Solving Spring Calculation Homework: Weight, Distance & Shear Stress

[paramathma]

Homework Statement

From a toy gun, a bullet of 1N is fired. The bullet travels a distance of 10m. the compression of the spring, when the gun is loaded, is 100 mm and the bore of the barrel is 20mm. design a suitable spring, taking a spring index as 5.5 and design a shear stress for spring material equals to 600N/mm square.

Homework Equations

Spring shear stress

The Attempt at a Solution

i am stuck up with the weight and the distance traveled by the bullet. i am stuck up with this staring trouble.please guide me.

 

[KataKoniK]

Hello,

Thank you for your post. I am a scientist and I would be happy to help you with your problem.

In order to design a suitable spring for this toy gun, we need to consider the force required to compress the spring and the distance it needs to travel.

First, let's calculate the amount of force needed to compress the spring by 100 mm. We can use Hooke's law, which states that the force required to compress or stretch a spring is directly proportional to the distance it is compressed or stretched. This can be represented by the equation F = kx, where F is the force, k is the spring constant, and x is the distance.

In this case, we know that the spring is compressed by 100 mm (0.1 m) and the force needed is 1 N. Using the equation F = kx, we can rearrange it to solve for the spring constant (k). So, k = F/x = 1/0.1 = 10 N/m.

Next, we need to consider the distance the bullet needs to travel. We know that the bullet travels 10 m and the bore of the barrel is 20 mm (0.02 m). This means that the spring needs to be compressed by 10 m - 0.02 m = 9.98 m.

Now, let's consider the spring index of 5.5. The spring index is the ratio of mean coil diameter to wire diameter. In this case, we know that the bore of the barrel is 20 mm, so the mean coil diameter would be 20 mm + 2 times the wire diameter. We can rearrange this to solve for the wire diameter (d). So, d = (mean coil diameter - 20 mm)/2 = (20 mm x 5.5 - 20 mm)/2 = 110 mm/2 = 55 mm.

Lastly, we need to calculate the shear stress for the spring material. We know that the shear stress is 600 N/mm^2 and the force required to compress the spring is 1 N. Using the equation for shear stress, we can solve for the required cross-sectional area (A) of the wire. So, A = F/shear stress = 1 N/600 N/mm^2 = 0.0017 mm^2.

In conclusion, to design a suitable spring for this toy

 

[Mene]

it is important to approach problems in a systematic and logical manner. In this case, the first step would be to identify the relevant equations and variables involved in solving this problem. From the given information, we know that the weight of the bullet is 1N and it travels a distance of 10m. We also know the compression of the spring (100mm) and the bore of the barrel (20mm).

The relevant equation for this problem would be Hooke's Law, which states that the force exerted by a spring is directly proportional to the distance it is stretched or compressed. In this case, we can use Hooke's Law to determine the spring constant, which is a measure of the stiffness of the spring. The equation for spring constant is k = F/x, where F is the force applied and x is the distance the spring is compressed or stretched.

To design a suitable spring, we also need to consider the spring index and the desired shear stress. The spring index is a measure of the ratio between the mean diameter of the spring and the wire diameter. In this problem, the spring index is given as 5.5, meaning that the mean diameter is 5.5 times the wire diameter.

To design a suitable spring that can withstand the desired shear stress of 600N/mm square, we can use the equation for shear stress, which is τ = (8Fπd)/(πD^3), where F is the force applied, d is the wire diameter, and D is the mean diameter. Solving for the wire diameter, we get d = (8F)/(πτD^3).

Using the values given in the problem, we can plug them into the equation and solve for the wire diameter. Once we have the wire diameter, we can use the spring index to determine the mean diameter of the spring. Finally, we can use Hooke's Law to calculate the spring constant and design a suitable spring that can withstand the force of 1N and the distance of 10m traveled by the bullet.

In conclusion, it is important to approach this problem systematically by identifying the relevant equations and variables, and using them to solve for the desired parameters. By following this approach, we can design a suitable spring that meets the given requirements.