## Problem StatementA block of mass 2 kg is moving to the right with a velocity \( V = 25 \, \text{m/s} \). The block then compresses the spring until it finally stops. The spring is compressed by an amount of \( \Delta X = 0.5 \, \text{m} \). Use conservation of energy to find the spring constant.## Graph/DiagramThe image shows a rectangle (representing the block) on the left side, moving to the right. On the right side, there is a compressed spring that appears to stop the block. The spring is shown in its compressed state with a line indicating the point where the block comes to rest.**Analysis Approach:**1. **Initial Kinetic Energy of the Block**: \[ KE_i = \frac{1}{2} m v^2 = \frac{1}{2} \times 2 \, \text{kg} \times (25 \, \text{m/s})^2 = 625 \, \text{J} \]2. **Final Potential Energy in the Spring**: \[ PE_f = \frac{1}{2} k (\Delta X)^2 \]3. **Conservation of Energy**: The initial kinetic energy of the block is converted completely into potential energy of the spring: \[ KE_i = PE_f \Rightarrow 625 \, \text{J} = \frac{1}{2} k (0.5 \, \text{m})^2 \]4. **Solving for the Spring Constant \( k \)**: Rearrange and solve for \( k \): \[ 625 = \frac{1}{2} k \times 0.25 \] \[ 625 = 0.125k \] \[ k = \frac{625}{0.125} = 5000 \, \text{N/m} \]In summary, using conservation of energy principles, the spring constant \( k \) is calculated to be 5000 N/m.

Apply principle of conservation of energy 12mv2=12k∆x2mv2=k∆x2k=mv2∆x2 =2 kg25 ms20.5 m2 =5000 Nm

A block of mass 2 kg is moving to the right with velocity V= 25 m/s. The block then compresses the spring until it finally stops. The spring is compressed by an amount of A X= 0.5 m. Use conservation of energy to find the spring constant.

A block of mass 2 kg is moving to the right with velocity V= 25 m/s. The block then compresses the spring until it finally stops. The spring is compressed by an amount of A X= 0.5 m. Use conservation of energy to find the spring constant.

College Physics

11th Edition

ISBN:9781305952300

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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