By second law of motion, acceleration is produced by applied force on a body. Then value of acceleration due to gravity would be different for different bodies on Earth, as the gravity force for them is different?
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asked Dec 30, 2017 at 10:41
6 Answers
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No, they're the same. It's true the force of gravity on them is different, but their masses are also different and the acceleration works out to be the same.
$$F_\mathrm{gravity} = mg = ma\ \rightarrow\ g = a\quad \text{(independent of mass)}$$
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Let me show you how acceleration due to gravity using derived:
$F = G \frac {M_E m}{R ^2}$ where $G$ is the universal gravitational constant, $M_E$ is the mass of the Earth, $m$ is the mass of the body, and $R$ is the distance between the body and the centre of the Earth.
Now, $F = mg$.
So, $mg = G \frac {M_E m}{R ^2}$
Simplifying,
$$g = G \frac {M_E}{R ^2}$$
So, for a body on the earth's surface or even at a height negligible when compared to the earth's radius, the value of acceleration due to gravity $g$ is a constant.
AccidentalFourierTransform
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answered Dec 30, 2017 at 10:49
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Newton's second law of motion states that $F = ma$. The gravity for all objects on earth experience the same gravitational acceleration of $9.81\ \mathrm{ms}^{-2}$. Thus, force acted on an object would be $mg$ (weight), which is mass X gravity. However, since $F = ma$, and force on an object is $mg$ (weight), $mg = ma$, so acceleration $a =$ gravitational acceleration $g$, of $9.81\ \mathrm{ms}^{-2}$.
acceleration is produced by applied force on a body
True, so all objects at rest experience the sole and only force of gravity, hence all have a downward acceleration of $9.81\ \mathrm{ms^{-2}}$.
AccidentalFourierTransform
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answered Dec 30, 2017 at 10:50
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The force on a larger body would be greater, but because this body is also greater in mass, its acceleration is the same as every other body on Earth (a = F/m).
The force of gravity on an object is directly related to its mass. However, an object's acceleration is inversely related to its mass.
Example:
Object A is 5 kg. Let's say the force of gravity on it is 49 N.
F = ma
a = F/m = 49N / 5kg = 9.8N/kg (this is Object A's acceleration).
Now let's increase Object A's mass by 2:
Object A is now 10kg, and since force is directly related to mass, force is now 98 N.
F = ma
a = F/m = 98N / 10kg = 9.8N/kg
As you can see, Object A's acceleration remains constant. Increasing an object's mass only changes the force on an object. This is why all objects on Earth have the same gravitational acceleration (ignoring air resistance, and assuming they are all an equal distance from Earth's center).
answered Dec 30, 2017 at 13:29
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$\begingroup$ Minor correction: gravity is not the same everywhere on earth. $\endgroup$ Commented Dec 30, 2017 at 13:53
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You are forgetting the $m$ in Newton's 2nd law:
$$\sum F=ma$$
Yes, some bodies feel a stronger gravitational force, so $\sum F$ is larger. But then they also have a larger mass $m$. Doubling one will double the other. So $a$ doesn't change.
The acceleration $a$ turns out to alway be equal to $a=-9. 82\mathrm{\frac m{s^2}} $. This numerical value is usually given the symbol $g$.
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The value of g is same for all object Because g= GM/r
gvaries depending on where you are on earth (or another celestial body). $\endgroup$