actual recoil speed to differ slightly from the calculated recoil speed.

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