Calculating Mu from a counterbalanced inclined plane

[Sadoian]

The physics homework for the weekend dealt with a lab we did the previous day. Currently I'm stuck, and wondering if anyone can help direct me in the right direction.

The lab consisted of an inclined plane with an attached pulley. We hooked up a rolling cylinder to a string, that went over the pulley, and on the other side we added weights to balance out the system. The next step was to slowly add weight until we could get the cylinder rolling up the plane at a nearly constant (or as close as we could get it) speed, and writing down how much mass we used to get the cylinder to move at that rate.

We students did this for a variety of angles for the plane, and took down just the mass of the counterbalance each time.


Now, our assignment for the weekend was to calculate mu from the data we took from the lab. We assumed that the pulley and string were both massless and frictionless. My train of thought (up to where I became stuck)

For the cylinder:

Sigma(F-subx) = m*a-subx
Sigma(F-subx) = 0 (since a-subx is 0, assuming nearly constant velocity)

T - m*g*sin(theta) - Friction = 0
T - m*g*sin(theta) - mu*m*g*cos(theta) = 0 (taken from vertical components of FBD)

So I get mu by itself and have:

mu = (T - m*g*sin(theta)) / (m*g*cos(theta))


Now, I have T, m, and mu that I do not have values for. I can find the numerical value for T -- (the weight of the counterbalance -> m*g). Even so, I'm still stuck with m without a value, and I don't really know how I can get m to cancel out, or to find a suitable substitute to solve the equation.

Any help would be appreciated. Thank you for your time.

-Jared

 

[topsquark]

The physics homework for the weekend dealt with a lab we did the previous day. Currently I'm stuck, and wondering if anyone can help direct me in the right direction.

The lab consisted of an inclined plane with an attached pulley. We hooked up a rolling cylinder to a string, that went over the pulley, and on the other side we added weights to balance out the system. The next step was to slowly add weight until we could get the cylinder rolling up the plane at a nearly constant (or as close as we could get it) speed, and writing down how much mass we used to get the cylinder to move at that rate.

We students did this for a variety of angles for the plane, and took down just the mass of the counterbalance each time.


Now, our assignment for the weekend was to calculate mu from the data we took from the lab. We assumed that the pulley and string were both massless and frictionless. My train of thought (up to where I became stuck)

For the cylinder:

Sigma(F-subx) = m*a-subx
Sigma(F-subx) = 0 (since a-subx is 0, assuming nearly constant velocity)

T - m*g*sin(theta) - Friction = 0
T - m*g*sin(theta) - mu*m*g*cos(theta) = 0 (taken from vertical components of FBD)

So I get mu by itself and have:

mu = (T - m*g*sin(theta)) / (m*g*cos(theta))


Now, I have T, m, and mu that I do not have values for. I can find the numerical value for T -- (the weight of the counterbalance -> m*g). Even so, I'm still stuck with m without a value, and I don't really know how I can get m to cancel out, or to find a suitable substitute to solve the equation.

Any help would be appreciated. Thank you for your time.

-Jared

You forgot one crucial step: Do a Newton's Law problem on the counterbalance mass. That will give you a value for T. As far as m is concerned, if you are doing the problem the way you state it then you need to have measured it. The only other way involves graphing and you didn't mention that.

-Dan

 

[kyle8921]

Hello Jared,

It seems like you are on the right track with your calculations. In order to solve for mu, you will need to use the data you collected during the lab. You mentioned that you recorded the mass of the counterbalance for each angle of the plane. This is a crucial piece of information that you will need to use in your calculations.

First, you will need to convert the mass of the counterbalance to the force it exerts on the inclined plane. This can be done by multiplying the mass by the acceleration due to gravity (9.8 m/s^2). This will give you the force of the counterbalance (T) for each angle of the plane.

Next, you can plug in the values for T and the angle (theta) into your equation: mu = (T - m*g*sin(theta)) / (m*g*cos(theta)). You will need to do this for each angle and solve for mu.

Once you have calculated the value of mu for each angle, you can take the average of those values to get a more accurate result. This is because there may be some experimental errors that could affect the individual values, but taking the average will help to minimize those errors.

I hope this helps guide you in the right direction. Remember to carefully review your data and equations to ensure accuracy in your calculations. Good luck!