How high above the ground would a 10 kg object needs to be to have the same GPE as the 30 kg object in the example

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How high above the ground would a 10 kg object needs to be to have the same GPE as the 30 kg object in the example

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Xavia 5 years 2021-07-18T06:58:12+00:00 1 Answers 21 views 1

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  1. Ladonna
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    2021-07-18T06:59:57+00:00
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    Answer:

    The 10 kg mass would have to be at a height 3 times that of the 30 kg mass to have the same gravitational potential energy as the 30 kg mass.

    Explanation:

    Gravitational potential energy, U = mgh where m = mass of object, g = acceleration due to gravity = 9.8 m/s² and h = height of object above the ground.

    Now, let U’ = gravitational potential energy of 10 kg mass = m’gh’ where m’ = 10 kg and h’ = height of 10 kg mass above the ground.

    So, U’ = 10gh’

    Also, let U” = gravitational potential energy of 30 kg mass = m”gh” where m” = 30 kg and h” = height of 30 kg mass above the ground.

    So, U” = 30gh”

    Since both object are supposed to have the same potential energy at a given height of the 10 kg mass,

    U’ = U”

    10gh’ = 30gh”

    h’ = 30gh”/10g

    h’ = 3h”

    So, the 10 kg mass would have to be at a height 3 times that of the 30 kg mass to have the same gravitational potential energy as the 30 kg mass.

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