What Are The Physics Principles Involved In This Weight Powered Car?

[muckamadboy]

I am sure that people have all seen this assignment before but just to recap. I have to build a vehicle that has to move 10 meters, using nothing other than the energy provided by a falling 2kg mass.

 

So this is what I am doing: building a car (kind of like a mousetrap racer car) however the mass is attached by string and wrapped around a spool, the other end of the string be attached to the axel of the car. When the mass is released, it should fall and pull the axle of the car, causing it to move. We are going to wind it up and place a block infront of it to stop it from moving, and move the block when we want it to go.

 

The conditions are that the car cannot be more than 1 meter high, and it must stop by itself. The brick is the only source of energy and we are allowed to hold the car and release it.

 

So we are using CD's for our wheels, 12cm in diameter, 2 on either side. When the weight of the 2kg mass are attached, the total mass of the car will be about 3 kg. We are thinking about utilising the total 1m in height and using longer string so that the mass will fall slowly instead of a sudden drop.

 

I am just wondering what are the physics principles behind this in form of formulae and theories. I know that gravity is acting on the mass but other then this i am pretty much in the dark. (I am in college, not having done much physics before, so I appologise if i sound a bit stupid)

 

I think this process is converting potential energy into kinetic energy?

 

And how can I figure out how much string i need to use if the car is to go as close to 10 meters as possible and stop by itself?

[CraigD]

Hi muckamadboy, & welcome to hypography! :)

 

I am just wondering what are the physics principles behind this in form of formulae and theories. I know that gravity is acting on the mass but other then this i am pretty much in the dark. (I am in college, not having done much physics before, so I appologise if i sound a bit stupid)

I’m guessing you already have a pretty good idea of the undetailed physics of your project – apply enough force to the vehicle to overcome friction by applying a force over a distance, resulting in work, which converts the potential energy of “the brick” to mostly heat due to friction while getting your car from where it starts to where you want it to stop. You’ll likely rely on having lots of available energy (that’s a pretty big brick!) and lots of friction, so work out the design and build mostly by feel, not mathematical physics.

 

What you seem to need in detail is an answer to the question “how much string needs to be wound around the spool on the axle to move the car exactly 10 m?” – though I think you really need to ask a slightly different question. In any case, the answer comes from simple geometry:

• You’re give the distance that point on the outside of the wheel (what touches the ground) attached to the axle should travel (many times around a circle) D_w = 10 m
  
• You need to calculate the distance traveled by a point on the outside of the spool (where the string is wound) D_s
  
• Call the radius of the wheel R_w, and the radius of the spool R_s.
  Since the distance a point on the outside of the wheel travels for a dingle turn of the wheel-axle-spool is [imath]D_w = 2 \pi R_w[/imath], and the distance the outside of the spool travels is [imath]D_s = 2 \pi R_s[/imath], you can get with just a little mathematical ingenuity:
  [math]D_s = \frac{R_s}{R_w}D_w[/math]
  
• As we’ll see below, though, you’ve really been given, after your designing and building is done, D_w, D_s, and either R_w or R_s. So what you need to calculate is, given R_w or R_s, one or the other. So we need to tweak our simple formula into
  [math]R_s = \frac{D_s}{D_w}R_w[/math]
  or
  [math]R_w = \frac{D_s}{D_w}R_s[/math]
  

Given your rules,

The conditions are that the car cannot be more than 1 meter high, and it must stop by itself. The brick is the only source of energy and we are allowed to hold the car and release it.

Let’s assume some of your 1 m allowed height is taken up by support parts, pulleys, and the thickness of the brick results in your brick having a vertical drop of 80 cm (0.8 m), that you opt for a simple design where the vertical drop of the brick, the distance moved by the string and by a point on the outside of the spool are all the same distance (that is, nothing complicated with compound pulleys of letting the string wrap over on the spool), and that the radius of your wheel is 10 cm (0.1 m). Now we need to what radius spool we need, using the formula we got above:

[math]R_s = \frac{D_s}{D_w}R_w = \frac{0.8}{10}0.1 \,\mbox{m} = 0.008 \,\mbox{m} = 8 \,\mbox{mm} [/math].

 

Since you may not be able to get a spool of exactly that radius (though a bit of care and cleverness with adhesive tape can usually get your pretty close with a machine that only needs to hold together a few times ;)), you might want to start with a spool or a measured radius and work backwards to the right wheel size, or more likely, find a good spool and wheels of about the right size, then find the vertical brick drop needed to travel 10 m.

 

The stopping right on the spot is where the challenge comes in. I’m sure if you think and tinker a bit, a solution will come to you. :)

[muckamadboy]

Wow! Thanks a lot of your help :) I was wondering about the potential and kinetic energy, and what part these have to do in this experiment?