12) if you will, a playground where small children play. It contains a merry-go-
ID: 1770012 • Letter: 1
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12) if you will, a playground where small children play. It contains a merry-go- Best read with Rod Serling's voice) Picture, round, but not just any ordinary one, though. It is the old kind made of steel, rusted bolts, a few drops of blood, a few tears (both of joy and pain), and more memories than most amusements have. It is the kind remembered fondly by a tired middle aged man who goes by the name Earl Renard. On this particular day, Earl is again dragging himself to work like he does on most days. Although he doesn't know it yet, this day Earl is actually going to work in The Twilight Zone. As the man gets out of his car, he hears the sound of children playing. This draws his attention since it is unusual to hear at the office complex. He did not even know that there was a playground near. He walks towards the noise until he sees a large playground where an office building was the day before. He smiles as he sees the children playing. He sees kids running around, a few seem familiar. As he walks closer he realizes that he recognizes the children. They were his friends from childhood. Suddenly one the kids turns to him and yells, "Hey Earl. Hurry up, you slow poke." Earl seems confused and wonders to himself; “Is he talking to me?" and “Isn't that Jay, I haven't seen him in 30 years." Earl points to himself with the "who, me?" look and posture. Jay yells back, "Of course, you dope. Come on, the Twirly-Thing is waiting for us." Before Earl responds, he realizes that he is a kid again, and there are no offices anywhere around. He is dressed in his t-shirt and jeans, wearing that pair of sneakers with the hole in the toe. He smiles and runs to join his friend. On the merry-go-round, Earl jumps on. Jay is already there, waiting to push it. Earl holds on tight as Jay starts to push it. After running in a full circle, Jay jumps on. [merry-go-round specs: Diameter: 3.197 m, I is an all steel construction covered in chipped leaded paint. The mass of the merry-go-round is 421 kg. Assume that the merry-go-round is a disk/cylinder. Earl specs: mass = 50 kg. Jay specs: mass = 45 kg.] a) Ifthe merry-go-round is traveling at 1.2 revolution per second, then what is its angular velocity in radians per second? b) If it took Jay 30 seconds to get the merry-go-round from rest up to its 1.2 revs, then what was its average angular acceleration while Jay was running? c If Earl sat on the edge of the merry-go-round, while Jay was running, what was the moment of inertia of merry-go-round/ Earl combination? (Assume Earl is small compared to the merry-go-round.) d) What torque did Jay apply to the Round-a-bout about the center of the merry-go-round? e If Jay was matching the tangential speed of the outside of the merry-go-round just before he jumped onto it, what was angular momentum of the merry-go-round/Earl/Jay combination? (Assume that Jay was right at the edge of the merry go-round before and after the jump.) What was Jay's linear speed after he jumped onto the edge of the merry-go-round? If Jay is barely hanging on, what is the magnitude of the force that Jay is applying? Earl then jumps up really high from the merry-go-round and projected him self face first on the rock and stick covered cement base. He sits up laughing; this was the best time he had had in years. However, when he jumped up, did the merry-go-round speed up, slow down, or stay the same speed? Justify the answer. Did this cause Jay to fall off also? Justify the answer. g) h) His mouth started to water as he Earl and Jay played for hours until Earl felt a need to see if his old home were still there. thought of the fresh baked pies his dad used to make. As he walked home, he felt a strange feeling, and after it passed he noticed he was back in his suit, and the office buildings were all around. He tumed quickly, but the playground was gone. He wondered if any of it really happened. Confused, he walked into the building. He was broken out of his fog when the security guard said good morning to him and added, "Mr Renard, did you hurt yourself? The guard pointed to his cheek to indicate the point of the injury. Earl felt his own cheek and smiled, "Not hurt, Sam." Earl paused briefly, laughed, and then added, "Just a reminder of the important things in life." Earl Renard, a man tired of his life when he woke up this morning, but renewed after a small respite spent in... The TwilightExplanation / Answer
(A) w = 1.2 rev/s = 7.54 rad/s
(B) wf = w0 + alpha t
alpha = 7.53 / 30 =0.25 rad/s^2
(C) I = (421 x (3.197/2)^2 / 2) + (50 (3.197/2)^2)
I = 665.6 kg m^2
(d) torque = I alpha
= 166.4 N m
(e) L = I w
w = 7.54 rad/s
I = 665.6 + (45 x (3.197/2)^2) = 780.6 kg m^2
L = I w = 5885.5 kg m^2 / s
(f) v = w r = 12.05 m/s
(g) F = m w^2 r = 4090 N
(h) jumping of Earl will increase the moment of inertia of system while angular momentum remaining same.
so L = Ii wi = If wf
wf = wi (Ii / If)
Ii /If < 1
hence wf < wi
so it will slow down.
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