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

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.

no

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