Analyzing Force and Mass Data: Finding the Force of a Fan

[Roze]

This is part of a lab I have to do, where we did an experiment with a car on a track and a fan, increasing and decreasing the number of batteries in the car to see the effect on its acceleration.

Another group of students did a similar experiment, only instead of varying the number of batteries in the fan they added the mass to the cart and measured the acceleration of the cart. There is a table of their data:
mass (kg) acceleration (m/s^2)
.535 .58
.735 .40
.935 .32
1.135 .24
1.335 .22
1.535 .18

First it asks to make a graph of acceleration vs 1/mass. I did this, although I don't know why it's 1/mass as opposed to just mass.

Then it says: If the force of the fan is equal to the product of the mass of the cart and the acceleration of the cart (Force=massxacceleration), how would you find the force of the fan from your graph? What is the force of the fan used to collect this data?

I used the equation given, Force=mass x acceleration and I made:

acceleration = Force x 1/mass -- which I think is important here, since my graph is acceleration vs 1/mass, but I still can't figure out how this helps me.

I figured out what the force is using this equation and the given data, and it averages out to be around .291, which is not the slope of the tangent line of my graph, and it's not the area under the graph.

So, I'm pretty much stuck looking at the graph. I feel like I'm just missing something obvious. Help?

Thanks!

 

[Poop-Loops]

The force of the fan changed whenever you added more batteries, so it shouldn't be a constant. The other group has an easier job.

In their case, they had a constant force, and changing mass and acceleration. Plotting it out they get a slope and that's the force.

In your case, the mass and you measured the acceleration, not knowing the force.

So I take it your graph is just a straight horizontal line?

No, this doesn't make much sense at all. The force is your independent variable, so it's not something you should be having to find. Are you sure you did the lab correctly?

 

[Roze]

The question asked me to graph their data, the one in the chart that was probably hard to read on the initial question. I probably should have included the 1/mass data as well.

The chart was this:
mass (kg) acceleration (m/s^2)
.535 .58
.735 .40
.935 .32
1.135 .24
1.335 .22
1.535 .18

But the question asked me to graph 1/mass so I had a new chart to graph that looked like this:

1/mass (kg) acceleration m/s^2
1.87 .58
1.36 .40
1.07 .32
.88 .24
.75 .22
.65 .18

So the above chart is what I graphed (because that's what part a told me to graph) and I got a line sloping upwards. I calculated the slope of this line:

.40-.58 / 1.36-1.87 which gives me .35 where when I use Force=mass x acceleration for the first data set I get .3103 and the second data set I get .294 which I assumed was not close enough to be the answer. Maybe I'm wrong there and it is the slope. I hope so, that would make my life much easier.

Hopefully that clarifies any confusion about the question or my method or any of that.

Thanks!

Roze

 

[Poop-Loops]

No, I was asking if you were certain you did the experiment correctly. It just doesn't make sense what you were told to do. You can't find the force of the fan if you keep changing how hard it blows, basically.

 

[Roze]

Ah, I understand the confusion here. The full question here is:

Another group of students did a similar experiment, only instead of varying the number of batteries in the fan (which is what we did) they added mass to the cart and measured the acceleration of the cart.

So they are not changing how hard the fan blows, we did but the data I'm working with here is when they change the mass of the cart. I understand now why that makes no sense with what I originally told you.

 

[Poop-Loops]

Oh, I see now. That makes perfect sense.

Yes, it is the slope, and you do have to use 1/mass like you are.

I think the point of the exercise is to show you that experiments are never "exact". You're manipulating the data correctly, so it's all good. The problem is that this "other group" took data that either wasn't very precise or very accurate. This is something that's very important for all sciences. That's why you use statistics -- things like standard deviation, chi-squared probability, etc. Basically to give your data some "buffer" so that even though it's not perfect, it's still useful.