Equal and Opposite Forces

[ln(]

I was wondering how Newton's Third Law is related to contact and normal forces. What about at an angle? The normal force is equal only to perpendicular force exerted downwards, perpendicular to the angle but does the addition of the perpen. force and the the parallel force to the angle equal weight? So does the law still fundamentally apply? But they are not exactly the same thing...?

Also, on forces that act at a distance, like gravitational forces, what is the reaction force? When the Earth pulls on you, calculated by f grav = m * g, does the Earth feel the same force towards you?

 

[A.T.]

does the addition of the perpen. force and the the parallel force to the angle equal weight?

Yes.

 

[D H]

Also, on forces that act at a distance, like gravitational forces, what is the reaction force? When the Earth pulls on you, calculated by f grav = m * g, does the Earth feel the same force towards you?

Yes.

does the addition of the perpen. force and the the parallel force to the angle equal weight?

If you tautologically define weight as the sum of the perpendicular and parallel forces (normal force and friction), the answer is "yes".

Otherwise the answer is "No".


There are two competing definitions of weight in physics: mass times the acceleration measured by an ideal accelerometer, and mass times acceleration due to gravity. Your vector sum is very close to the first definition. However, you have volume as well as mass. You displace air, and the weight of that displaced air buoys you upwards a tiny bit. You are displaced by one Earth radii from the center of the Earth. Your gravitational acceleration toward the Sun and Moon are not quite the same as that of the Earth as a whole. The difference between these are tidal forces. The tides come into play in another way. The Earth as a whole undergoes tidal distortions. These Earth tides lift you up / drop you down by about half a meter over about a 12 hour interval. That first definition of weight, called apparent weight or scale weight by some, is the sum of the tidal forces, the buoyant force and the forces exerted by the ground.

Whatever you want to call it, scale weight is not equal but opposite to weight defined as mass times gravitational acceleration. The Earth is rotating, one revolution per sidereal day. An object at rest on the surface of the Earth is thus undergoing (nearly) uniform circular motion about the Earth's axis of rotation. This means the net force on an object at rest on the surface of the Earth is not zero.