How do I answer questions 5, 6 and 7 on page 28? I have typed up the work for page 29 in case my hand writing wasn't easy to read

Procedure In this lab you will determine the coefficient of static friction, us, between a ramp and a box, first (Part A) by attaching a string to the box and increasing the tension until the box begins to slide when the ramp is horizontal, then (Part B) by increasing the angle of the ramp (no strings attached) until the box begins to slide. Part A: 1. Use the scale to determine the mass of the wooden box. 2. Adjust the ramp so that it is perfectly horizontal. 3. Attach a string to the object at one end and, draped over the pulley, to hanging weights at the other end. Be sure the string is horizontal between the box and the pulley. 4. Add weights until the box begins to slide. Record the total hanging mass on the data sheet. 5. Repeat the previous step nine more times, placing an additional 100 grams inside the box each time, and recording the necessary hanging weight under the column marked "Part A" on the data sheet. Part B: 1. Remove the string and extra masses from the box. 2. Slowly increase the slope of the support plane until the box begins to slide. 3. Record the angle between the support plane and the horizontal when sliding begins. 4. Repeat the previous step nine more times, placing an additional 100 grams inside the box each time, and recording the angle at which the box begins to slide. 275. Static Friction The maximum frictional force between two objects depends upon the two surfaces, how hard they are pressed together, and whether or not they are relatively static. Apparatus An adjustable ramp, a wooden box, a set of weights, string, and a scale. Physical Principles Leonardo da Vinci (1452-1519) was the first to do the experiment which you will repeat today. He examined, as will you, the force of friction in two distinct situations; when an object is sliding along a surface, and when an object is at rest upon a surface. These are called "sliding friction" and "static friction." In both cases, the frictional force depends upon only two things; the surfaces themselves (for example, a hockey puck will experience less friction sliding upon ice than it will upon wood) and how hard the two surfaces are pressed together, also known as the "normal force". Thus, f = HN (1) The force of friction "f' (or, if no sliding is taking place, the maximum available frictional force) is proportional to the normal force "N", and the constant of proportionality "y" is a measure of the two surfaces (inverse) slipperiness. Since f and N are both forces, M must be a dimensionless number. Its value depends almost exclusively on what the two surfaces are. It is virtually independent of the area of contact between object and support surface, and even of the speed of the object, as long as there is some sliding. If, on the other hand, the object is at rest on the support surface, then p is usually significantly greater than in the cases where there is relative motion, since the molecules on the two surfaces have time to nestle into each other somewhat, electrostatically speaking. In view of this distinction we will refine our definition, and speak separately of a static coefficient of friction, "Us", and a kinetic coefficient of friction, "MK", where, as stated above, Us > Mk. 25Calculations: Is from part A (slope of the graph) : 0.2308 rounded to 0.2 Formula: 2 1 100-80 20 - = 0.2 x2-x1 503.2-403.2 100 Us from part B [ the tangent of the average maximum angle of repose): 0.19 Way #1: 8, = avg (0) = 11 + 11 + 11 + 10 + 10 + 11 + 12 + 10 + 10 + 13 10 -= 10.9 >> Tan (10.9) = .1925696473 Rounded to 0.19 Way #2: Tan (11) = 0.19438 Tan (11) = 0.19438 Tan (11) = 0.19438 Tan (10) = 0.17632 Tan (10) = 0.17632 Tan (11) = 0.19438 Tan (12) = 0.21255 Tan (10) = 0.17632 Tan (10) = 0.17632 Tan (13) = 0.23 Avg: 1.92535 1.92535 / 10 = 0.19 Percent difference between us as determined in part A and us as determined in part B (using the value from part A as the standard): HS(A)-Hs(B)* 100=> > 0.2-0.19 0.01 0.01 IS ( A ) + HS ( B ) 0.2+0.19 * 100 =>> 0.39 * 100 =>> 0.195 = 5.128 = 5.13Part A Part B Trial Number Mass of box plus added mass (g) Hanging mass (g) Maximum angle of repose (degree) 1 203.2 47 11 2 303.2 57 11 3 403.2 80 11 4 503.2 100 10 5 603.2 115 10 6 703.2 135 11 803.2 150 12 903.2 200 10 9 1003.2 230 10 10 1103.2 250 13Data Analysis . For Part A, plot your ten data points on a graph of frictional force divided by g (this ratio equals the hanging mass) on the y-axis vs. normal force divided by g (this ratio equals the mass of the box plus added masses) on the x-axis. Infer a "best fit" straight line through your ten data points, and determine its slope, us, clearly showing on the graph which two points (NOT data points) you used to find the slope. For Part B, determine the average value of the ten angles you found. Then use your average Or in Eq. (2) to find us. Finally, calculate the percent difference between us as determined in Part A) and us as determined in Part B), using the value from Part A) as the standard. Questions 1. Why is it necessary that the string in Part A be horizontal? (see Part A, Step 3) (HINT: Your answer should include the word "component".) 2. Explain why, from a molecular perspective, the value of the static coefficient of friction is generally greater than that of the kinetic coefficient of friction. 3. How do cars with ABS (antilock braking system) make use of the fact that us is greater than uk? 4. When the brakes are gently applied to a moving car, so the wheels do not lock, a) where does kinetic friction occur? b) where does static friction occur? 5. Follow the steps immediately preceding Eq. (2) to show where it comes from, i.e., "derive" that equation. 6. Why do the ten angles found in Part B vary somewhat? Note that, in theory, the maximum angle of repose is independent of the weight of the object since, as you have shown in answer to the previous question, the masses cancel out in the derivation of Eq. (2). 7. Discuss the precision of part A of this experiment. To within about how many grams do you trust your results of a given trial in part A? What margin of uncertainty in the value of us do you feel is warranted? How does the graphical analysis of the data help to reduce this margin of uncertainty? 28In both cases, the frictional force is the macroscopic manifestation of the electrical attractions between the molecules on the two surfaces, as well as some mechanical interlocking if the two surfaces are not smooth. Because of the first of these two factors, the value of the coefficients of friction are generally greater when the two surfaces are made of the same material than when they are different, since in the former case the molecular arrays fit together better. If the supporting surface is horizontal and there are no vertical forces on the object other than the normal force and gravity, then the normal force in Eq. (1) is equal to the object's weight. On the other hand, if the supporting surface is not horizontal, then the normal force is merely one component of the object's weight (N = W cos 0). When the two surfaces involved in friction are in static contact with each other the frictional force will be less than or equal to UsN. In other words, UsN is the maximum force of friction. When at rest on a horizontal surface with no applied force, an object feels no friction. As you gradually make the support surface steeper a frictional force arises which is equal in size and opposite in direction to the component of gravity which tends to pull the object down the ramp. Since the sizes of these counterbalancing forces grow together the object feels no net force, and remains at rest. This situation continues until the downhill component of gravity (W sin 0) reaches the maximum force of friction (Ms N = Is W cos 0), after which the object will start to slide. The angle at which this threshold is reached is called the "maximum angle of repose, Or" and is related to us as follows: tan Or = Us (2) 26