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Weight = mass x gravity. Therefore, this will happen as long as gravity doesn't change.

Q: When does an object with twice as much mass as another weigh twice as much?

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weight = mass * gravity, so as long as the force of gravity is the same on both, an object with twice the mass will weigh twice as much.

inertia

In the same gravity, downward force (weight) is directly proportional to the mass. (F=mA) If you had two objects of equal mass, and combined them, the weight would be the same as the total of the two.

If the object doesn't move to another planet while you double its mass,its weight will also double.

The heavy and light objects travel at the same rate because there are two competing factors that cancel each other out. The force of gravity is greater on the heavier object than on the lighter object, proportional to the object's mass. This means that an object with twice the mass will be pulled toward the earth with twice the force. On the other hand, the acceleration is proportional to the force divided by the mass. This means that an object that is twice the mass of another object will be accelerated twice as slowly as the lighter object given the same force. So in order for an object with twice the mass to move at the same rate as the lighter object, the heavier object must be submitted to twice the force. And this is exactly what the force of gravity does. For more information on gravity and forces, you might try the Physics section

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weight = mass * gravity, so as long as the force of gravity is the same on both, an object with twice the mass will weigh twice as much.

inertia

In the same gravity, downward force (weight) is directly proportional to the mass. (F=mA) If you had two objects of equal mass, and combined them, the weight would be the same as the total of the two.

it is equal to the mass of the original object

If the object doesn't move to another planet while you double its mass,its weight will also double.

The heavy and light objects travel at the same rate because there are two competing factors that cancel each other out. The force of gravity is greater on the heavier object than on the lighter object, proportional to the object's mass. This means that an object with twice the mass will be pulled toward the earth with twice the force. On the other hand, the acceleration is proportional to the force divided by the mass. This means that an object that is twice the mass of another object will be accelerated twice as slowly as the lighter object given the same force. So in order for an object with twice the mass to move at the same rate as the lighter object, the heavier object must be submitted to twice the force. And this is exactly what the force of gravity does. For more information on gravity and forces, you might try the Physics section

An easy way to do that is to weigh the object. In principle, the mass can be derived from the weight.

On Earth, you weigh it. In space you must determine its inertia ... usually done by noting its orbit around another object.

The idea here is that if - for example - one object has twice the inertia than another (i.e., twice the "inertial mass"), its reaction to gravity (its "gravitational mass") will also be twice as much. Thus, the gravitational mass and the inertial mass are directly proportional to one another, and you can just as well choose the proportionality constant to be one, making them equal.

The only "weigh" to determine the mass of an object is to compare it with the mass of a known object. The mass of an object is determined by force and acceleration.

As it turns out, inertial mass is equivalent to gravitational mass, so if you simply weigh an object, you can determine both its weight and its inertia. These are always in direct proportion; twice as much weight equals twice as much inertia. The main difference is that weight does change in different locations; an object can become weightless while in orbit, while inertia does not change. But here on the surface of the Earth, it is very simple to weigh an object and get a meaningful result which applies both to gravitational mass and inertial mass. If you were in orbit, then the problem becomes a bit trickier.

Twice the mass --> twice the kinetic energy.