Question Video: Describing the Gravitational Potential Energies of Objects in Deep Space | Nagwa Question Video: Describing the Gravitational Potential Energies of Objects in Deep Space | Nagwa

# Question Video: Describing the Gravitational Potential Energies of Objects in Deep Space Physics • First Year of Secondary School

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A speck of dust with a mass of 0.22 g is at a distance of 1250 m from a tiny shard of ice that has a mass of 1.5 g. Both of the objects are located in deep space, extremely far away from any stars or other objects of any kind. The gravitational force that the objects exert on each other is negligible, as is the gravitational force on either the speck of dust or the shard of ice from any other objects. Which of these statements about the gravitational potential energy of the speck of dust and the shard of ice is correct? [A] The gravitational potential energies of both objects are zero. [B] The gravitational potential energies of both objects are equal and nonzero. [C] The gravitational potential energies of both objects are nonzero, but they are not equal.

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### Video Transcript

A speck of dust with a mass of 0.22 grams is at a distance of 1250 meters from a tiny shard of ice that has a mass of 1.5 grams. Both of the objects are located in deep space, extremely far away from any stars or other objects of any kind. The gravitational force that the objects exert on each other is negligible, as is the gravitational force on either the speck of dust or the shard of ice from any other objects. Which of these statements about the gravitational potential energy of the speck of dust and the shard of ice is correct? (A) The gravitational potential energies of both objects are zero. (B) The gravitational potential energies of both objects are equal and nonzero. Or (C) the gravitational potential energies of both objects are nonzero, but they are not equal.

To answer this question, let’s start by briefly recalling that we can use gravitational potential energy, or GPE, to calculate changes in the energy of an object in a gravitational field. We can also recall that the gravitational potential energy transferred to increase the height of the position of an object by ℎ is given by GPE equals 𝑚𝑔ℎ, where 𝑚 is the mass of the object and 𝑔 is the gravitational field strength at the position of the object.

Notice that both of these qualitative and quantitative descriptions of GPE refer to a gravitational field. This is key to answering this question. To help us think about this further, let’s clear some room on screen.

Here, we’re considering two tiny objects out in deep space. We were told that their gravitational influence on one another is negligible, or essentially zero. So we know that these objects are too tiny and far apart to influence each other gravitationally. And it would be incorrect to think that either object has potential energy due to its own gravitational field. So while, yes, a lone speck of dust would produce a very weak, but still nonzero, gravitational field around it, we have to remember that an object’s GPE is always measured with respect to some other position within the field. And an object can’t move relative to its own gravitational field.

Now, we were also told that there is negligible, or basically zero, gravitational influence on the two objects from any other object, since they’re isolated in deep space. Thus, we can reason that there is effectively no external gravitational field around either object or, more accurately, that the strength of the field is zero. With a strength of zero, the field can do no work. And no gravitational potential energy can be transferred to an object.

Note that if we try to use a field strength of zero in the formula for GPE, the entire expression simply equals zero. Therefore, the best answer is (A). The gravitational potential energies of both objects are zero.

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