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Dynamics and uniform circular motion

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I am working on the unit review questions in my textbook in order to prepare for a major assessment this week. Can someone please help me? Thank you very much! :)


1) Obtain the value of g at the surface of Earth using the motion of the Moon Assume that the Moon's period around Earth is 27 d 8 h and that the radius of its orbit is 60.1 times the radius (6.38 x 10^6 m) of Earth.


2) In a disaster film, an elevator full of people falls freely when the cable snaps. The film depicts the people pressed upward against the ceiling. Is this good physics? Why or why not?


3) A 1.12 m string pendulum has a bob of mass 0.200kg. What is the magnitude of tension at the bottom of the swing if the pendulum is moving at 1.20m/s.

[Currently, I have only learnt uniform circular motion where there is constant speed and constant radius throughout. But for this pendulum question, the bob is definitely not in uniform circular motion because the speed is changing at every point. Can I still use the formula Fc = mv^2 / r ? Why or why not?]

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First question, why is the direction of the tension given 27 degrees below the horizontal, not 27 degrees above the horizontal? (The tension force should point AWAY from the climber, right? i.e. 27 degrees above the horizontal) Does that matter?


Second question, from the diagram I can see that there seems to have 2 ropes and so 2 tension forces? Is the tension on each rope 729N or do they "sum up" to 729N? Or is there just 1 rope?


Thirdly, the answer provided in my textbook is 729N [27.0 degrees above the horizontal]. I can't make the slimmest sense out of it. Shouldn't the force exerted by the cliff on the climber's feet be horizontal?

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