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# AP Physics Potential Energy

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A month ago
 AP Physics Potential Energy 3. Planet X-39 has a mass equal to 1/3 that of Earth and a radius equal to 1/3 that of Earth. If v is the escape speed for Earth, what is the escape speed for X-39? Read 90 times 2 Replies

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Anonymous
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A month ago
 Escape velocity is the minimum velocity needed for an object to overcome the gravitational force exerted by the planet. It is given by the following relation :V = √(2GM/r)where,V - escape velocityG - gravitational constantM - mass of planetr - radius of planetWe can take the ratio of escape velocities as follow :V1/V2 = √(M1/M2) * √(r2/r1)where, 1 is for Earth and 2 is for X-39given that,V1 = VM2 = (1/3)*M1 => M1/M2 = 3r2 = (1/3)*r1 => r2/r1 = 1/3therefore,V/V2 = √3 * √(1/3) = 1ie. V2 = Vie. Escape velocity of X-39 is same as that of Earth.
Anonymous
wrote...
A month ago
 The escape speed for a planet is determined by its mass and radius, and it can be calculated using the formula:v = √(2GM/R)where G is the gravitational constant, M is the mass of the planet, and R is its radius.Since X-39 has a mass equal to 1/3 that of Earth and a radius equal to 1/3 that of Earth, the escape speed for X-39 can be calculated as follows:v = √(2G * (1/3M) / (1/3R)) = √(2G * M / R) / √(1/3) = √(2GM/R) / √(1/3) = v / √(1/3)So the escape speed for X-39 is 1/√(3) times the escape speed for Earth.
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