# Why does the mass of an object not affect its acceleration on an inclined plane?

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Wouldn’t Newton’s second law mean the acceleration is indirectly proportional to the mass?

In: Physics

This comes back to the concept that if you drop objects of different masses in a gravitational field they will all fall at the same rate.

It might not seem intuitive that is how it works, because as you point out something with a greater mass will have a greater attraction under the force of gravity. That is why more massive things are heavier, right? But more massive things also have greater inertia or resistance to acceleration.

It turns out that the increased inertia exactly cancels out the increased attraction of gravity, so a feather and a dumbbell fall at the same speed in a vacuum.

The force is proportional to the mass. An object that weights 2kg will be subject to twice as much force as an object that weighs 1kg(assuming they’re the same distance from the Earth). But force is mass * acceleration. 1 newton is the force needed to accelerate 1 kg 1m/s^2. So even though it’s twice as much force, it needs to move twice as much mass, so it cancels out and ends up being the same acceleration.

>Wouldn’t Newton’s second law mean the acceleration is indirectly proportional to the mass?

Yes, acceleration would be inversely proportional to the mass if the force is constant.

In this case the force is not constant. It is gravity and according to Newton’s law of universal gravitation f= G m1 m2/r^2 where G is the universal constant, m1 is the mass of the object, m2 is the mass of earth and r is the distance to the center of earth.

So the force is directly proportional to the mass. The result is the acceleration from gravity is independent of mass. If you look at formaulas for acceleration the mass will be cancled out.

Because f = m a => a=f/m or in this case a= f/m1 we can create it as a= Gm2 /r^2 Close to the earth’s surface Gm2 /r^2 is equal to about 9.8m/s^2. This is freefall acceleration on earth, that is when gravity is the only force. On an inclined plane, only a percentage of that force will accelerate the object. The force will still be directly proportional to the mass.