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Chapter 4: Problem 14

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

Expert verified
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

01

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.
02

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.
03

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.
04

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.
05

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.

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Most popular questions from this chapter

A large ice block of mass \(M=80.0 \mathrm{~kg}\) is held stationary on a frictionless ramp. The ramp is at an angle of \(\theta=\) \(36.9^{\circ}\) above the horizontal. a) If the ice block is held in place by a tangential force along the surface of the ramp (at angle \(\theta\) above the horizontal), find the magnitude of this force. b) If, instead, the ice block is held in place by a horizontal force, directed horizontally toward the center of the ice block, find the magnitude of this force.

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