What is the coefficient of friction for different surfaces and ramp heights?

[COBRA1185]

Co-efficient of friction HELP!

Homework Statement

Hello I am new to physics forums, I am looking for some help with my Year 11 Extended Experimental investigation. My investigation is looking at how different surfaces and different ramp heights (inclined planes) affect the stopping distance of a toy car. I am having difficulty finding out what the coefficient of friction is for the different surfaces are. Please Help.
Note: The ramp is sheet metal and rolls down onto different surfaces eg. carpet, concrete etc..

PLEASE HELP I AM IN DESPERATE NEED

Homework Equations

The Attempt at a Solution

 

[PeterO]

Homework Statement

Hello I am new to physics forums, I am looking for some help with my Year 11 Extended Experimental investigation. My investigation is looking at how different surfaces and different ramp heights (inclined planes) affect the stopping distance of a toy car. I am having difficulty finding out what the coefficient of friction is for the different surfaces are. Please Help.
Note: The ramp is sheet metal and rolls down onto different surfaces eg. carpet, concrete etc..

PLEASE HELP I AM IN DESPERATE NEED

Homework Equations

The Attempt at a Solution

Is this car rolling? If it is, I suspect the only friction you have is the friction in the "bearings"
of the wheels - so will be indepenent of the surface - unless you had a surface "soft" enough for the wheels to sink in.

 

[COBRA1185]

Yes it is rolling, it is just a toy car. What I am really trying to determine is the coefficient of friction on the different surfaces which the car is rolling off the ramp onto.

 

[PeterO]

Yes it is rolling, it is just a toy car. What I am really trying to determine is the coefficient of friction on the different surfaces which the car is rolling off the ramp onto.

Good Luck!

 

[Harrisonized]

If you're doing this experimentally on a level surface (not an inclined plane), determining the coefficient of rolling friction is exactly the same as determining any coefficient of friction. (Friction coefficients are approximations anyway.)

The three numbers you need are:
1. the velocity at which the car begins free motion
2. the time that it takes the car to stop
3. the distance of travel (only after release)

From these three numbers, you should be able to deduce the friction coefficient.

v_f = 0 = v_i - at
F = μ ma
W = F d
E = 1/2 mv_i²
W = E

From the above:
1/2 mv_i² = F d
1/2 mv_i² = (μ ma) * d
a = v_i /t

Therefore:
μ = 1/2 v_i t / d
(for level surfaces)

Try to take measurements using faster initial velocities, since this will make time and distance measurements more accurate.

Also, make sure you understand how to find the velocity of the car after it leaves the inclined plane and onto the surface that you're testing. Make sure that you use a ramp that provides as much friction as possible, so the car's wheels roll without slipping. Then you can find the final velocity of the car at the bottom of the ramp via the time that it takes the car to roll down the ramp.

For the ramp:

v_f = v_i + at, where v_i = 0
a = g sin θ, where θ is the angle that the ramp makes with the level surface

Therefore:
v_f = g sin θ t

Instead of timing the car moving down the ramp, however, it's much more accurate instead to measure the distance the car travels down the ramp.

d = 1/2 at²
d = 1/2 g sin θ * t²
2d / (g sin θ) = t²
t = √ (2d / (g sin θ))

Therefore:
v_f = g sin θ √ (2d / (g sin θ))
v_f = √ (2d g sin θ)

Notice that this v_f is equal to the v_i of the level surface mentioned above.

By the way, you should mention as an experimental error that the bottom of the ramp will cause deviation from experimental results. The car will lose momentum from the impact of of the front wheel with the level surface, and the car's angle will continuously change from the time the front wheels hit the level surface to the time that the car is totally off the ramp.

 

[COBRA1185]

Thanks everyone for the responses, removed some stress from my life.
Harrisonized could you please tell me what vi, vf and W stand for.. Thanks in advance

 

[Harrisonized]

v_i = initial velocity
v_f = final velocity
W = work

... doh.

 

[COBRA1185]

Thanks thought that was it, just wanted to clarify

 

[Darth Frodo]

The Coefficient of friction is Tan A where A is the angle at which the car just begins to roll.

 

[Harrisonized]

It's actually very difficult to obtain accurate measurements of the coefficient of rolling friction using the angle of inclination, because the angle required is hilariously small.

 

[COBRA1185]

Can someone help me please,
If the incline increases should the time of the toy car going over a surface increase or decrease?

 

[PeterO]

Can someone help me please,
If the incline increases should the time of the toy car going over a surface increase or decrease?

