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 please 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

 

[russ_watters]

Well, work equals force times distance, power equals force times distance times time, torque is force times length of the lever arm, acceleration is force divided by mass, and circumference is pi times diameter.

Resistance to roational acceleration is called moment of inertia, though how big of a deal that is depends a lot on the load of whatever this driveshaft is connected to. Can you provide more info about the application?

 

[ravenprp]

Hi there,

First of all, I am not a mechanical engineer, so my response may not be completely accurate. However, here are some general steps you can take to calculate the energy and rotational speed of the drive shaft in this scenario:

1) Calculate the potential energy of the cylinder at the starting distance using the formula PE = mgh, where m is the mass of the cylinder, g is the acceleration due to gravity, and h is the starting distance between the drive shaft and cylinder.

2) As the cylinder falls and turns the drive shaft, it will lose some of its potential energy and gain kinetic energy. The kinetic energy can be calculated using the formula KE = 1/2mv^2, where m is the mass of the cylinder and v is its velocity.

3) The energy produced by the drive shaft can be calculated using the formula E = Fd, where F is the force exerted by the drive shaft and d is the distance traveled by the cylinder.

4) To calculate the rotational speed of the drive shaft, you will need to know the diameter of the drive shaft and the circumference of the cylinder. You can then use the formula v = ωr, where v is the linear velocity of the cylinder, ω is the angular velocity of the drive shaft, and r is the radius of the drive shaft.

5) As for the optimal fall distance, I am not sure if there is a specific formula for that. It may depend on the specific design and materials used in the setup. However, as a general rule, the cylinder will continue to lose potential energy and gain kinetic energy until it reaches the ground or the drive shaft stops turning due to friction or other factors.

I hope this helps guide you in the right direction. It's always best to consult with a mechanical engineer or someone with expertise in this area for more accurate calculations and solutions. Good luck!