Tarzan, who weighs 820 N, swings from a cliff at the end of a 17.4 m vine that h

Question

Tarzan, who weighs 820 N, swings from a cliff at the end of a 17.4 m vine that hangs from a high tree limb and initially makes an angle of 25.5° with the vertical. Assume that an x axis points horizontally away from the cliff edge and a y axis extends upward. Immediately after Tarzan steps off the cliff, the tension in the vine is 740 N. Just then, what are (a) the force from the vine on Tarzan in unit-vector notation, and (b) the net force acting on Tarzan in unit-vector notation? What are (c) the magnitude and (d) the direction (measured counterclockwise from the positive x-axis) of the net force acting on Tarzan? What are (e) the magnitude and (f) the direction of Tarzan's acceleration just then?

Explanation / Answer

surface charge density of sphere 1 is q1/(4*pi*R1^2) = (0.5*10^-6)/(4*3.142*R1^2)

surfacec harge density of spehere 2 is q2/(4*pi*R2^2) = (2.5*10^-6)/(4*3.142*25*R1^2)

required ratio is 2.5*25/0.5=125

A) force from the vine is F1 = -740*sin(25.5) i + 740*cos(25.5)j

F1 = -318.6 i + 667.9 j

B) net force is Fnet = -318.6 i +(667.9-820) j = -318.6 i - 152.1 j

C) magnitude is V = sqrt(318.6^2+152.1^2) = 353.1 N

D) direction is theta = atan(152.1/318.6) = 25.5 degrees from below the -ve x-axis

but the required angle is 180+25.5 = 205.5 degrees

e) magnitude of accelaration a = F/m = 353.1/(820/9.81) = 4.22 m/s^2

F) direction is same as in the direction of force

direction is 205.5 degrees

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