Mass in projectile motion

[nm825]

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Can you tell me if I am right here? For projectile problems, we assume that mass does not affect length of the trip because g = ~ 10, right? For the sake of the MCAT, no matter the size of let's say a ball, it will always be accelerating towards earth at 10 m/s2.

Technically, this assumption is incorrect, right? G is technically different for every object, right? The earth's mass is so large that the effect of the ball's mass is negligible, right?

 

[dcamkl1]

The mass of an object is negligible when the problem says to ignore the effects of air resistance. In a vacuum (no air resistance), a bowling ball and a feather fall down and hit the ground at the same time.

If air resistance is considered, then the object with a larger contact area - to - mass ratio takes longer time.

 

[nm825]

The mass of an object is negligible when the problem says to ignore the effects of air resistance. In a vacuum (no air resistance), a bowling ball and a feather fall down and hit the ground at the same time.

If air resistance is considered, then the object with a larger contact area - to - mass ratio takes longer time.

I understand that, but why do the bowling bowl and the feather hit the ground at the same time? Its because the accelerating downwards at 10m/s^2. What I am asking is isn't it true that, technically, they won't hit the ground at the exact same moment because the force of gravity on each object is ever so slightly different? F=m1m2/r^2.

 

[dcamkl1]

Oh okay. Yes, both objects (when ignoring air resistance) experience the same g = -10m/s^2. In your gravitational force equation, the mass of the earth is so big, compared to the objects, that the mass of the objects have a miniscule effect. In the same formula, we see that Fgrav is inversely proportional to radius squared; however, when you you're on top of a mountain, the difference in radius between you and the earth is really insignificant. If it were significant, then you'd be floating around on the mountain.

So whether the bowling ball is heavier than the feather, or you're farther away from earth on a mountain than on land, "g" is still equal to -10m/s^2 for all practical purposes.

 

[grburst]

technically, they won't hit the ground at the exact same moment because the force of gravity on each object is ever so slightly different? F=m1m2/r^2.

So whether the bowling ball is heavier than the feather, or you're farther away from earth on a mountain than on land, "g" is still equal to -10m/s^2 for all practical purposes.

So in this case, it is air resistance that is the major contributor to the difference in flight times -- not the minute difference between their their F_grav = (G*(M_earth)*(m_object))/(r^2)'s?

 

[grburst]

Technically, this assumption is incorrect, right? G is technically different for every object, right? The earth's mass is so large that the effect of the ball's mass is negligible, right?

Also, I think I can make one clarification -- someone can correct me on this. The gravitational field produced by Earth creates vectors at all points in space (at all distances r). These vectors have units N/kg, or equivalently m/s^2. At a specific radius R from the source (which in the case of Earth, itself has a radius) every single one of these acceleration vectors has the same value. When R is small, these values are about 9.80 m/s^2. When you get further away, this value decreases proportionally to (1/r^2) (for example, at high altitudes or in outer space).

When you "place" an object somewhere in the gravitational field, you multiply the acceleration vector at that point by the mass of that object -- creating a force vector with units N. (Notice that the units cancel out: (N/kg) = (m/s^2) multiplied by kg gives you N). When two objects are at the the same altitude (so the same R, i.e. "drop them from the same height"), all of the acceleration vectors in that contour line are equal. So the F_grav's are what are "different" (because of differing masses), not the accelerations, unless you're comparing objects at different altitudes.

 

[HesitantManatee]

Can you tell me if I am right here? For projectile problems, we assume that mass does not affect length of the trip because g = ~ 10, right? For the sake of the MCAT, no matter the size of let's say a ball, it will always be accelerating towards earth at 10 m/s2.

Technically, this assumption is incorrect, right? G is technically different for every object, right? The earth's mass is so large that the effect of the ball's mass is negligible, right?

I am surprised no one has mentioned inertia, because that is the answer to you question. The acceleration of any object in any field (gravitational,electric, magnetic...ect) is determined by the force and the inertia (F=ma). Mass is the same thing as inertia. Force causes an acceleration whiles inertia resist the acceleration. In an electrical system the force will be determined by the charge. In a gravitational system unlike other systems the force is determined by the mass and the mass is also what resist the change. So a bowling ball will experience a greater gravitational force than a ping pong ball, but it will also have a greater inertia than the ping pong ball. The ping pong ball will experience less gravitational force than a bowling ball but it will have less inertia. In a gravitational system mass of the falling object never matters when determining acceleration. In other systems it does. Say a blowing ball and a ping pong ball with +1 charge were placed between a plate capacitor. What you would see is that the ping pong ball will have a higher acceleration than the bowling ball. This is because the force depend on the charge not the mass. But inertia is resisting change and it depend on mass. So the two objects will have different accelerations.

 

[nm825]

Thanks for the responses, but I think I figured out my question.

Assuming no other forces, gravitation force is equal to GMm/r^2 which is equal to ma. Solving for a shows that acceleration of an object due to gravity is always 10.

 

[mehc012]

Thanks for the responses, but I think I figured out my question.

Assuming no other forces, gravitation force is equal to GMm/r^2 which is equal to ma. Solving for a shows that acceleration of an object due to gravity is always 10.

Yes, exactly...while the force of gravity increases proportionally to the mass of the object, the force required to accelerate it also increases proportionally to the mass of the object...this means that ANY two objects at the same distance from the earth will experience the same gravitational acceleration.