Question

A heavy wooden ball is hanging from the ceiling by a piece of string that is attached from the ceiling to the top of the ball. A similar piece of string is attached to the bottom of the ball. If the loose end of the lower string is pulled down sharply, which is the string that is most likely to break?

Short answer

Answer: The bottom string is more likely to break when the loose end is pulled down sharply, as it experiences higher forces due to the added tension from the sharp pull.

Step-by-step solution

Identify the forces acting on the strings

When the lower string is pulled down sharply, two main forces come into play: The gravitational force (weight of the ball) acting on the upper string, and the tension force in the lower string due to the sharp pull.

Analyze the forces acting on the top string

The top string has the weight of the ball acting on it, which is the gravitational force. The gravitational force can be calculated as: Force = Mass × Gravity Since the problem doesn't provide the mass of the ball or the gravitational constant value (which is usually denoted as "g"), we can represent this force as F_gravity = m × g.

Analyze the forces acting on the bottom string

The bottom string has two forces acting on it: The gravitational force (weight of the ball) and the tension force caused by the sharp pull. Since we have already determined the gravitational force in Step 2, we just need to represent the extra tension force acting on this string by pulling it down sharply. We do not have any numerical values for this tension force but we can represent it as F_tension.

Compare the forces on both strings

Now, let's compare the forces on the two strings: 1. Top string: F_gravity (m × g) 2. Bottom string: F_gravity + F_tension (m × g + F_tension) Since F_tension is an additional force that is acting on the bottom string when it's pulled down sharply, it is evident that the total force experienced by the bottom string is higher than that of the top string.

Conclusion

Based on the force comparison, the bottom string experiences higher forces due to the added tension from the sharp pull. Therefore, the bottom string is more likely to break when the loose end is pulled down sharply.

Key concepts

Tension in Physics

In the context of physics, tension is a force that is transmitted through a string, rope, cable, or any other flexible connector when it is pulled tight by forces acting from opposite ends. Imagine tension as a taut line. This force can only pull with a set intensity without causing the string to break. In simple terms, when you have a piece of string attached to an object and pull on it, you're applying a force that creates tension.
Tension is not an extra force added from nowhere. Instead, it results from the forces acting on the object to which the string is connected.
When a string experiences too much tension, it can malfunction. This 'malfunction' usually means breaking or snapping in the context of strings or ropes. Tension is crucial in this exercise because the sharp downward pull increases the tension in the lower string.

• It increases beyond the breaking point, making the bottom string more likely to snap.
• This scenario illustrates why tension is an important concept in physics and why understanding how it works can prevent structural failures.

Understanding Gravitational Force

The gravitational force is one of the most fundamental forces in nature. It is the force of attraction that objects exert on each other due to their masses. On Earth, this force gives weight to physical objects. Every object with mass generates a gravitational pull, whether it's a planet or a pencil.
The Earth's gravitational force is commonly denoted by the symbol "g," which is approximately 9.8 m/s². This value means that objects on Earth accelerate towards the center of the planet at this rate.
In our problem, the heavy wooden ball suspended from the ceiling is constantly under the effect of Earth's gravity.

• This pull downwards is calculated by the formula: \( F_{gravity} = m \times g \), where \( m \) is mass and \( g \) is the gravitational acceleration.
• The gravitational force plays a crucial role here because it acts on both the upper and lower strings, contributing to the overall tension.

Force Analysis and Its Importance

Force analysis is a systematic way of understanding all the forces acting on a body. It helps in predicting how these forces will affect the motion or stability of the object they're acting upon. Analyzing forces involves identifying all acting forces, determining their directions and magnitudes, and seeing how they interact.
In the given exercise, force analysis helps us break down and understand the forces acting on the strings. These include the gravitational force on the ball and the additional force from the sharp pull on the lower string. When you analyze forces:

• You start by listing all the forces, like gravity and tension in the problem.
• Understanding how they add up or counteract each other shows why the bottom string breaks more easily.

Force analysis is crucial in solving real-world problems. In engineering, it ensures structures like bridges or buildings stand firm. In mechanics, it predicts how machines will behave under certain conditions. Grasping this concept is vital for anyone studying physics or engineering.