2. A rock is suspended by a string wound around a fixed pulley. The rock accelerates down- ward. Which one of the following statements concerning the tension in the string is true? (a) The tension is greater than the mass of the rock. (b) The tension is less than the mass of the rock. (c) The tension is equal to the weight of the rock. (d) The tension is greater than the weight of the rock. (e) The tension is less than the weight of the rock.

Glencoe Physics: Principles and Problems, Student Edition
1st Edition
ISBN:9780078807213
Author:Paul W. Zitzewitz
Publisher:Paul W. Zitzewitz
Chapter5: Displacement And Force In Two Dimensions
Section: Chapter Questions
Problem 87A
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**Question 2: Tension in a String with a Fixed Pulley**

A rock is suspended by a string wound around a fixed pulley. The rock accelerates downward. Which one of the following statements concerning the tension in the string is true?

**Answer Options:**
(a) The tension is greater than the mass of the rock.

(b) The tension is less than the mass of the rock.

(c) The tension is equal to the weight of the rock.

(d) The tension is greater than the weight of the rock.

(e) The tension is less than the weight of the rock.

---

**Explanation:**

When analyzing the problem, we consider the forces acting on the rock:

1. **Gravitational Force (Weight of the Rock)**: This force acts downward and is equal to the mass of the rock (\(m\)) multiplied by the acceleration due to gravity (\(g\)).
   
   \( \text{Weight} = mg \)

2. **Tension in the String**: This force acts upward.

Since the rock accelerates downward, we know that the net force on the rock must also be downward due to Newton's Second Law. The tension in the string is not enough to completely counterbalance the weight of the rock. Therefore, the tension in the string is less than the weight of the rock. Thus, the correct statement is:

(e) The tension is less than the weight of the rock.
Transcribed Image Text:**Question 2: Tension in a String with a Fixed Pulley** A rock is suspended by a string wound around a fixed pulley. The rock accelerates downward. Which one of the following statements concerning the tension in the string is true? **Answer Options:** (a) The tension is greater than the mass of the rock. (b) The tension is less than the mass of the rock. (c) The tension is equal to the weight of the rock. (d) The tension is greater than the weight of the rock. (e) The tension is less than the weight of the rock. --- **Explanation:** When analyzing the problem, we consider the forces acting on the rock: 1. **Gravitational Force (Weight of the Rock)**: This force acts downward and is equal to the mass of the rock (\(m\)) multiplied by the acceleration due to gravity (\(g\)). \( \text{Weight} = mg \) 2. **Tension in the String**: This force acts upward. Since the rock accelerates downward, we know that the net force on the rock must also be downward due to Newton's Second Law. The tension in the string is not enough to completely counterbalance the weight of the rock. Therefore, the tension in the string is less than the weight of the rock. Thus, the correct statement is: (e) The tension is less than the weight of the rock.
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