9EarthTplanet Part 8 of 8 Analyze Tamsen and Vera Imagine visiting another plane

Question

9EarthTplanet Part 8 of 8 Analyze Tamsen and Vera Imagine visiting another planet, planet X, whose gravitational acceleration, sx is different from that of Earth's. They envision a pendulum, whose period on Earth is 2.243 s, that is set in motion on planet x, and the period is measured to be 1.300 s. What is the ratio of 9x/gEarth? Neglect any effects ca by air resistance. " 2.976 9E Ir the average density of planet X is equal to Earth's average density, Pe, what is the ratio of Rx/Re, where Re is the mean radius of Earth? (Assume both planets are spherical. Recall that -m/V and Vsphere = 4tr3.) 3 Rx Your response differs from the correct answer by more than 10%. Double check your calculations. For the pendulum to have the same period on planet X as on Earth, would the string length need to be longer xc 0 or shorter?

Explanation / Answer

acceleration due to gravity is given by

g=GM/R2

Time period is given by

T=2pi*sqrt(L/g)

a)

gx/ge =(Te/Tx)2 =(2.243/1.3)2=2.977

b)

Rx/Re =sqrt(ge/gx)=sqrt(1/2.977)=0.58

c)

Longer

_________________________________________________

From

A=Aoe-bt/2m

Given A=Ao/2

(1/2)=e-bt/2m

Ln(1/2)=-bt/2m

t=ln(2)*2*(0.3*10-3)/0.1

t=4.16*10-3s

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