Conservation of momnetum or Newtons second law?

[vkash]

conservation of momnetum or Newtons second law?

Homework Statement

An acrobat of mass 'm' clings to a rope ladder hanging below a balloon of mass 'M'. the balloon stationary with respect to ground
(a) If the acrobat begins to climb the ladder at a speed 'v' (with respect to the ladder), in what direction and with what speed (with respect to earth) will the balloon move?
(b) If the acrobat stops climbing, what will be the velocity of the balloon.

Homework Equations

The Attempt at a Solution

I put my answer and figure in attachment.

you tell me where am i wrong

 

[PeterO]

Homework Statement

An acrobat of mass 'm' clings to a rope ladder hanging below a balloon of mass 'M'. the balloon stationary with respect to ground
(a) If the acrobat begins to climb the ladder at a speed 'v' (with respect to the ladder), in what direction and with what speed (with respect to earth) will the balloon move?
(b) If the acrobat stops climbing, what will be the velocity of the balloon.

Homework Equations

The Attempt at a Solution

I put my answer and figure in attachment.

you tell me where am i wrong

In the absense of any unbalanced external force, the centre of mass will remain stationary.
If you alter the position of part of the mass of the system, you will probably alter the position of other parts of the system. If some part of the system began moving at some speed, the rest of the system would also move at a certain speed

Imagine if the man and the balloon had the same mass, so the centre of Mass was exactly half way between them, and the ladder was 100m long.

 

[bjd40@hotmail.com]

u r wrong in thinking that the man, as moving with const. velocity, exerts no force on balloon, where the actual case is the man starts from rest and acquires a velocity and in doing so acquires some accln. also, until he reaches a const. velocity and hence applies force to the balloon also. this force is to be counted as an external force for the balloon, but there is no external force for the balloon+ man system. hence it follows that although the balloon moves downward as the man moves upward the centre of mass of man+ balloon does not move.

 

[vkash]

In the absense of any unbalanced external force, the centre of mass will remain stationary.
If you alter the position of part of the mass of the system, you will probably alter the position of other parts of the system. If some part of the system began moving at some speed, the rest of the system would also move at a certain speed

Imagine if the man and the balloon had the same mass, so the centre of Mass was exactly half way between them, and the ladder was 100m long.

u r wrong in thinking that the man, as moving with const. velocity, exerts no force on balloon, where the actual case is the man starts from rest and acquires a velocity and in doing so acquires some accln. also, until he reaches a const. velocity and hence applies force to the balloon also. this force is to be counted as an external force for the balloon, but there is no external force for the balloon+ man system. hence it follows that although the balloon moves downward as the man moves upward the centre of mass of man+ balloon does not move.

thanks to both persons.
I got the point.

 

[rwisz]

I would like to clarify that both the conservation of momentum and Newton's second law are relevant in this scenario. The conservation of momentum states that in a closed system, the total momentum remains constant. In this case, the acrobat, rope ladder, and balloon make up a closed system.

According to Newton's second law, the net force acting on an object is equal to its mass multiplied by its acceleration. In this scenario, the acrobat's upward motion on the ladder creates a force on the balloon in the opposite direction, causing it to move.

(a) The direction of the balloon's motion will be in the opposite direction of the acrobat's climb, and its speed can be calculated using the equation: mV = (m+M)V', where V is the acrobat's climbing speed, m is the acrobat's mass, M is the balloon's mass, and V' is the balloon's velocity with respect to the earth.

(b) If the acrobat stops climbing, the balloon will continue to move in the same direction with a constant velocity. This is due to the conservation of momentum, as the total momentum of the system remains constant even when the acrobat stops climbing.

In conclusion, both the conservation of momentum and Newton's second law are important concepts to consider in this scenario.