This is due when you come to lab June 26 or 27 An astronaut is marooned on a dis

Question

This is due when you come to lab June 26 or 27 An astronaut is marooned on a distant planet and is attempting to repair his spaceship. In order to be successful in reaching orbit, the astronaut needs to know the acceleration due to gravity on this planet. (It is NOT 9.80 m/s2.) To determine this value, he constructs a frictionless inclined plane and slides an object down the incline. The object has a mass of 3.2 kg. The plane is inclined at 35°. The object starts from slides a distance of 1.72 m. The speed of the object is 2.98 m/s at this point. Calculate the acceleration due to gravity on this planet. (free body diagram - 10 pts, calculation - 10 pts, 20 pts total)

Explanation / Answer

Given m = 3.2 kg

distance s = 1.72 m

initial speed u = 0

final speed v = 2.98 m/s

from the   equation

v^2 - u^2 = 2 * a * s

2.98^2 - 0 = 2 * a * 1.72

acceleration a = 2.58 m/s

The acceleration down the inclined plane is given by

a = g * sin (theta)

2.58 = g * sin(35)

the acceleration due to gravity g = 4.498 m/s^2

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