If you fully understand that you don’t really have a problem. You know that it takes just as much force to accelerate the space station by 100 mph in its orbit in space as it would on the surface of the earth, friction not included.
This question actually touches on a complex physics principle. The force an object feels while sitting on the Earth is due to the gravitational mass of the Earth. The resistance an object has to a change in velocity is its inertial mass. My understanding is that all comparisons we have made have said these two masses for any given object are exactly the same, but by our understanding of the universe they don’t have to be.
Good point. Hey you relativistic physicists how about this? An object going fast takes a bigger force to accelerate by a certain amount than one going slower. It’s as if its mass has increased. Now, does that apparent increase in mass affect the deflection from its path by a lateral force as well as an increase in the magnitude of its velocity?
Handy link, thanks.
You are correct, of course, I should have been thinking of Newtons, not dynes.
The now mostly discredited concept of relativistic mass resulted in different masses for a moving object.
Longitudinal mass = gamma[sup]3[/sup]m[sub]0[/sub]
Transverse mass = gamma*m[sub]0[/sub]
Longitudinal force = gamma[sup]3[/sup]m[sub]0[/sub]a[sub]l[/sub]
Transverse force = gammam[sub]0[/sub]*a[sub]t[/sub]
In between these two directions the force depends on some kind of a matrix.
I love these layperson explanations. 
So we no longer say mass changes with acceleration?
I don’t know if I’m remembering incorrectly that that’s the way I learned it or not, but I think that’s the way I learned it. But it’s wrong, right?
-FrL-
Sorry. Gamma just equals (1 – v[sup]2[/sup]/c[sup]2[/sup]) [sup]-1/2[/sup]. The minus ½ exponent just means the square root of one over what’s in the parentheses. So as velocity increases gamma gets larger and larger.
Longitudinal just means in the same direction and transverse means at right angles. So to obtain a given acceleration in the L direction requires mucho more force than in the T direction. However this isn’t evident until the object is moving close to the speed of light.
Relativistic mass isn’t necessarily wrong, it just isn’t necessary. And the term can cause a lot of confusion. For instance a lot of folk think an increase in RM would cause gravity to increase, and if the object is going fast enough it could turn into a black hole.
This is totally wrong and can be easily seen by imagining that you were riding on the object. You are perfectly allowed to consider yourself at rest and the rest of the universe to be moving, so there is no way you’d find yourself getting heavier and heavier.
The vast majority of physicists would not use the term relativistic mass except as shorthand when talking to other physicists or maybe when trying to sell books to non physicsts.
I should also have mentioned that as an object reaches relativistic velocities it takes less force to accelerate an object in the T direction, but it still takes a larger force than if the object was at rest. This can be somewhat unintuitive.
It might be worth mentioning that gravity is an acceleration.
The mass of an object remains constant. It’s weight is the force of gravity acting on its mass. Gravity is dependent on the mass of an object, the mass of any other objects around the object and the distance between objects.
This depends on your reference frame though, right? From the frame of the mover it makes not difference which way you want to accelerate, doesn’t it?
So then, is it that mass stays the same, but the relationship between the object’s mass and inertia changes with acceleration?
-FrL-