Relative momentum and relative mass

[Amr Elsayed]

PeterDonis ,I think direction is not that important. If you affect a moving object with a right angle to its motion, this has nothing to do with its movement. Just will move in 2 direction. And you will find only rest mass as a resistance. Resistance increases to acceleration in its direction when speed increases, and that's because of inertia. Only if there is a relative velocity between the force and the object.
I hope you correct any wrong point of mine
regards,

 

[harrylin]

PeterDonis ,I think direction is not that important. If you affect a moving object with a right angle to its motion, this has nothing to do with its movement. Just will move in 2 direction. And you will find only rest mass as a resistance. Resistance increases to acceleration in its direction when speed increases, and that's because of inertia. Only if there is a relative velocity between the force and the object.
I hope you correct any wrong point
regards,

Hi Amr, if you are moving an object in a right angle to its motion then you measure not its "rest mass" m₀ but its "relativistic mass", γm₀. That is a measure of its already increased total energy, which doesn't change by that action as the speed remains constant. A fast moving object should thus feel "heavier" even when pushing sideways.

However, if you accelerate an object in the direction of its motion then you need to do much extra work as you are not only measuring its energy but also increasing its kinetic energy. This doing of extra work is felt as additional resistance to acceleration.

 

[Nugatory]

I think direction is not that important. If you affect a moving object with a right angle to its motion, this has nothing to do with its movement. Just will move in 2 direction. And you will find only rest mass as a resistance.

If you apply a force at right angles to the direction of movement of an object, the object's speed will not change but its velocity will change. The change in velocity is given by $\vec{F}=\gamma{m}_0\vec{a}$.

If you apply a force in the direction of movement of an object, the object's speed and velocity will both change. The change in velocity is given by $\vec{F}=\gamma^3{m}_0\vec{a}$.

Thus, the direction is important; one way you get a factor of $\gamma$ and the other way you get a factor of $\gamma^3$. In neither case is the resistance equal to the rest mass.

 

[Amr Elsayed]

if you are moving an object in a right angle to its motion then you measure not its "rest mass" m0 but its "relativistic mass", γm0. That is a measure of its already increased total energy,

Hi , yeah and that's also because of inertia which gets bigger for a moving object even when you try to change its direction ?? " that's a question"

Thus, the direction is important; one way you get a factor of γ\gamma and the other way you get a factor of γ3\gamma^3. In neither case is the resistance equal to the rest mass

Velocity as a component will of course change, but velocity in the first direction will stay same, right ??
Would you please tell me how to get those equations. I mean resistance as gamma^3 times mass or gamma times mass

 

[Amr Elsayed]

By the way, I meant " correct any wrong point of mine "

 

[Nugatory]

Velocity as a component will of course change, but velocity in the first direction will stay same ??

I have no idea what you mean by "velocity as a component", but the component of the velocity vector in the direction of motion does not stay the same. This is elementary circular motion from classical physics.

Would you please tell me how to get those equations. I mean resistance as gamma^3 times mass or gamma times mass

If you google for "longitudinal transverse mass" you will find plenty of good derivations.

 

[harrylin]

Hi , yeah and that's also because of inertia which gets bigger for a moving object even when you try to change its direction ?? " that's a question" [..]

Yes, once more: the already increased energy can be detected as increased inertia.
If I recall correctly, that is the Feynman procedure to measure relativistic mass.

 

[Amr Elsayed]

but the component of the velocity vector in the direction of motion does not stay the same. This is elementary circular motion from classical physics.

I mean the force will not be affecting it all the time. Like a projectile moving forward under effect of gravity. my push has nothing to do with vertical component downward. And so, If an object is moving and I affected it by a force perpendicular to its movement, I shall experience a resistance bigger than its rest mass because of inertia. This means that mechanics which I was talking about is just an approximate of realty The thing I don't know is how both resistances are different but I will be searching after it. I needed to know that direction really affects it as PeterDonis said and he was right

Thank you all