Tarzan, with a mass of 60 kg, wants to swing across a ravine on a vine, but the

Question

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 ravine is 0.80 m higher than the cliff where Tar/an 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 Use g = 10 m/s^2. If Tarzan wants to red, the cliff on the far side, what is the minimum kinetic energy he must have when he leaves the cliff where he suits? Assuming Tarzan leaves the lower cliff with that minimum kinetic energy, what is Tamm's speed at the bottom of his swing? 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 ) The work done by the force of tension acting on Tarzan as he swings is Briefly justify your answer 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) energy is always conserved ,

therefore, kinetic energy(KE) + potential energy(PE) = constant

so, KE(initial) + PE(initial) = KE(final) + PE(final)

when tarzan reaches other side, KE(final) = 0

therefore, KE(initial) = minimum kinetic energy to reach other cliff = PE(final) - PE(initial) = mg(final height - initial height) = mg(0.8) = 60*10(0.8) = 480 KJ

b) again energy is conserved ;

change in potential energy = 0.5*mu2

mgh = 0.5*mu2

10*1 = 0.5*u2

u = 4.47 m/s

c) tension at the lowest point = mg + m*v2/R = 60*10 + 60*(4.47)2/10 = 719.8 N

d)negative (tension is against the direction of his displacement)

e) intial energy = final energy

KE(intial) + PE(initial) + WD(air_R) = KE(final) + PE(final)

WD(air_R) = mgh = 60*10*1.2 = 720 KJ

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