You could expect it to increase. However, if you had a sharp angle between the ramp and the floor, the nose of the car might dig in and then it is difficult to work out what will happen. The steeper the slope [is sharper the change in surface angle], the more like it is that the nose digs in.

 

[COBRA1185]

Thanks for the quick reply, but if the speed the car is going at on the level surface is very fast shouldn't it take a smaller time to stop regardless of the distance travelled?

 

[PeterO]

Thanks for the quick reply, but if the speed the car is going at on the level surface is very fast shouldn't it take a smaller time to stop regardless of the distance travelled?

Suppose the car reached the level surface at 2 m/s. It would take a certain time to stop.

Suppose the car reached the level surface at 3 m/s. It would take a bit of time to slow to 2 m/s, then presumably just as long, as the example above, to stop from the "new" 2 m/s. That means the time would be longer to stop from the higher speed.

What do you think?

 

[COBRA1185]

Yes that is what I thought as well but when I tried to find out the time using:

t= distance travelled/ average velocity
it gave me a lesser time when the average velocity and distance traveled was bigger

 

[PeterO]

Yes that is what I thought as well but when I tried to find out the time using:

t= distance travelled/ average velocity
it gave me a lesser time when the average velocity and distance traveled was bigger

So you say - but you are only saying. Let's see some data and calculations.

 

[COBRA1185]

Ok

if the toy car was traveling at 1.31m/s and took 50.28cm to come to a complete stop then
s=(u+v)xt/2
0.5028=0.655 x t
t= 0.77 seconds

then if the same car was traveling at 1.83m/s and took 56.52cm to stop
then
0.5652= 1.83/2 x t
t= 0.617

see what i mean isn't it supposed to be longer, i agree with what you are saying, but why am i getting this?

 

[PeterO]

Ok

if the toy car was traveling at 1.31m/s and took 50.28cm to come to a complete stop then
s=(u+v)xt/2
0.5028=0.655 x t
t= 0.77 seconds

then if the same car was traveling at 1.83m/s and took 56.52cm to stop
then
0.5652= 1.83/2 x t
t= 0.617

see what i mean isn't it supposed to be longer, i agree with what you are saying, but why am i getting this?

These calculations are assuming constant acceleration - presumably it isn't.

Constant acceleration would result if there was a constant friction force - which would mean a constant co-efficient of friction. That is a problem for you.

How did you know the car was traveling at those speeds? I hope you were not just assuming a perfect transformation of energy as the car went down the hill.

 

[fleem]

Hope this isn't too pedantic but just so its clear to the OP: Technically these values are not the "coefficient of friction for a given surface" as stated in the first post. They are the "coefficient of friction between that particular car rolling on a given surface". A wood block without wheels would, of course, exhibit far different coefficients of friction on those same surfaces.

 

[COBRA1185]

We are trying to determine how different surfaces affect the stopping distance of toy cars.
Therefore we will be assuming that they all should hit at the same time and at the same velocity, if so the formulas state that it should stop quicker, do you agree? but in real life it doesn't due to friction etc...

Any ideas ?

 

[PeterO]

We are trying to determine how different surfaces affect the stopping distance of toy cars.
Therefore we will be assuming that they all should hit at the same time and at the same velocity, if so the formulas state that it should stop quicker, do you agree? but in real life it doesn't due to friction etc...

Any ideas ?

Compared to you calculations - this statement makes no sense at all?

Here you say "Therefore we will be assuming that they all should hit at the same time and at the same velocity"

but in your calculations you had two different speeds?

 

[PeterO]

Ok

if the toy car was traveling at 1.31m/s and took 50.28cm to come to a complete stop then
s=(u+v)xt/2
0.5028=0.655 x t
t= 0.77 seconds

then if the same car was traveling at 1.83m/s and took 56.52cm to stop
then
0.5652= 1.83/2 x t
t= 0.617

see what i mean isn't it supposed to be longer, i agree with what you are saying, but why am i getting this?

Are these speed and distance figures something you measured or something you made up?

If measured, how did you measure the speed?

 

[COBRA1185]

The distance was measured, and we are assuming that the final velocity at the end of the ramp which was done using the formula from harrisonized, is the initial velocity of the level surface. The velocities are different due to the different inclines.
Im just wondering why the time is less for a longer distance travelled.

 

[PeterO]

The distance was measured, and we are assuming that the final velocity at the end of the ramp which was done using the formula from harrisonized, is the initial velocity of the level surface. The velocities are different due to the different inclines.
Im just wondering why the time is less for a longer distance travelled.

Have you tried timing it to see if the time actually is longer?
You might need high speed video or strobe photography to time such small intervals.

