The Angle of Repose


Place a coin on the cover of either a binder or your textbook. Slowly raise the cover of the textbook, while observing the motionless coin. Eventually, you will reach an angle where the coin breaks free and starts sliding down the slope of the binder. This is the phenomenon we will be analyzing today.

Notable recent UC coin (cupro-nickle) masses: Mdime = 2.264g; Mpenny = 3.110g; Mnickel = 4.999g; Mquarter = 5.669g

Q1: Observe the coin on the binder. Before the coin slides, what kind of friction holds it in place? Sketch what a microscopic veiw of the coin and binder's interacting surfaces might look like. Continue tilting the binder until the coin starts sliding. What is the name of this new type of friction after the coin is moving and how is it different? How would your sketch change?

Q2: Try to determine the angle at which the coin exactly breaks free. Is this possible? Why or why not? This is known as the Angle of Repose for an object on a slope. What is the Angle of Repose you measured for your coin and the binder or book?

Q3:Draw a free body diagram for the inclined plane and the coin. Choose coordinate axes so that the normal force is +y-hat and uphill is +x-hat. Identify and label the following forces on the coin: Normal force (FN), Friction (Fs = mkFN)and Weight (W = mg).

Q4: Write Newton's Second Law of Motion (N2) for any object in equilibrium. What can we mathematically state about objects in equalibrium? Is the coin in equalibrium at the Angle of Repose? Before and After? Explain.

Q5: We will use N2x and N2y. What calculations must be done to the three forces you have drawn? Which forces do not require such calculations?

Q6: Write component expressions for N2x and N2y. What do they mean (in words)?

Q7: Solve for FN and fs alone. What do these expressions mean (in words)?

Q8: Calculate the division N2x/N2y. Using the identity: tan q = (sin q) / (cos q) to simplify your answer. What does this mean about the role of an object's mass with regard to the Angle of Repose and the coefficient of static friction? What are the units of static friction? Does this make sense? Why?

Q9: What do you calculate as your coefficent of static friction for the binder and coin?



Seat Activities