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$\bullet$ A 2.50 kg rock is attached at the end of a thin, very light rope 1.45 $\mathrm{m}$ long and is started swinging by releasing it when the rope makes an $11^{\circ}$ angle with the vertical. You record the observation that it rises only to an angle of $4.5^{\circ}$ with the vertical after 10$\frac{1}{2}$ swings. (a) How much energy has this system lost during that time? (b) What happened to the "lost" energy? Explain how it could have been "lost."

(a)$\operatorname{mg}\left(L-\operatorname{Lcos} \theta_{2}\right)$$0.54 J$(b) damping

Physics 101 Mechanics

Chapter 11

Elasticity and Periodic Motion

Equilibrium and Elasticity

Periodic Motion

University of Michigan - Ann Arbor

Hope College

University of Winnipeg

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guy. I suppose the first question we're looking for to find out home much energy He was lost during the process. Or a first. It was having angle off 11 degree with the vertical lie. Okay, He's the H one. Here is the heights for a potential energy. But initial potential and which is equal to MGH one and H one is equal to hell minus. Oh, cause I ain't 801 Why is that? Because you see, here this far is l close. I think that one Hey, you can t reduce the triangle. This will be the core Scientists are remember the whole land on the road is out. So this bar H one is elc minus Oh course tonight they don't want okay and updates on swings The angles turned to four point by degree with the worst composition. Is he here? So this is the final potential energy What is happening here? Ok, if u s you have u of m g h two. And just like the previous case is to book is right here, right? Remember, this is the no oh co sign. Say that to Yeah, And this right here. This fell so age too. Is he With l minus? L cause I data to so final potential and you re going to m g times l minus l cause I not to. Okay, so now we can find out how much energy was lost, which is stuff that you just the changing potential energy. Which is you. I minus u f This will give us MGI l my eyes. Oh, co sign no one minus MGI l minus. L course I they're too okay. And if we take the l out got em. Geo one minus co sign Data one minus mgl one minus cause I to now we can combine skater yoga mgl times one minus co sign They go one minus one minus negative. Co sign? Yes, You okay? And this will give us the chain gene financial engines Since the energy that is lost Your suit Legal two mg times now. Times co sign data to minus co scientist one. Okay, Nike plugging the value will get down. How you It's legal to M, which is? The mass is 2.5 kilograms. Okay. To bring bio kilogram times the gravitational constant. I'm pulling a meter per second square plans the plans of the robe. It was just 1.45 years. So one going full by meter times because I am data to is co sign. Well, point by degree minus cause I 11 degree, which is, of course, I could go on. And this will give us about zero point by four Jew. Okay, so that's the NGOs have lost during the process. Well, uh, the second question was asking us. Well, what kind of thing costs the los ing energy? Well, I think the angel's laws, because off Demming, okay. And low cost MP. Well, the first possibility is the molecular proficient friction. Okay, Tillerson friction between the barbecues. Because, remember, molecule was like the basic unit up a matter. So of course, they have a bunch of mod accuse inside of rope. Okay, so, Malika friction is the first possibility here. I think the second possibility, maybe the air resistance. Okay. And, you know, era resistance everywhere. So this to while it is my cost MP, and then him costs the Angelus. Okay. Thank you. It's my answer for these questions.

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