Physics of mouse-trap driven car?

[mastermind3001]

For our physics project (senior in high school), we have to build cars driven by nothing other than mouse traps, and they have to propel the cars at least 10 meters. Of course, me being me, I want to make my car go as far as possible. I would like to know exactly what equations I'm going to need to build a car of certain specifications and predict how far it's going to go. I'm thinking that torque, force, and work are going to be part of it, but I don't know everything. Any ideas what else I'm going to need to take a complete design-first attempt at this car? Any ideas on how to maximize the distance the car will travel?

 

[Andrew Mason]

For our physics project (senior in high school), we have to build cars driven by nothing other than mouse traps, and they have to propel the cars at least 10 meters. Of course, me being me, I want to make my car go as far as possible. I would like to know exactly what equations I'm going to need to build a car of certain specifications and predict how far it's going to go. I'm thinking that torque, force, and work are going to be part of it, but I don't know everything. Any ideas what else I'm going to need to take a complete design-first attempt at this car? Any ideas on how to maximize the distance the car will travel?

You have to figure out a way of using the stored spring energy in the mouse trap to turn the wheels. One obvious way would be to tie a string onto the trap and wrap it around the wheel axle. As the trap opens, it pulls on the string and the wheels spin.

You then have to make it as efficient as possible by reducing friction loss, so you want to make it reasonably light. But you may not want to make it too light because you will need friction for traction. You may want to add weight to it to slow its acceleration down in order to avoid spinning the wheels at the beginning. The added weight will reduce its ultimate speed but may allow it to continue moving farther after the spring energy has been exhausted. Good luck. It sounds like fun.

AM

 

[Wudan]

I'm thinking a flywheel with a large reduction ratio would help maintain the available energy from the mousetrap spring Without inducing massive wheelspin.

Might kill your top speed but should go for awhile.

 

[Andrew Mason]

I'm thinking a flywheel with a large reduction ratio would help maintain the available energy from the mousetrap spring Without inducing massive wheelspin.

Might kill your top speed but should go for awhile.

I like the flywheel idea. It just needs to be relatively heavy. What you want to do is regulate (slow down) the closing speed of the trap. One way to do this simply, without gears, would be to tie the string to an extended arm, the other end of which is attached to the trap. This effectively reduces the force of the trap on the string by using the mechanical disadvantage of a long lever.

AM

 

[mastermind3001]

I am looking for some kind of equations I can use to figure some of this stuff out, because I plan to use an extended arm, or if not an extended arm then gear ratios will accomplish a similar effect. I plan to use some of my Lego Technic sets for part of the contraption to help control the weight, but my teacher told me that the part where the trap is has to be sturdy because the trap can easily bend it if it isn't sturdy enough. I also like the idea of legos because some cars I looked at that people have done in previous years didn't have very straight wheels and veered off, while legos are made very precise and will help me in that respect. My wheels are going to be cds.

 

[Andrew Mason]

I am looking for some kind of equations I can use to figure some of this stuff out, because I plan to use an extended arm, or if not an extended arm then gear ratios will accomplish a similar effect. I plan to use some of my Lego Technic sets for part of the contraption to help control the weight, but my teacher told me that the part where the trap is has to be sturdy because the trap can easily bend it if it isn't sturdy enough. I also like the idea of legos because some cars I looked at that people have done in previous years didn't have very straight wheels and veered off, while legos are made very precise and will help me in that respect. My wheels are going to be cds.

If you are going to use CD's you may wish to put several together. The extra weight and surface area will give you more traction force.

The formula for a lever is:

$$Force_{trap} \times d_{trap} = Force_{earm} \times d_{earm}$$ where the subscripts 'trap' and 'earm' refer to end of the trap arm and extended arm (eg. the distances from the trap pivot to the end of the trap and extended arm).

Once you measure the torque (force x distance) of the trap arm itself you can then work out the torques at the end of the extended arm, on the axle, and, ultimately, the force between the road and the wheels.

In order to make it go as far as possible, you must make sure that that force does not exceed the static friction force ie. $F_{traction} < \mu_sN$ where N is the normal force and $\mu_s$ is the coefficient of static friction. Otherwise you will lose energy due to slippage. In other words, to achieve greatest distance, you want a low rate of acceleration.

AM

 

[mastermind3001]

I like the idea of several cds. Thanks. I also plan to cut them in some way so the middle is empty air, which will concentrate the mass at the outside of the wheel and give it a greater moment of inertia. But I have some questions.

How do I measure the force of the lever arm? For $$F=ma$$, do I need to measure the time it takes for the arm to go from release until stop? Because that's going to be a tough one. As for the mass, do I use the mass of the whole arm?

And thanks for the formula. I think it's going to help me quite a bit.

 

[Andrew Mason]

I like the idea of several cds. Thanks. I also plan to cut them in some way so the middle is empty air, which will concentrate the mass at the outside of the wheel and give it a greater moment of inertia.

That will reduce the moment of inertia. The mass at centre doesn't contribute as much to the moment of inertia as the mass farther out, but it still contributes. If you took that mass near the centre and moved it farther out, you would increase I but not if you just remove it.

How do I measure the force of the lever arm? For $$F=ma$$, do I need to measure the time it takes for the arm to go from release until stop? Because that's going to be a tough one. As for the mass, do I use the mass of the whole arm?

You want to find the 'k' of the mousetrap spring as in $\tau = k\theta$. I think you can ignore the mass of the arm. You have to have some way of measuring a force (eg. a spring scale, or weights and a pulley) required to pull the trap open to a certain angle. (What you want is a trap with a strong spring to store as much energy as possible).

Measure the angle of the trap with various forces (eg. weights attached) and plot them out on a torque (force x length of trap arm) vs angle diagram to determine the k. You use only the component of force that is perpendicular to the trap arm to find the torque.

Once you have the k of the trap, work out the torque at 180 degrees (trap fully opened). That gives you the maximum force delivered by the trap arm to your drive train. It is then just a matter of working out the mechanical advantages of the extended arm to axle to wheel to find the force of the wheel on the road. You then want to make sure that that force does not exceed the maximum static friction force between the wheels and the surface.

AM

 

[Andrew Mason]

I just thought of an easier way to measure the spring force. Drill a hole in the trap and hang a weight on it with the string going through the hole. Add weights until the spring bends back completely. That gives you the force. Multiply that by the arm length to give you the torque. Divide by 180 to give you the spring constant.

AM

 

[Buck268]

Run "skinnies" up front (single disc CD wheels) and "slicks" out back (multi disc wheels) :D

 

[cronxeh]

I remember back in first year of undergrad engineering class we had to do this mousetrap car in 2 hours.. and we were using legos

Needless to say, the best way to make sure it goes 10 m+ is to have wheels that rotate freely and gears that arent too tight so you don't lose your energy to friction. I'd give you my design but it won't be fair, besides its fun