A mass is suspended from a string in railway carriage, What happens from start to a stop (from the train accelerating, at steady speed and deaccelarating) and why? If instead a helium balloon is floating in the carriage above the point of attachment what happens to it when the carriage starts what happens from a start to a stop and why?
I know that the mass will move backwards because of newtons laws of inertia but can someone give me a broader explanation. The helium balloon moves forward when the train starts to accelarate but why does it stand still when the train travels at a constant speed and why does it go backwrds when the train starts to deaccelarate? Can someone please help me!
the train accelerates but since the connection to the mass is non-rigid, the force felt by the mass initially is less than that felt by the train. therefore the train accelerates more than the mass and from the train, the mass appears to accelerate backwards.
at constant velocity there is no acceleration on the train and therefore none on the mass, because of no resultant force, so they move together
You cannot treat an accelerating frame as an inertial frame if you are at rest relative to it. You have to apply a psuedo force of ma in the opposite direction of motion to all objects in the room. For the balloon this will cause it to 'move' in the opposite direction to the direction of acceleration of the train.
made it better:
as the carridge accelerates, there are more collisions with the gas molecules on the back wall than the front because the back wall is going into the air and the front away from it. so the pressure at the back is higher and a balloon with helium will move forwards where the pressure is lower.
As the train accelerates, the air molecules towards the back of the train will be colliding with the back of the train. This is because the back of the train is accelerating forward whereas the gas is not under the same force that causes the train to accelerate, so relative to the back of the accelerating train, the gas molecules will collide into it. Therefore an ever increasing collision rate due to the acceleration of the train, means that the pressure of the air at the back of the train increases over time. Comparatively, the air at the front of the train will be at a lower pressure because the front of the train will always be accelerating forwards, away from the air at the front of the train that similarly does not feel the same force that causes the train to accelerate forward. So, the collision rate is much less and it also decreases over time as the velocity of the train increases over time.
Hence, this pressure differences causes a force to be exerted in the same direction that the train is travelling in, as there is a natural tendancy for motion in the direction of least pressure, as it is easiest to do so in this direction. So, the force exerted is felt by the balloon, which is light and has a very low density, so it moves forward.
This effect is summarised by this equation:
A (P1 - P2) = mair * a
A = Acceleration of gas in the train
P1 = Pressure at back of train
P2 = Pressure at front of train
m = mass
a = acceleration of train.
Is this correct: when the train starts to decelearate the balloon goes backwards since the air in the train moves forwards creating more pressure in the front
yes. since the train's front wall is now applying a force to the gas the pressure increases in the front and the less dense balloon moves to the back.
it's exactly like how a balloon floats to the surface of water.