PART 3: STATIC FRICTION COEFFICIENT FROM ANGLE OF REPOSE & NEWTONS 2ND LAW Pair of Surface Materials Used: Trial # Angle of Repose (degrees) normal force L > friction 2 3 mg sin 0 4 Mean 9. Using the setup shown, draw a free body diagram for the cart on an inclined track with friction. 10. Beginning with Newton's 2"d Law and using your knowledge of the free body diagram, derive an equation for calculating the coefficient of static friction. The final result should be us = tane. Coefficient Of Static Friction = (Materials: 11. Compare your value here to what you obtained in Part 1 for the static coeff. Explain which method you believe gives the more consistent result. Which do you believe gives the more true result?Theory. Part 3: We have seen we can easily modify our experimental setup to find a second way of determining the coefficient of friction between two surfaces. Even though different measured variables were used and different mathematical analysis was performed. the results should roughly agree with the earlier method. Better consensus is reached if you can arrive at the same result from different paths. This is how the majority friction of science is performed. Physical reality and the laws governing it should be self consistent, and if everything is done correctly it should not matter the path taken or equations used. We can do the same to find a different way of measuring the coefficient of static friction. Using free body diagrams. Newton's 2nd Law. and some geometry we can determine the static friction coefficient simply by my sin - measuring the angle of incline needed to just make our Object begin to move. Since static friction is just overcome before it starts to move. this angle is an approximation for when static friction force is maximum. Look at the sitation in the free body diagram to the right. If we assume the object is at rest, and at an angle where the component of gravity down the incline is just about to overcome the static friction force (F) holding it still, then we have the following Fnet = ma = Fox - F= = 0 Substituting expressions for the various forces. using algebra and geometry. and simplifying it can be shown that the coefficient of static friction depends only on the angle of incline found. Us = tan0 It is left as an exercise for you to prove how you get from Newton's 2nd Law to that simple expression. This angle is known as the Angle of Repose. Amazingly. it says that between any two material surfaces there is an angle of incline above which the surfaces will always begin moving with respect to one another. As long as some amount of gravity is present. it does not matter how strong the gravity is or even how massive the object is. you could determine the coefficient of static friction. This explains why ant hills tend to always have Set the same slope. why sand dunes have the same slope. and how you can determine the viscosity of lava from the slope of the volcano it creates. Angle of Repose Setup. Part 3: H 12.4 For this part remove the Force Probe from the Cart Object. The Object should consist of just the friction block underneath the cart. Do not use any additional mass. Remove the Motion Sensor from the track. Make sure N 12.7 the Angle Indicator is attached to the track. 3 12.0 Procedure, Part 3: 4 12.3 With the Object near the middle of the track and the track horizontal, begin slowly increasing the incline of the 5 12.1 track. Once you reach an angle where the Object starts to move. lower the angle slowly. and oscillate around this point until you find the angle where it just starts to move. Record this angle. Repeat for a total of 5 trials. 6 Record this information on your worksheet. Mean 12.3 Std. Dev. 0.3