2010 HSC question (2 Viewers)

[Kimyia]

I'm still a bit confused with part (b) of this question. This is how someone explained it to me but I have no idea whether their reasoning is legit or not:
If you look at the mass on the string and draw arrows north, south, east, and west the north arrow would be the normal weight force, south - weight force, east - force due to acceleration of train, west - opposing force due to acceleration. The sum of the vectors of the normal weight force and the opposing force due to acceleration would give you the force of the tension on the string and in the same manner, the sum of the vectors of the weight force and the force due to acceleration would give you a force that follows along the line of the string (because normal and weight forces are equal, and force due to acceleration and opposing force are equal). If the string breaks, the force that's left is the one which follows along the line of the string and thus the mass will take this path.

Is this correct??

 

[barbernator]

I'm still a bit confused with part (b) of this question. This is how someone explained it to me but I have no idea whether their reasoning is legit or not:
If you look at the mass on the string and draw arrows north, south, east, and west the north arrow would be the normal weight force, south - weight force, east - force due to acceleration of train, west - opposing force due to acceleration. The sum of the vectors of the normal weight force and the opposing force due to acceleration would give you the force of the tension on the string and in the same manner, the sum of the vectors of the weight force and the force due to acceleration would give you a force that follows along the line of the string (because normal and weight forces are equal, and force due to acceleration and opposing force are equal). If the string breaks, the force that's left is the one which follows along the line of the string and thus the mass will take this path.

Is this correct??

Yes, the mass will follow a straight line in the opposite direction to the force of the string. As the sum of the forces acting upon the mass is 0, taking away a force in one direction will cause the mass to move in the opposite direction if nothing else is changed. As you have said

everyone is over-explaining this question. For part a) the force of gravity acting downwards on the mass is counteracted by the initial tension in the string when its just hanging directly downward and the train is stationary. (like a normal force on a mass). When the train is accelerating horizontally, the force due to gravity is exactly the same, and hence, the upward(vertical) tension on the string must be the same value as when the train is not moving. EXCEPT, there must now be another force to cause the mass to hang at an angle, and this force must be acting in a horizontal direction because a train moves horizontally. Now from einsteins intertial frame of reference postulate, the train MUST be accelerating or decellerating if motion is to be detected as is occuring with this mass. Hence, the train must be accelerating, resulting in the tension in the string increasing due to the horizontal force of the acceleration (as F=ma), but this force must also be constant, otherwise the addition of vectors horizontally and vertically would result in the direction of the tension to continually change and the mass continually moving, which isn't happening.

EDIT: LOL i saw Kimya's post and thought the whole thread was recent.

 

[bleakarcher]

Does this show what you mean?

 

[barbernator]

Does this show what you mean? View attachment 26381

exactly