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$\bullet$$\bullet$ Measuring the co-efficients of friction. Onestraightforward way tomeasure the coefficientsof friction between a boxand a wooden surface isillustrated in Figure 5.54The sheet of wood can beThe sheet of wood can beraised by pivoting it aboutone edge. It is first raisedto an angle $\theta_{1}$ (which is measured) for which the box justbegins to slide downward. The sheet is then immediatelylowered to an angle $\theta_{2}$ (which is also measured) for which thebox slides with constant speed down the sheet. Apply Newton'ssecond law to the box in both cases to find the coefficients ofkinetic and static friction between it and the wooden sheet interms of the measured angles $\theta_{1}$ and $\theta_{2}$ .

$\mu_s =\tan \theta_{1}$ , $\mu_k=\tan \theta_{2}$

Physics 101 Mechanics

Chapter 5

Applications of Newton's Law

Motion Along a Straight Line

Motion in 2d or 3d

Newton's Laws of Motion

Applying Newton's Laws

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question 41 say that one straightforward way Commager the coefficients of friction between a box and it wouldn't surface is illustrated in the figure here where the blocks that rectangle laying on it well here and plywood sheet What's being angle that people data now the sheet of wood can you raise by pivoting about pinning it about one edge in his first race to an angle. Fate a one to the first scenario call state of one and subsequently able dictated to book almost from that second. So sorry. Its first raised to an angle data one, which is measured for which the box just begins to slide downward, that she is immediately lowered. Twin angle Fated to, which is also measured for which the box slides with constant speed down the sheet. Apply Newton's second law to the box in both cases to find the coefficients of Connecticut. Zach frictions between it and the wooden sheet in terms of measure angles, Data one and stated to Okay, so this question we're seeing basically have what angle stated. Does the box begin to slide so stated wine would correspond to determining the coefficient of static friction, and they had to be lower it to see it, which, um, constant speed of the boxes sliding on the ramp so that would correspond to the kinetic friction of the box. I mean, I guess cook, uh, these coefficients of friction from the surface due to sliding box, etcetera, etcetera. Those angle here that is adjustable. So if we take a look at if a free body diagram of her box my first established my coordinate system, my access to be x and y angled along the same single data. You know the muscle want to slide down the ramp due to its weight. So let me first, if we to find what the weight is. Wait, there's a why. Component of the weight. Why w Therefore the SP horizontal component of the weight W X Well, that's honest. Really. The normal of the box points away from the surface of the sheet and because it's lying on the friction force opposes that motion and were angled here in angle theta in this angle year between why and why w the weight and why the y component other way. Excuse me. This is also data which means W why is the wait Times, Coast data and W X to this company here. Is it going to the wait Times Scientific believe it generally is data for now. But as we'll see, whichever term they don't data one dated to doesn't really matter which one used because it really we're measuring the same thing in both of these experience. So we'll get applying Newton's second law. Look, the forces in our X direction here along the surface of the ramp this time we call the fictional Foresee positive. And down the ramp is, um wait times signed dinner Initially, this a static sort of things, you know, And it will be true for the second part where acceleration will be zero. And as it does state the question that it does, um, signs down with constant speed. The white components of our forces have our normal force being positive and r minus Wait, Times Co sign data three. So if you want to solve from you here, of course, that's their fictional term. So we could be right. This first equation are frictional term equals You wait. Times sign data friction. Forces are mule, so I get living it for generically as mu because, um, each will apply in the same scenario. So that's mu times the normal people's W science data. And from this equation that we rewrite expression for the normal just to be the wait Times Co sign data. You can substitute that to our original equation. So if mu times the weight cause I data, he goes await. I'm signed, Dana. So you see there's a weight Chairman Bill signs that will cancel out the divine divide both sides by co sign data. Our left side, it just remains new and right side is tan data. So that means and the question of ask find the coefficients of Connecticut static friction in scenario one again resented here data one corresponds to the coefficients static friction because the box starts motionless and that moves. That means the coefficient of static friction would be tan data one. In our second scenario to keep it moving with constant speed meeting again. Zero acceleration. So this this term here remains accurate. So in UK, equals can dated two. There you go.

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