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This is kind of a simple question.

I was basing it off Newton's second law, $$F=ma$$

With the same applied force, an object with more mass will accelerate less.

However, what if two objects of unequal mass are pushed downward?

That factors in gravity, and we know that objects with more mass fall faster in air. Essentially, which one would accelerate quicker?

Do we follow Newton's law, or base the answer off gravity?

Or would the object with more mass accelerate less initially, then begin to speed up? Thanks!

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    $\begingroup$ Re, "Objects with more mass fall faster in air." That is not generally true because its the shape of an object that determines how it will interact with the air. I'm not an aeronautical engineer, and I can't really explain, but I can imagine, for example, that a tiny, streamlined, metal dart might fall faster than a giant beach ball, even though the beach ball might have more mass than the dart has. $\endgroup$
    – Solomon Slow
    Commented Jun 12 at 15:12
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    $\begingroup$ How are the two masses arranged? $\endgroup$
    – Bob D
    Commented Jun 12 at 15:29
  • $\begingroup$ @user386598 "what if two objects of unequal mass are pushed downward" Why do you think downwards makes Newton's second law different from other directions? $\endgroup$
    – Vincent Thacker
    Commented Jun 12 at 16:46
  • $\begingroup$ I don't think it makes it different, I think that it adds another layer of complexity to the problem because the problem is now dealing with multiple forces (contact and gravity). $\endgroup$
    – user386598
    Commented Jun 12 at 22:04

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and we know that objects with more mass fall faster in air.

That is not necessarily the case. For two independently falling objects, the object subjected to the greater net force (force of gravity minus the opposing air drag force) will have the greater acceleration.

The mass of the object determines the force of gravity acting down on the object. But the shape and surface characteristics of the object, which is independent of the mass, determines the opposing air drag force.

But the example you have given does not involve independently falling objects. Assuming one object is above the other, then logically the only way one object can accelerate more quickly is if it's the lower object. And the only way that can happen is if the net force acting on the lower object is greater than the net force acting on the upper object.

Complicating matters is that the drag force acting on the upper object depends on the degree to which its surface area is blocked from air resistance by the lower object. And that will change if and when the objects begin separating. Moreover, prior to the objects separating, if in fact they do, both objects will experience some portion of the applied pushing force. If separation does occur, then only the upper object will experience the pushing force.

Bottom line, without additional details regarding the two objects and their arrangement, there are too many variables in your example to determine whether or not the lower object will accelerate faster than the upper object.

Hope this helps.

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  • $\begingroup$ I should have mentioned this before, but I am taking 8th grade physical science currently and I do not really understand the concept of a free body diagram. Would you mind quickly explaining what the above answer means? $\endgroup$
    – user386598
    Commented Jun 12 at 22:46
  • $\begingroup$ @user386598 That’s ok. I’ll include some diagrams in my answer $\endgroup$
    – Bob D
    Commented Jun 12 at 23:20
  • $\begingroup$ @user386598 A free body diagram of a body is one where you "free" the body of any physical contact with any objects and replace those objects with the forces and torques that they exert on the body. $\endgroup$
    – Bob D
    Commented Jun 13 at 13:50
  • $\begingroup$ @user386598 After further consideration, I have entirely revised my answer. $\endgroup$
    – Bob D
    Commented Jun 13 at 20:40

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