Physics Lab #9

 

Inclined Plane and Friction Virtual Lab

Theory

The Simple Frictionless Ramp

 

Consider a block of mass m sliding down a ramp inclined at an angle θ.  If we begin by ignoring friction on the block the free body diagram (FBD) for the block will have two forces on it: weight of the block and the normal force from the ramp.  (Draw a labeled diagram of the whole thing, ramp and all.)  If we choose coordinates that are tilted to have the x-axis along the ramp, as in the example I did in class, you can then take components of the weight and find the net force (the forces in the y-direction will balance – add to zero -- since the block will not rise off of or sink into the ramp in the y-direction – explain why).  From the net force, the mass and N2 you can find an expression for the acceleration down the ramp.  Find it.  (You can use the web page below to help with the FBDs by clicking on the diagram and watching the FBDs pop up.)

 

Ramp with Friction

Now consider the case we did together in class, where friction does exist.  We will be looking for the critical case where the angle of inclination,  θ, is such that the block is just about to start sliding.  That is, the block is at rest, but the force of static friction is at its MAXIMUM = μ_sN.  You will do the same thing as in class and above – Draw a FBD and choose a coordinate system tilted to have the x-axis lie along the ramp.  You will then need to take components of the weight again (friction and normal will lie along the x and y axes respectively).  By balancing the forces in the x-direction and then the y-direction you will get two equations that can be solved for the critical angle θ.  It turns out that this is simply a trigonometric function of μ_s.  Find the expression for the angle.
 

To find the acceleration from the distance and time information in the virtual lab you will need the formula for an object experiencing constant acceleration:

s = ½at²

Procedure

The virtual lab equipment you will be using is here.

1. You will start by confirming your calculation for the acceleration for the simple plane above.  Choose zero for the initial velocity and coefficient of friction and turn off the rebound.  Drag the bottom red target down and over to get as close as you can to an angle of 30º.  Note the angle and its error.
2. Start the experiment and allow the block to run to the end.
3. The dots are just like those of the sparker timer lab.  Here they have a separation of EXACTLY 0.2 s.  Find the time separation from the first dot to the last one still ON the ramp.  There is a complication here -- the first dot is not from when the block is at rest but rather 0.2s after it was at rest.  You can deal with this in one of two ways: add one dots time onto your time (this is not exactly accurate but close) or do the math to figure out how this affects your results.
4. While pressing the ctrl key click on the first dot and then drag down to the last dot.  The screen will read out the distance between the dots in meters.  Note this.
5. Use the equation for constant acceleration and the data to find the acceleration down the ramp and compare it to the expected value.
6. Now turn the coefficient of static friction up to its maximum value.  Using the formula you found in the theory section find the critical angle for this coefficient.   Try different values of angle to test your predicted value.
7. I will bring some REAL stuff to try this in a different way.  You can put different items on the ramp I bring to see at what angles they begin to slide.  From this critical angle you can deduce the coefficient of static friction for the surfaces in contact.  Try a few things and make a table.