PROBLEM 4 - 8 points Vine is 10 m long Tarzan, with a mass of 60 kg, wants to sw

Question

PROBLEM 4 - 8 points Vine is 10 m long Tarzan, with a mass of 60 kg, wants to swing across a ravine on a vine, but the cliff on the far side (the left side) of the 2 ravine is 0.80 m higher than the cliff where Tarzan is now ---_- and 1.8 m higher than the - lowest point in his swing Consider Tarzan as a simple particle (no rotation and no shape changes) so that these height changes apply to his center of mass Use g = 1 0 m/s2 T- 0.8 m 1.0 m Path of Tarzan's center of mass [2 points] (a) If Tarzan wants to reach the cliff on the far side, what is the minimum kinetic energy he must have when he leaves the cliff where he starts? 2 points] (b) Assuming Tarzan leaves the lower cliff with that minimum kinetic energy, what is Tarzan's speed at the bottom of his swing? [2 points] (c) If Tarzan swings along a circular arc of radius 10 m, what is the tension in the vine when Tarzan reaches the lowest point in his swing? (Neglect the mass of the vine.) [2 points] (d) For parts (a) - (c), above, you should have assumed no air resistance acted on Tarzan. It turns out that air resistance is important here (but don't change your answers above!), and Tarzan, when he leaves the lower cliff with the minimum kinetic energy found in (a), reaches a maximum height of just 1.2 m above his lowest point. Find the work done by air resistance during the swing for this case

Explanation / Answer

(A) Applying energy conservation,

PEi + KEi = PEf + KEf

m g (1) + KE = m g (1.8) + 0

KE = 60 x 9.8 x 0.8 = 470.9 J .......Ans

(B) m g (1) + 470.9 = 0 +m v^2 /2

(60 x 9.81) + (470.9) = 30 v^2

v =5.94 m/s

(C) T - m g = m v^2 / L

T = 60 (9.81 + 5.96^2/10) =800.5 N

(d) Work done by gravity + work done air resistance = change inKE

- 60 x 9.81 x 0.2 + W = 0 -470.9

W = - 353.3 J

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