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Quiz3B_Solutions - determine the speed of the skier at the...

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Quiz 3B DL SEC _ _ Grade: 04/26/10 Last 6 digits of student ID _ _ _ _ _ _ Last name, first name: ________________ ________________ First three letters of your last name _ _ _ Useful formulae: Δ E TOT = Q + W; Δ E th = mc Δ T; Δ E bond = ±| Δ m Δ H|; Δ PE grav = mg Δ h; Δ KE tr = ½ m Δ v 2 ; Δ PE ms = ½ k Δ x 2 Useful constants: g=9.8 m/s 2 1. A skier skis down a mountain slope as shown below, beginning with a certain speed v i . Suppose you can entirely neglect the effects of friction and air resistance. a) ) Can you change the speed at the bottom by increasing the mass, m , of the skier (without changing the height h or θ )? If so, how? If not, why not? Explain. You will be graded on the completeness and the quality of your explanation. No you cannot. Δ PE + Δ KE = 0 mg Δ h + 1/2m(v f 2 – v i 2 ) = 0 g Δ h + 1/2(v f 2 – v i 2 ) = 0 so the masses cancel out. Changing the mass has no effect. b) If the 60 kg skier is then initially at rest, and begins skiing down the slope from an initial height of 300 m,
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Unformatted text preview: determine the speed of the skier at the bottom of the slope. g Δ h + 1/2(v f 2 – v i 2 ) = 0 v f = sqrt[-2gDh] = sqrt[(2)(10)(300)] = sqrt[6000] ≈ 77 m/s h θ m 2. The potential energy graph shown here is similar in shape to the 2-d Higgs potential in particle physics. The horizontal axis here is given in meters and the vertical axis in Joules. a) At which point ( A or B ) would the force be greatest? Clearly explain your reasoning. Point A would have a greater force than point B. Force is related to slope, and the slope at B=0 whereas the slope at A is >0. [Note that it doesn’t matter which direction you think the force is (pos or neg slopes), just that the magnitude is bigger.] b) In which direction is the force at point C ? Explain . A C B The force at point C is to the left. Force is always in the direction to locally decrease the PE....
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