Sam is stranded on an unknown location in space. To alleviate his boredom Sam sw

Question

Sam is stranded on an unknown location in space. To alleviate his boredom Sam swings a pendulum at 10° angle of amplitude, with a string length of 81 cm. Sam finds period to be 2.9 seconds.What is the gravitational acceleration, g, on the unknown planet? Sam remembers the gravitational acceleration for several locations in space. (Phobos = 0.0057 m/s2 , Pluto = 0.42 m/s2 , Titania = 0.38 m/s2 , Europa = 1.31 m/s2 , Moon = 1.622 m/s2 , Mars = 3.77 m/s2 , Venus = 8.87 m/s2 ) Which location is Sam most likely stranded on (closest value)? What is the %Error for gravitational acceleration? Would the period change if Sam swings the pendulum at higher angle of amplitude (assume in vacuum)?

Explanation / Answer

accleration due to gravity of space is

T = 2 pi root L/g

g =4 pi^2 L/ T^2

= 4 pi^2 ( 0.81)/( 2.9)^2

=3.79 m/s^2

so same standaed on Mars planet

percentage of error

g- g'/g = 9.8-3.77/9.8 =0.61 or 61%

No period does not change because period does not depend on the angle

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