Help my noodle- Falling weight and driveshaft problem

[silverfish]

Hi folks,

Am clueless in the area of physical / mechanical engineering, but I need to get an idea of how to calculate the following problem, can someone guide me to the necessary formulas needed to calculate the following problem

Assume there is a weighted cylinder suspended by a drive cable which is wound around a drive shaft. Known factors are the weight of the cylinder, weight and diameter of driveshaft, total weight of drive cable, total length of cable wrapped around the driveshaft and starting distance between the driveshaft and cylinder. Ignoring aerodynamic / friction / Heat Issues, just broadly calculated and starting from a static point, once the cylinder is released to fall thus turning the shaft

How do I calculate

1) How much energy would the drive shaft produce at a given distance of travel by the cylinder ?

2) What would the rotational speed of the driveshaft be at a given distance
of travel by the cylinder ?

3) Am I correct in assuming (though I know what assumption does) that there is an optimal fall distance whereby the cylinder has reached its maximum potential to deliver power to the driveshaft.


Cheers

 

[lippyka]

To answer your questions:1) You would need to calculate the potential energy of the cylinder at its starting point, and then subtract the potential energy of the cylinder at its ending point. The difference between these two values is the amount of energy that the drive shaft produces. 2) You can calculate the rotational speed of the driveshaft by using the equation: Speed = Distance / Time. You can calculate the time it takes for the cylinder to travel a given distance by using the equation: Time = Distance / Speed. 3) It is possible that there is an optimal fall distance, but it depends on the specific parameters of the problem. You would need to do some calculations to determine the optimal fall distance.

 

[m2003]

,

I can provide you with some information and guidance on how to approach this problem. First, we need to understand the basic principles involved in calculating the energy and rotational speed of the drive shaft in this scenario.

The key concept here is conservation of energy, which states that energy cannot be created or destroyed, only transferred from one form to another. In this case, the potential energy of the suspended cylinder will be converted into kinetic energy as it falls, which will then be transferred to the drive shaft.

To calculate the energy produced by the drive shaft at a given distance, we can use the formula for potential energy (PE) and kinetic energy (KE):

PE = mgh (mass x gravity x height)

KE = 1/2mv^2 (1/2 x mass x velocity squared)

We know the mass of the cylinder, the height it falls, and the velocity it reaches at the bottom, so we can calculate the energy produced by the drive shaft using these equations.

To determine the rotational speed of the drive shaft, we can use the formula for angular velocity (ω):

ω = v/r (velocity / radius)

We know the velocity of the cylinder and the radius of the drive shaft, so we can calculate the rotational speed at a given point.

As for the optimal fall distance, it is possible to determine the maximum potential for the cylinder to deliver power to the drive shaft. This would depend on factors such as the weight and length of the drive cable, as well as the starting distance between the drive shaft and cylinder. Calculating this distance would require more information and a more detailed analysis of the system.

I hope this helps guide you in your calculations. Remember to always check your units and assumptions, and feel free to consult with a mechanical engineer for more specific and accurate calculations.