If mass increases, what must happen to the force in order to achieve that same changes in motion?

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The answer to your question comes from Newton's Second Law of Motion. Newton's Second Law, in simple terms, states,

When a force acts on an object, the object accelerates in the direction of the force. If the mass of an object is held constant, increasing force will increase acceleration. If the force on an object remains constant, increasing mass will decrease acceleration. In other words, force and acceleration are directly proportional, while mass and acceleration are inversely proportional. ( How Newton's Laws of Motion Work" 29 July 2008.)

Let's use an example. Suppose you have a concrete block weighing five pounds. To move the block, you push or apply force to one side, pushing the block forward. The more force you place on the block, the faster the block will move. Suppose you have a twenty-pound block to move. Common sense tells you that you will need to push harder or apply a higher amount of force to move the block in the direction you want it to go. Acceleration is the speed at which the object moves.

From this example, we can deduce that the higher the weight of the object, the more force you will need to apply to move the object. Mass is the amount of matter in an object, and we calculate mass by weighing the object. Two objects can be the same approximate size of each other and have very different weights. For example, a softball is the same approximate size as a cannonball. Because the composition of the materials used to construct a softball is so different from that of a cannonball, the force required to move a softball will be less. The two objects have different densities and mass, even though they may be identical in size and shape.

The answer to your question using Newton's Second Law of Motion is as follows. If the mass increases, the force must increase proportionally to move an object in a direction.

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