Marvin's challenge
Marvin the Martian places a block on a frictionless plane that makes a 60 degree angle with the ground. He releases the block and measures the acceleration. He then sends you a radio message that arrives a few minutes later. In this message he challenges you to place a block on a frictionless plane and adjust the plane's angle so that your block's acceleration is equal to his. At what angle do you set the plane? (Use: 9.8 meters per second squared as Earth's surface gravity; 3.7 meters per second squared as Mars' surface gravity.) Choose the closest integer angle value.
The answer is 19.
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1 solution
The block acceleration a = Force/mass.
The force is mgSin(A)
(A) = plane angle. This reduces to a = gSin(A)
You have to adjust the plane's angle so that your block's acceleration gsin(A) equals Marvin's gSin(A)
We have g (Mars) = 3.7; g (Earth) = 9.8 Marvin's block angle (A) = 60 degrees. Sin(60) = 0.866
9.8sin(A) = 3.7(.866)
The plane's angle on Earth equals the inverse sine of [3.7(.866)/9.8]
= invSin (0.327) = 19.08 rounded off to 19 degrees