Why is acceleration of an object inversely proportional to its mass, but directly proportional to force?


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A force is needed to readjust the speed of an object, and also the adjust of rate is the acceleration. And mass can be thought of together a home of an object with which it resists acceleration (this is referred to as inertia, https://en.wikipedia.org/wiki/Inertia for further reading). The relationship between these quantities is then $vec F= m cdot vec a$.

You are watching: Acceleration is inversely proportional to mass


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By convention we decide the mass is an crucial attribute of an object (since it steps the amount of "stuff" in the object), and then the equation

$displaystyle a = frac F m$

establishes the acceleration is proportional to used force but inversely proportional to mass. This renders intuitive feeling - the much more "stuff" over there is in one object, the more complicated it is to accelerate it.

But we could instead decide that the mutual of mass was the necessary attribute (in the same method as we occasionally talk about the electric conductance of things rather 보다 its resistance). Let"s speak to the mutual of mass "ssam", and denote it by "w". Climate we would have

$a = F w$

In various other words, acceleration is now straight proportional come both applied force and also "ssam".


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answered may 23 at 16:13
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gandalf61gandalf61
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Force is price of adjust of momentum:

$$ vec F = fracdvec pdt$$

and $vec ns = mvec v$. So:

$$ vec F = mfracdvec vdt + dot m vec v$$

With $dot m= 0$ and also $vec aequiv dvec v/dt$:

$$ vec F=mvec a $$


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answered might 23 at 18:47
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We recognize $F = m * a$ . Climate , you rearrange the equation.

a = $frac F m$.

Case 1: Considering F to be const :

Acceleration is inversely proportional to mass.

Case 2: Considering m to be constant:

Acceleration is straight proportional come Force.

It will certainly be a different question if friend ask why is F = m *a. Friend can check this price of mine if you perform have.https://sdrta.net/a/638836/287551

Hence proved. Perform let me understand if you have any kind of difficulty.


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answered might 26 at 14:32
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