# Calculating spring constant of a spring loaded cannon

• alphaQ
In summary, the conversation revolves around building a spring-launched cannon that can shoot over a building with specific dimensions. The goal is to determine the spring constant needed for this to work. The attempt at a solution involved finding the velocity and solving for the spring constant, but it was suggested to start by solving for the trajectory and using that to find the launch energy. SUVAT equations were also mentioned as a helpful tool.
alphaQ

## Homework Statement

if you wanted to build a spring launched cannon that will shoot you over a building that is 35 m high and 30 m wide, and the cannon is being shot at 60 degrees. If the cannon can be no more than 2 m long, what spring constant do you need in the spring to make this work? here is what I have been able to do, any feed back would be appreciated.

^2= r/()
PE = KE
½ Fx = ½ mv^2
K = F / x

## The Attempt at a Solution

to find the velocity I used:

v = sqrt((30* 9.8 m/s^2)/sin(60))
v = 18.425 m/s

Theoretically, humans can handle any velocity, it’s acceleration that we cannot handle well. A typical human can handle up to 5Gs of acceleration, that’s 49 ^2.

Since the maximum PE of the spring is the maximum KE of the mass PE = KE ½ Fx = ½ mv^2 Rearranging the formula, we get: = ^2/

F = ma = (70kg) (49m/s2) = 3430 N

KE = ½ mv2 = ½ (70kg) (18.425 m/s2) = 644.875 J

So, x = (644.875 J) / (½ ) (3430 N) x = 0.3760204082 m

We can now use x to solve for the spring constant

K = F / x

K = 3430N / 0.3760204082m + 2m(for the length of the cannon)

K = 1443.590294 N/m

is this K the right spring constant for this question?
[/B]

alphaQ said:
v = sqrt((30* 9.8 m/s^2)/sin(60))
Not so fast: the building has a height and a width. You must clear it completely.
Draw a diagram.

haruspex said:
Not so fast: the building has a height and a width. You must clear it completely.
Draw a diagram.
thats where i have the problem, i don't know how to incorporate the width and height into the equation

alphaQ said:
thats where i have the problem, i don't know how to incorporate the width and height into the equation
You are looking for the minimum energy, so only just clearing the building.
If the launch is at speed v and distance x from the building, what equations can you write for just clearing it?
(Take the launch speed as being at ground level.)

haruspex said:
You are looking for the minimum energy, so only just clearing the building.
If the launch is at speed v and distance x from the building, what equations can you write for just clearing it?
(Take the launch speed as being at ground level.)
i was thinking of getting the spring constant and then checking whether that constant would allow me to get over the height of the building

alphaQ said:
i was thinking of getting the spring constant and then checking whether that constant would allow me to get over the height of the building
To find the spring constant you need the launch energy, and to find that you need to find the minimum speed that will get you over the building. Start with solving the trajectory.

haruspex said:
To find the spring constant you need the launch energy, and to find that you need to find the minimum speed that will get you over the building. Start with solving the trajectory.
can you please give me an equation to get the launch energy?

alphaQ said:
can you please give me an equation to get the launch energy?
As I wrote, you need to start by finding the trajectory.
You did not quote any relevant equations for that. Do you know what I mean by SUVAT equations? If not, look them up.

## What is a spring loaded cannon?

A spring loaded cannon is a type of cannon that uses the force of a compressed spring to shoot a projectile.

## What is the purpose of calculating the spring constant of a spring loaded cannon?

The spring constant of a spring loaded cannon is used to determine the amount of force needed to compress the spring and launch the projectile, as well as the maximum distance the projectile will travel.

## How is the spring constant of a spring loaded cannon calculated?

To calculate the spring constant, you will need to measure the mass of the projectile, the distance the spring is compressed, and the distance the projectile travels. Then, use the formula F = kx, where F is the force applied to the spring, k is the spring constant, and x is the distance the spring is compressed. Rearrange the formula to solve for k.

## What factors can affect the spring constant of a spring loaded cannon?

The spring constant can be affected by the material and thickness of the spring, as well as the amount of compression and the weight of the projectile. Other external factors, such as air resistance and friction, can also affect the spring constant.

## Why is it important to know the spring constant of a spring loaded cannon?

Knowing the spring constant allows you to make accurate predictions about the performance of the cannon, such as the distance the projectile will travel and the amount of force needed to launch it. This information is crucial for safety reasons and for optimizing the design of the cannon.

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