Pleas solve this A 200 g block is connected to a string that is 50 cm long and s

Question

Pleas solve this

A 200 g block is connected to a string that is 50 cm long and swings in a circle on a horizontal, frictionless table at 75 rpm. What is the speed of the block? What is the tension in the string? Now suppose that the Moon is held in orbit around the Earth by a large massless cable instead of by gravity. What would the tension on this imaginary cable be? Look up all relevant astronomical data and remember to cite your source. Draw free body diagrams for both situations (the Earth-Moon system and the block-string system).

Explanation / Answer

a)

v = R w = R (2 pi f) =0.50 * 2 * 3.1416 * 75/60 = 3.927 m/s

b)

T = m v^2/R = 0.200*3.9278*3.92/0.50 = 6.16 N

c)

period_moon = 27.321582 days = 2360585 s

==> w = 2pi/T = 2*3.1416/2360585 = 2.6617x10^-6 rad/s

m_moon =7.3477e22 kg

r_moon = 384400000 m

T = m r w^2 = 7.3477e22 * 384400000 * 2.6617e-6 * 2.6617e-6 = 2.00 x 10^20 N

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