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title: "A block is attached to a horizontal spring and is initially at rest at the equilibrium position \\( x = 0 \\), as shown in Figure \\( 1 \\). The block is then moved to position \\( x = -A \\), as shown in Figure \\( 2 \\), and released from rest, undergoing simple harmonic motion. At the instant the block reaches position \\( x = +A \\), another identical block is dropped onto and sticks to the block, as shown in Figure \\( 3 \\). The two–block–spring system then continues to undergo simple harmonic motion. Which of the following correctly compares the total mechanical energy \\( E_{\\text{tot},2} \\) of the two–block–spring system after the collision to the total mechanical energy \\( E_{\\text{tot},1} \\) of the one–block–spring system before the collision?"
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url: "https://nerd-notes.com/ubq/88468/"
date_modified: "2025-04-19T04:03:59+00:00"
---

# A block is attached to a horizontal spring and is initially at rest at the equilibrium position \( x = 0 \), as shown in Figure \( 1 \). The block is then moved to position \( x = -A \), as shown in Figure \( 2 \), and released from rest, undergoing simple harmonic motion. At the instant the block reaches position \( x = +A \), another identical block is dropped onto and sticks to the block, as shown in Figure \( 3 \). The two–block–spring system then continues to undergo simple harmonic motion. Which of the following correctly compares the total mechanical energy \( E_{\text{tot},2} \) of the two–block–spring system after the collision to the total mechanical energy \( E_{\text{tot},1} \) of the one–block–spring system before the collision?

A block is attached to a horizontal spring and is initially at rest at the equilibrium position \( x = 0 \), as shown in Figure \( 1 \). The block is then moved to position \( x = -A \), as shown in Figure \( 2 \), and released from rest, undergoing simple harmonic motion. At the instant the block reaches position \( x = +A \), another identical block is dropped onto and sticks to the block, as shown in Figure \( 3 \). The two–block–spring system then continues to undergo simple harmonic motion. Which of the following correctly compares the total mechanical energy \( E_{\text{tot},2} \) of the two–block–spring system after the collision to the total mechanical energy \( E_{\text{tot},1} \) of the one–block–spring system before the collision?

![Diagram](https://nerd-notes.com/wp-content/uploads/2025/04/shmblockeddroppedoneachotherenergy.png)

- **A.** \[ E_{\text{tot},2} = E_{\text{tot},1} \]
- **B.** \[ E_{\text{tot},2} = \frac{1}{2} E_{\text{tot},1} \]
- **C.** \[ E_{\text{tot},2} = 2 E_{\text{tot},1} \]
- **D.** \[ E_{\text{tot},2} = \frac{1}{4} E_{\text{tot},1} \]

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/88468/*