Effect of mass on skid distance of car experiment

[NihalRi]

Homework Statement

I know this is long, but that is only because this question requires me to be thorough, conceptually I think it isn't difficult. To make it easier to read I bolded the important parts.

In Physics lab, we were told to conduct an experiment to investigate the effect off mass on the skidding distance of a car. We conducted the experiment using a model cart, a dynamic track, a spring launcher(one in which the force could be altered), a motion detector and weights.

The spring launcher was used to supply a constant force for each trial of the independent variable. The motion sensor was connected to logger pro and recorded the distance and velocity per 0.05 seconds. Unfortunately our experiment was flawed because we didn't have a strong enough spring to launch the cart when the wheels were taped. We were told to proceed without taping them.

As we added 200g masses to the cart, we also used hooks law(f=kx) on the spring launcher to increase the force that pushes the cart. We did this because the extra weight would cause the launch velocity drop even when we needed it to stay constant. Just in case this wasn't enough, we used the motion sensor as a precautionary measure to see if we succeeded at keeping the velocity constant. We recorded the position the cart was at when it stopped. The first problem is that even though I believe we used hook's law correctly, according to the motion sensor, the cart started off going much faster as we added weights.

So we ended up using the data collected by the motion sensor to find out at what position the velocities were constant. Then found the difference between this and where the car stopped. This was our skid distance. We took the average of all skid distances per each independent variable value and our results are shown below. The standard deviation of the trials was not small.

mass of cart (g) Avg skid distance (cm)
566.9 17.9
766.9 24.35
966.9 22.7
1166.9 19.45
1366.9 19.9

Second problem is that there appears to be no trend in our results. We had hypothesized that as we increased the weight, the skid distance would increase proportionally because of inertia. This does not appear to be the case.
2. Homework Equations

F = ma = m(vf-vi)/t = kx (vi is zero because the car starts at rest)
F = m(vf/t) = kx
vf = kxt/m

F(friction) = N*(coefficient of friction)

The Attempt at a Solution

I have no explanation for the first problem except for the possibility that time might not have been constant.
In the second problem, I thought of the force of friction and how it should increase proportionally with the added weight. So effectively this should cancel out the effect of the weights on increasing the skid distance resulting in a constant skid distance. I really think this is plausible especially because of the last two points in our graph. With more data I believe we would see the trend better. What do you think, Do you spot any other flaws is the experiment.[/B]

 

[haruspex]

I don't see enough detail about the spring launcher and your use of Hooke's law to comment on the first problem.
For the second, you are right that there should be no change in distance. The acceleration during a skid should be -μ_kg.
With hindsight, it would have been a good idea to retry each weight.

 

[NihalRi]

I don't see enough detail about the spring launcher and your use of Hooke's law to comment on the first problem.
For the second, you are right that there should be no change in distance. The acceleration during a skid should be -μ_kg.
With hindsight, it would have been a good idea to retry each weight.

Firstly, thank you so much for your reply.

here's a little sketch of our spring launcher system before the spring had been compressed at all. We can alter how much it's bee compressed(x) by moving the second purple block back and forth. so in our first test with just the cart we compressed the spring two cm. Then after we added weights we found out by what fraction the weight increased and multiplied that by two to get the new value for x. for example if the mass of the car doubles we doubled x.

What about the fact that the cart was actually rolling instead of skidding, do you think that changes how we should deal with friction? With rolling there is static friction instead of kinetic friction, does that also increase with mass?

 

[rcgldr]

What about the fact that the cart was actually rolling instead of skidding,

Assuming simple axles, the axles were ""skidding", so the issue is the material(s) involved in the skidding. Rubber has a load sensitivity where coefficient of friction decreases as the load increases. The axles probably don't have this effect or at least it's different.

 

[NihalRi]

Assuming simple axles, the axles were ""skidding", so the issue is the material(s) involved in the skidding. Rubber has a load sensitivity where coefficient of friction decreases as the load increases. The axles probably don't have this effect or at least it's different.

interesting, so when the load increases the surface of the rubber changes making it more slippery? that makes sense. Our track was a kind of metal and the wheels were a hard plastic. Is it safe to say these materials do not have an interesting property like rubber?

 

[rcgldr]

Our track was a kind of metal and the wheels were a hard plastic. Is it safe to say these materials do not have an interesting property like rubber?

I don't know. Wiki has an article about tire load sensitivity:

http://en.wikipedia.org/wiki/Tire_load_sensitivity

 

[haruspex]

Yes, the wheels make it more complicated. Immediately after release, there could briefly be kinetic friction between wheel and ground as the cart accelerates. Thereafter, as @rcgldr mentions, there will be axle friction, but that should behave pretty much the same as normal kinetic friction. The retarding torque should increase more-or-less linearly with load.
The third loss of energy is rolling resistance between wheel and ground as both deform slightly. Increasing weight depresses the ground, making it so that the cart is having to go uphill, effectively. That effect may well be nonlinear. Deformation of the wheel is a bit different. This costs because of imperfect elasticity. The force required to squeeze the leading part of the contact area is greater than the rebound force at the rear.
See section 4 of https://www.physicsforums.com/insights/frequently-made-errors-mechanics-friction/

 

[NihalRi]

Thank you so much for your replies I found them extremely helpful. I didn't know about axle friction @rcgldr and that link you sent was very helpful @haruspex.