A block of mass m = 3.00 kg situated on an incline at an angle of 8 = 38.0° is connected to a spring of negligible mass having a spring constant of 100 N/m (Fig. P8.54). The pulley and incline are frictionless. The block is released from rest with the spring initially unstretched. k= 100 N/m ww (a) How far does it move down the frictionless incline before coming to rest? m Magnitude (b) What is its acceleration at its lowest point? Direction 8 m/s² m O up the incline O down the incline

College Physics
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Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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### Physics Problem Explanation

A block of mass \( m = 3.00 \, \text{kg} \) is situated on an incline at an angle of \( \theta = 38.0^\circ \). It is connected to a spring with negligible mass, which has a spring constant of \( 100 \, \text{N/m} \). The setup is depicted in Figure P8.54. Both the pulley and the incline are frictionless. The block is released from rest with the spring initially unstretched.

#### Diagram Description
- **Diagram Components:**
  - A spring connected to a block on an incline.
  - The spring has a constant \( k = 100 \, \text{N/m} \).
  - The incline is at an angle \( \theta = 38.0^\circ \).
  - The block has a mass of \( 3.00 \, \text{kg} \).
- **Key Features:**
  - Spring starts in an unstretched state.
  - System is frictionless.

#### Problem Questions
(a) **How far does it move down the frictionless incline before coming to rest?**

Provide an answer in meters (m).

(b) **What is its acceleration at its lowest point?**

1. **Magnitude:** Provide the acceleration in meters per second squared (m/s\(^2\)).
2. **Direction:** Indicate whether the acceleration is "up the incline" or "down the incline".
Transcribed Image Text:### Physics Problem Explanation A block of mass \( m = 3.00 \, \text{kg} \) is situated on an incline at an angle of \( \theta = 38.0^\circ \). It is connected to a spring with negligible mass, which has a spring constant of \( 100 \, \text{N/m} \). The setup is depicted in Figure P8.54. Both the pulley and the incline are frictionless. The block is released from rest with the spring initially unstretched. #### Diagram Description - **Diagram Components:** - A spring connected to a block on an incline. - The spring has a constant \( k = 100 \, \text{N/m} \). - The incline is at an angle \( \theta = 38.0^\circ \). - The block has a mass of \( 3.00 \, \text{kg} \). - **Key Features:** - Spring starts in an unstretched state. - System is frictionless. #### Problem Questions (a) **How far does it move down the frictionless incline before coming to rest?** Provide an answer in meters (m). (b) **What is its acceleration at its lowest point?** 1. **Magnitude:** Provide the acceleration in meters per second squared (m/s\(^2\)). 2. **Direction:** Indicate whether the acceleration is "up the incline" or "down the incline".
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