You attach one end of a spring with a force constant k = 813 N/m to a wall and the other end to a mass m = 2.62 kg and set the mass-spring system into oscillation on a horizontal frictionless surface as shown in the figure. To put the system into oscillation, you pull the block to a position xi = 7.16 cm from equilibrium and release it.(a) Determine the potential energy stored in the spring before the block is released.____J(b) Determine the speed of the block as it passes through the equilibrium position.______m/s(c) Determine the speed of the block when it is at a positionxi/4._____m/s This image depicts a horizontal spring-mass system.**Description:**- The spring with spring constant \( k \) is attached to a fixed wall on the left side.- The other end of the spring is connected to a block of mass \( m \).- The system is positioned horizontally on a surface, which may indicate either a frictionless scenario or one with friction, though friction is not depicted.- Three positions along the horizontal axis are labeled: - \( x = 0 \): The equilibrium position of the spring where it is neither compressed nor stretched. - \( x = x_i/4 \): A position a quarter of the amplitude from equilibrium, to the right. - \( x = x_i \): The position where the block is at maximum displacement (amplitude) to the right.

Given data: Force constant (K) = 813 N/m mass (m) = 2.62 kg xi = 7.16 cm = 0.0716 m (a) Calculate the potential energy stored in the spring before the block is released. PE = 0.5 * K * xi2 PE = 0.5 * 813 * 0.07162 PE = 2.084 J(b) Calculate the speed of the block as it passes through the equilibrium position. using conservation of momentum 0.5 * m * vm2 = PE 0.5 * 2.62 * vm2 = 2.084 vm = 1.26 m/s(c) Consider the speed of the block when it is at a position xi/4 is v Apply law of conservation of energy. PE = 0.5 * k * (xi /4)^2 + 0.5 * m * v^2 2.084 = 0.5 * 813 * ( 0.0716/4)^2 + 0.5 * 2.62 * v^2 v = 1.22 m/s Hence, the speed of the block when it is at a position xi/4 is 1.22 m/s.

Answered: You attach one end of a spring with a…

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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You attach one end of a spring with a force constant k = 813 N/m to a wall and the other end to a mass m = 2.62 kg and set the mass-spring system into oscillation on a horizontal frictionless surface as shown in the figure. To put the system into oscillation, you pull the block to a position x_i = 7.16 cm from equilibrium and release it.

(a) Determine the potential energy stored in the spring before the block is released.
____J

(b) Determine the speed of the block as it passes through the equilibrium position.
______m/s

(c) Determine the speed of the block when it is at a position

x_i/4.

_____m/s

This image depicts a horizontal spring-mass system.

**Description:**
- The spring with spring constant \( k \) is attached to a fixed wall on the left side.
- The other end of the spring is connected to a block of mass \( m \).
- The system is positioned horizontally on a surface, which may indicate either a frictionless scenario or one with friction, though friction is not depicted.
- Three positions along the horizontal axis are labeled:
- \( x = 0 \): The equilibrium position of the spring where it is neither compressed nor stretched.
- \( x = x_i/4 \): A position a quarter of the amplitude from equilibrium, to the right.
- \( x = x_i \): The position where the block is at maximum displacement (amplitude) to the right.

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