The bigger the mass, the smaller the acceleration?

Question

then why do all objects accelerate towards the ground at the same rate regardless of their mass? Why don't bigger masses fall slower than smaller ones? Infact the opposite happens! why?
please explain as simply as possible for a GCSE student

Answer 1

Don't listen to HarperDL, please.



You've hit upon a fantastically important question, by the way. There is no obvious reason why "gravitational mass" should be the same as "inertial mass", but it appears that they ARE the same.



By "gravitational mass" I mean the force that gravity exerts on a given mass (given by, for example, F = m*g, where "g" is the strength of the gravitational field wherever the mass "m" is sitting). Notice that if you double the mass here, the force doubles; if you triple the mass, the force triples, and so on.



By "inertial mass" I mean the mass which tells you how the object is going to accelerate for a given force, and this is given by Newton's 2nd Law: a = F/m. Here, "a" is the acceleration of the object, "m" is the mass, and "F" is the force that's doing the accelerating.



If you say that F = m*a, and that F = m*g, then m*a = m*g, and the mass cancels out. For gravity, no matter what mass you're dealing with, the acceleration will be the same "g" for a given situation!



This is NOT an obvious result, and you've asked a very good question. People are still trying to figure out if gravitational and inertial masses are always exactly the same; so far, it appears that they are.

Answer 2

Because the FORCE of gravity is proportional to the mass of the two objects (i.e. earth and object).



So a heavier object doesn't accelerate slower because the force of gravity is stronger (than a lighter object).



Here is the constant gravity approximation:



F = mg = ma



So no matter WHAT the mass:



a = (mg) / m = g



Here are Newton's equations for gravity:



F = GMm / r^2



again:



assuming that everyting except m is constant, then you can write the acceleration:



GMm/r^2 = ma

-->

a = GM/r^2



(M - mass of the earth, or whatever object you are experiencing gravity due to).



Edit:

since everyone else seems to be confusing you, here is a simple result. Let's look @ the acceleration due to charged particles (electromagnetic field).



Both the proton AND electron have the same charge and therefore experience the same force due to an electric field. However, the proton WILL accelerate at a slower rate than the electon because the electromagnetic force is NOT dependent on the mass, it depends on the charge (something completely independent of mass...well that's debatable, but for classical physics certainly the case).



here are the equations:



F = kQq/r^2 <-- looks just like Gravity, except q's instead of m's



So now:



we have:



kQq/r^2 = ma

-->



a = kQq/(mr^2)



(m's don't cancel like with gravity, so the larger the mass, the smaller the acceleration)

Answer 3

Good question. F = ma indicates that for a fixed force ma is also fixed. You can have a large mass x a small acceleration or viceversa. If you push with all your might you can accelerate a small car faster than a big car. Gravity is different because a large mass weighs more than a small mass and the weight is the force in F = ma. Also consider that in a vacuum a rock and a feather fall at the same rate. A single carbon atom would fall at the same rate as a solid pure carbon diamond. The earth attracts each atom the same whether or not they are joined together or falling individually. If you and a friend skydived from a plane you would fall at the same rate whether you joined hands or let go.

Answer 4

The answer to your question probably will not make sense until you get to and understand General Relativity. But, the answer is gravity is not a Force. Gravity is an acceleration that results from mass warping Space-Time.



What this means is if we look at Newton's 2nd Law. Gravity is the A term not the F term in:



F = MA



For all masses on earth A = 9.8 m/s^2 ====> All masses accelerate in free fall at the A for gravity.





If you drop 2 Pinewood racers, both fall at the same acceleration. The more massive cars are faster on a slope because they generate more force and that gives them additational force over that needed to over come friction in the wheels to accelerate the car down the slope

Answer 5

Weight as in W = mg is mass m circumstances a g value that has the units m/sec^2, that are the units for acceleration. So we call g the acceleration simply by gravity. yet, and this could be a great yet, this is not consistent as you propose. g = GM/R^2 in actuality; the place G is a real consistent, M is the mass source of the gravity field, and R is the middle to center distance between regardless of mass is being weighed m and the source mass M. If r is Earth's radius and h is the top of m above floor, then R = r + h. As you will discover if h gets larger and the gap above floor gets bigger, R additionally gets larger. this means that g gets smaller because of the fact that M is Earth's mass and caught. And there you're, g varies "depending on its distance from the floor." Your confusion comes from poorly written textbooks who declare gravity acceleration g is persevering with. this is not. g is persevering with in basic terms for a fastened place R and mass M...in any different case g varies. whilst i exploit g = 9.eighty one m/sec^2 in my solutions, it particularly is a uncomplicated form we see in textbooks, I very almost continuously specify "close to Earth's floor," which fixes R and M for a given question. wherein case, g is in actuality 9.eighty one m/sec^2, yet in basic terms for those circumstances. in case you have been to crunch g = GM/R^2 for the Moon mass M and radius R, you will locate that g is a pair of million/6 that of Earth's g. So once you're slightly obese in the worldwide, you will be able to desire to weigh in at a million/6 your Earth weight on the Moon.

Answer 6

force = Ma, if the force is downwards due to acceleration Ma = Mg so you have acceleration due to gravity, the mass of an object is immaterial as they all fall at 9.81 ms-2, most objects achieve a velocity of about 54 ms-1 (120 mph) air resistance stops them travelling any faster.

s =ut + 1/2at^2 is the equation, and ignore the ut as there's no upward thrust with gravity.

Answer 7

cuz of gravity being the same. the keyword in ur question is 'towards the ground' bigger masses actually accelerate faster because gravity is pulling on them more. That's why heavier pine wood derby cars ALWAYS win