In the end of the section on incline motion there is a discussion of a way to measure both the value of very low friction coefficients and the slope of a hill on which an object slides or rolls by simply measuring the acceleration both up and down the same hill or ramp.  For objects with very little friction like a snowboard or an object like a carts rolling on a track, or a bicycle rolling along the road, this friction can be treated like sliding friction discussed in this chapter: [math]F_{f,kinetic}=\mu F_N.[/math] where the coefficient of friction is really the coefficient of rolling resistance. There are more precise ways to model the friction associated with rolling resistance, but such precision is not needed when speed doesn't vary dramatically. I should also mention that such models are more appropriate for pneumatic tires anyway, and our cart doesn't have air-filled tires.[br][br]It is difficult to measure friction coefficients for objects that roll very well. This is true of everything from a well-made toy car to a racing bicycle.[br][br]Techniques that could be employed to try to measure such low friction coefficients would likely require the use of a force sensor, but the sensor would have to have very high precision to measure very small friction forces. Using the technique in lab today, however, it will be easy to measure very small friction coefficients rather accurately.[br]

[list=1][*]Set up a track on which a cart will roll to roughly a 5% grade.  The exact value is not important since we will actually be able to determine it by simply measuring the acceleration of our cart. [color=#ff7700]Q1: If there is an unknown amount of friction between the cart and the track, is it possible to determine the slope by just measuring the acceleration up or just down the track?[/color] When written as a percentage - as are road signs - slope implies the rise over run, or slope of a surface. [color=#ff7700] Q2: What angle in degrees corresponds to a 5% slope? Radians? What does a small angle approximation have to do with the radian value? [/color] Orient a tape measure along the track with numbers increasing in the downward direction.[/*][*]Tape a little paper indicator on your cart so that perspective won't make it hard to discern the cart's position in movie frames that you'll capture on your phone.  Consider parallax in the video when deciding how to attach a pointer. The idea is to have a needle-like indicator pointing to the built in measuring tape on the track and to be able to get an accurate reading even if perspective of the cart in the video changes a bit. [color=#ff7700]Q3: Is it better to the have pointer tip close to the track or higher above the track to minimize parallax? [/color][/*][*]Make three movies of the cart in which you briefly push the cart to give it a velocity up the track. Record the cart as it rises, stops, and rolls back down.accelerating down the track. [b]Make sure the hand releases early so that your push doesn't affect the car for very long, since we don't want to know about the force of your push, but rather about gravity and the friction present.[/b][b][br][/b][/*][*]Once the movies are made, make six curve fits of position vs. time in GeoGebra for the three runs (3 up and 3 down) and from the fits, find the rate of acceleration.  Please don't confuse which run was which in your data.  Make sure you have the display set to 3 significant digits or more. [color=#ff7700]Q4: Will the sign of the acceleration change as the cart reverses direction at the highest point on the ramp? Q5: Will the magnitudes of the accelerations up and down the track be the same? Why or why not?[/color][/*][*]Once you have the acceleration values, find the slope and friction coefficient corresponding to each of the three pairs of acceleration values using the physics described in the section on motion on an incline.[/*][*]Calculate the value of the slope of the ramp and the friction coefficient using 95% confidence intervals based on the three values obtained from knowing pairs of values of upward and downward acceleration.[br][br][/*][/list]

Use +x as the direction down the ramp and -x as the direction up the ramp. Answer the following questions while understanding that I am asking about either a force or a component of a force that acts along the x direction. [br][list=1][*]In which direction does friction act when the cart rolls down the track?[/*][*]In which direction does gravity act when the cart rolls down the track?[/*][*]In which direction does friction act when the cart rolls up the track?[/*][*]In which direction does gravity act when the cart rolls up the track?[/*][*]Do you gain speed going down a hill at the same rate that you lose it while going up the same hill coasting on a bicycle?  Explain carefully... perhaps with diagrams if need be.[/*][*]What are your values of slope and friction coefficient reported using a 95% confidence interval?[/*][/list]

Please submit all questions from the procedures section, the questions from the 'QUESTIONS' section, all lab data and plots with curve fits as either a .doc or .pdf file.