How Does Pulley Radius Affect Car Movement in a Mechanical Engineering Project?

In summary, the conversation discusses an engineering project involving creating a car that can move forward and launch a projectile using springs and weight displacement. The goal is to estimate the distance the car will travel in 1 minute based on the radii of the pulleys used in the design. The variables involved include torque, force, mass, and acceleration. The person is seeking help with setting up equations and balancing them. A helpful resource is provided for reference.
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ennova
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First, this isn't really a "homework" problem, it is more to help me with my design for an engineering project for ME1000. I'm am trying to model how my "car" will move with my current design. The aim being to power and move a car forward and then launch a projectile using a set weight and allowing the weight to be displaced 2 meters, a torsion spring, an extension spring and a compression spring. We've decided to use the compression spring to fire the projectile and we will try and use the other springs and the displacement of the weight by 2 meters to power the drive train of the car. I'm trying to set up equations to get an estimate of the distance that the car will travel in 1 minute as a function of the radii of the pulleys I'll be using for my design.

Homework Statement


we "know" everything but we need to solve for "how far" the car will go. I say we "know" everything because I have a finite set of pulleys that I can choose from and once I know how to find the distance as a function of these pulleys (ie with their radii and mass), I can plot them in excel and find the design that I want etc. So I guess the variables would be the radii.


Homework Equations


sum(torque) = I*alpha
sum(force) = m*a
torque = -k*theta (for a torsion spring)
force = -k*x (for the extension spring)
W = m*g
a = alpha*r
I = (1/2)MR^2
d = vi*t + (1/2)*a*t^2


The Attempt at a Solution


I'm a bit lost on how to set this up. If anyone has any ideas/comments as a better way to approach this problem let me know. I guess I don't understand how to set up the (torque)force-diagrams for each pulley when I'm trying to balance the equations. Thanks for any help.

http://img228.imageshack.us/img228/4083/img021nc.th.jpg

[PLAIN]http://img839.imageshack.us/img839/2415/examplea.jpg
 
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FAQ: How Does Pulley Radius Affect Car Movement in a Mechanical Engineering Project?

1. How does the number of pulleys affect the mechanical advantage of a pulley system?

The mechanical advantage of a pulley system is directly proportional to the number of pulleys used. As the number of pulleys increases, the mechanical advantage also increases. This means that less force is required to lift a load, making the system more efficient.

2. What is the relationship between the weight of the load and the force needed to lift it in a pulley system?

In a pulley system, the force needed to lift a load is equal to the weight of the load. This is due to the conservation of energy - the work done on the load by the input force is equal to the work done by the load as it is lifted. Therefore, the force needed to lift the load is directly proportional to its weight.

3. How can friction affect the efficiency of a pulley system?

Friction can greatly reduce the efficiency of a pulley system. The more pulleys and ropes involved, the higher the chances of friction occurring. To maximize the efficiency of a pulley system, it is important to use smooth and well-lubricated pulleys and minimize the number of ropes used.

4. What is the difference between fixed and movable pulleys in terms of mechanical advantage?

A fixed pulley has a mechanical advantage of 1, meaning it does not provide any mechanical advantage. On the other hand, a movable pulley has a mechanical advantage of 2, as it reduces the force needed to lift a load by half. This is because the weight of the load is distributed between the input force and the movable pulley.

5. How can I calculate the mechanical advantage of a pulley system?

The mechanical advantage of a pulley system can be calculated by dividing the output force (force needed to lift the load) by the input force (force applied to the rope). For example, if a load of 100 pounds is lifted with an input force of 25 pounds, the mechanical advantage would be 4 (100/25 = 4).

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