Trent Carpenter

2020-10-28

A stone hangs by a fine thread from the ceiling,and a section of the same thread dangles from the bottom of the stone.If a person gives a sharp pull on the dangling thread,where is the thread likely to break:below the stone or above it?

Faiza Fuller

When a sharp pull is given,alarge sudden force is applied to the bottom string and it will have a large tension acting on it. Because of the inertia of the stone, the upper string does not experience this force. Therefore,the bottom string breaks first.
If a slow and steady force is applied, the tension at the bottom string increases slowly.
The free body diagram is as shown.
At equilibrium ${F}_{up}={F}_{down}+mg$
Thus, we see the tension on the upper string is more than the tension in the lower string because of the weight of the string acting down. Hence the string above the stone will break first.

Jeffrey Jordon

Condition 1: When person gives a sharp pull -

Shape and sudden pull will cause large tension in the bottom thread and due to the inertia of the stone upper thread will not feel this force hence bottom thread will break.

Hence,

Thread will break from below the stone.

Note: Inertia of stone will play a major role here because it was in rest position and wants to be in rest position, also the mass of thread is negligible in compare with stone.

Stone is in equilibrium until the following condition -

T=F+mg

Where

T = Tension in upper thread

F = Applied force

mg = Weight of stone

Now,

When we apply slow and steady pull it increases the tension in both threads, above as well as below.

Upper thread already has tension due to weight of stone. Now applied pull will increase the total tension experienced by the upper thread than lower thread.

Hence, Thread will break from above the stone.

Step 1:
Let's analyze the situation using basic physics principles. When a person gives a sharp pull on the dangling thread, they apply a force to the thread. This force is transmitted throughout the thread, including the portion attached to the stone.
Now, we need to consider the forces acting on the stone and the section of the thread attached to it. The stone experiences two main forces: the tension force exerted by the thread and the force of gravity pulling the stone downward.
Using Newton's second law of motion, we can express the net force acting on the stone as:
${F}_{\text{net}}={F}_{\text{tension}}-{F}_{\text{gravity}}$
Since the stone is hanging motionless, the net force must be zero. Therefore, the tension force must balance out the force of gravity:
${F}_{\text{tension}}={F}_{\text{gravity}}$
Step 2:
Now, let's consider the forces acting on the section of the thread attached to the stone. This section experiences the tension force from the rest of the thread above it and the tension force from the stone below it. Since the stone is motionless, the tension force transmitted through the thread above and below the stone must be equal:

Therefore, the tension force in the thread above the stone must be equal to the tension force in the thread below the stone. This means that the tension force is continuous throughout the thread.
Now, let's think about what happens when a person gives a sharp pull on the dangling thread. This sharp pull increases the tension force in the thread. However, since the tension force is continuous, it will be transmitted throughout the entire thread, including the portion attached to the stone.
As a result, the tension force in the thread below the stone will also increase. This increased tension force will prevent the thread from breaking below the stone. Instead, if the tension force exceeds the breaking strength of the thread, the thread is more likely to break above the stone where the sharp pull is applied.
Therefore, the thread is likely to break above the stone when a person gives a sharp pull on the dangling thread.

Eliza Beth13

When a person gives a sharp pull on the dangling thread, the thread is likely to break below the stone.
To understand why, let's consider the forces acting on the thread. The weight of the stone exerts a downward force on the thread, and this force is transmitted throughout the thread. When the person pulls the thread sharply, an additional force is applied to the thread from below.
Since the thread is fine and likely weaker than the forces acting upon it, it will break at its weakest point. In this case, the force applied by the person's pull is likely to exceed the force exerted by the weight of the stone. As a result, the thread will break below the stone.
Therefore, the thread is more likely to break below the stone when a person gives a sharp pull on the dangling thread.

Nick Camelot

To solve the given problem, let's consider the forces acting on the stone and the thread.
When a person gives a sharp pull on the dangling thread, a tension force is created in the thread. This tension force is transmitted throughout the thread and acts in both directions.
Let's assume the tension force in the thread above the stone is ${T}_{1}$ and the tension force in the thread below the stone is ${T}_{2}$.
Since the stone is in equilibrium, the sum of the forces acting on it must be zero. The forces acting on the stone are the weight of the stone $W$ and the tension forces ${T}_{1}$ and ${T}_{2}$.
Using Newton's second law, we can write the equation of equilibrium as:
${T}_{1}+{T}_{2}=W$
Now, let's analyze the situation. If the thread were to break above the stone, there would be no tension force ${T}_{1}$. In this case, the equation of equilibrium would become:
$0+{T}_{2}=W$
This implies that the tension force ${T}_{2}$ would have to be equal to the weight of the stone $W$. However, since the thread is fine, it is not capable of supporting the weight of the stone. Therefore, the thread is likely to break above the stone.
In conclusion, the thread is likely to break $\mathbf{\text{above}}$ the stone when a sharp pull is given on the dangling thread.

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