 

[COBRA1185]

Yes, when i timed it, it took longer but when i did the calculations to see what it should be it gave me that it was less(see above).

Also how would i find out the coefficient of friction for that surface, i tried doing it with the accelerations but they give me different coefficients of friction for that surface when the incline is changed, should that happen?

 

[PeterO]

The distance was measured, and we are assuming that the final velocity at the end of the ramp which was done using the formula from harrisonized, is the initial velocity of the level surface. The velocities are different due to the different inclines.
Im just wondering why the time is less for a longer distance travelled.

If the ramp is straight, and thus meets the level surface at an angle, there will be an initial force opposing the direction of motion when the toy first hits the floor. The steeper the ramp angle, the larger the effect of that force.

Those formulas wre based on the ramp being completely frictionless. There is friction i the bearings of the wheels/axles of the toy, which act all the way down the slope, AND all the way across the level surface as well.

If you wanted to check their significance, make the level surface the same material as the ramp and see if the car ever stops.

Perhaps you should consider uncertainties in your calculations to see how certain you are of the initial speed.

How accurately can you measure the angle of the ramp?

 

[COBRA1185]

Thanks a lot for your help, would you have any idea how to find the coefficient of the surface which it is rolling onto?

 

[PeterO]

Thanks a lot for your help, would you have any idea how to find the coefficient of the surface which it is rolling onto?

If I wanted to find the coefficient of the surface, I wouldn't be rolling on to it.

If you were to drive a Formula 1 car [or Indy car], and a family sedan, side by side, at 60 km/hr along an airport runway, then at the same time, disengage the drive [push the clutch pedal?] would the two of them stop at the same time, having traveled the same distance?
If you "swapped lanes" and repeated the experiment, would that reverse the outcome?
What would that tell you about the influence of the surface friction on the stopping distance or stopping time.
[remember it would be possible to fit the same type tyres to each car -either "road" tyres to the race car or "race" tyres to the road car].

 

[PeterO]

Yes, when i timed it, it took longer but when i did the calculations to see what it should be it gave me that it was less(see above).

That proves that either you don't know how to time accurately, or the calculations you used don't give the correct answer for something - perhaps the speed at the bottom of the slope or perhaps you shouldn't be assuming the acceleration is constant??

If you drop a rock from a tall building, and using a stop-watch carefully note it takes 5.34 seconds to reach the ground - then that is how long it took. Just because Newtons laws say it should only have taken 4.65 seconds doesn't alter what ACTUALLY happens. It just means you used the equations incorrectly - most probably forgetting to allow for air resistance.

Perhaps a more reasonable way to get a higher speed would be to use a longer ramp at the same angle, not the same ramp at a bigger angle? Still don't like the idea however.

Also how would i find out the coefficient of friction for that surface, i tried doing it with the accelerations but they give me different coefficients of friction for that surface when the incline is changed, should that happen?

The co-efficient shouldn't change, so if you are getting significantly different values, you calculation methods are not appropriate.

 

[COBRA1185]

Do you have any equations that i may be able to use to find the coefficient of friction for a specific surface. I know the initial velocity, the final velocity, the distance and the time taken. Any ideas?

 

[PeterO]

Thanks a lot for your help, would you have any idea how to find the coefficient of the surface which it is rolling onto?

Perhaps you should be trying to investigate something else - using the same apparatus.

Option 1: The relationship between ramp angle and stopping distance

Set the ramp at different angles, but release the toy from the same height [so a shorter distance on the ramp]

If the toy was to go further with a steeper ramp, this may show that Potential Energy is transformed to Kinetic energy more efficiently of a steeper / shallower ramp.


Option 2: Release height vs Stopping distance
Release the toy from greater and greater distances up the ramp [keep angle fixed, but do it for separate angles to confirm that the angle does/doesn't make any difference.

I would suspect one of the following.

Ramp length x two ---> stopping distance x two

Ramp length x two ---> stopping distance x four

Ramp length x two ---> stopping distance x 1.4 [root two]

But it might be something else?

Careful measurement and graphical analysis should lead you to an answer.

You could still vary the level surface to see if the relationship between release height and stopping distance is independant of surface.
[ it might stop quicker on one surface, but the direct/direct square/ direct square-root relationship might still apply?]

Extended Investigations are often about carefully collecting data, and logically and meaningfully analysing it - being sure to consider uncertainties - than actually finding an answer.

 

[COBRA1185]

I found the coefficient of friction for one surface, and it didnt change, i had put in the wrong starting velocity.