How does friction affect data in a modified Atwood machine?

[dbakg00]

Homework Statement

I have a modified atwood machine which is made up of a vertical mass hanger (hanging over the side of a table) connected to a horizontal cart (on the table) via a rope (un-stretchable) and a pulley (massless, frictionless, etc). The cart wheels have negligible friction. There are four equal masses stacked on the cart, each weighing 1.0kg. The mass hanger has a mass of 2.0 kg. The questions are:

(a) if I were to double the mass on the vertical hanger, without changing the mass of the entire system, would the acceleration double?

(b) how would the data be affected if the frame of the cart were bent so that one of the wheels were rubbing

Homework Equations

$F_{net}=ma$

The Attempt at a Solution

(a) After drawing free-body diagrams for both the cart and the mass hanger, I used F=ma to derive the following equation for the acceleration:

$a=\frac{m}{M+m}*g$

where "M" = the mass of the cart/weights on top and "m" is the mass of the vertical hanger and any weights it may contain

After plugging a few values in this formula, it appears that the acceleration will double if I double the mass on the hanger without changing the mass of the system.

Did I get the formula right?

(b)

If one of the wheels were rubbing on the cart, that would skew the position-time data for the experiment. It would look like there was a greater amount of mass on the cart that what was there in reality. This would make your acceleration appear slower than it actually was. Also, if you didn't realize that the wheel was rubbing, you wouldn't include the friction force on the free-body diagram; therefore, your skewed data could induce the erroneous conclusion that $F_{net}\neq ma$.

Is my reasoning correct? Did I miss anything?

Thanks

 

[Spinnor]

You wrote,

"(a) if I were to double the mass on the vertical hanger, without changing the mass of the entire system, would the acceleration double?"

Check your math, I got different results.

 

[dbakg00]

I see where I made the mistake now, I was making the denominator the entire mass of the system instead of adding the vertical mass to the entire system mass. The acceleration will increase, but not double.

Did part b look ok?

Thanks

 

[Spinnor]

Part b looked right to me.

 

[dbakg00]

Thanks for your help.