One mass on, one half off, attached by a string

[issisoccer10]

Homework Statement

Two equal masses (A and B) are attaced by a massless string of length L. Mass A is on a cliff and B is being held even with the cliff but a length L/2 away from the edge. If you drop mass B from this position, would mass B swing down and hit the edge of the cliff before mass A reaches the edge of the cliff?

Homework Equations

No equations are necessary according to the problem

The Attempt at a Solution

I'm just supposed to explain my reasoning for my answer. So my answer goes...

Mass A would reach the edge of the cliff because as mass B falls and pulls on A, the radius of the arc that B would need to make to reach the edge of the cliff would continually increase, thus not allowing B to hit the edge of the cliff.

Does this make sense or am I just making stuff up? Is there a better "logical" explanation that would seem to fit better with physics?

 

[issisoccer10]

Addition... as for the actual question, mass A is L/2 away from the edge of the cliff. So the string is taut (the string won't stretch as mass B falls either).

 

[ogb p]

Your reasoning is correct. As mass B falls, it will pull on mass A through the string, causing mass A to move towards the edge of the cliff. This movement will increase the tension in the string, making it difficult for mass B to reach the edge of the cliff before mass A does. Additionally, the radius of the arc that mass B would need to make to reach the edge of the cliff would continuously increase, making it impossible for mass B to reach the edge of the cliff before mass A. This can be explained by the fact that the velocity of mass A will increase as it falls, while the velocity of mass B will decrease due to the tension in the string. Therefore, mass A will reach the edge of the cliff first. This is an example of conservation of energy, where the potential energy of mass A is converted into kinetic energy as it falls, allowing it to reach the edge of the cliff. Overall, your explanation is logical and in line with the principles of physics.