**Question 7**A block of mass \( m \) is on a rough horizontal surface and is attached to a spring with spring constant \( k \). The coefficient of kinetic friction between the surface and the block is \( \mu \). When the block is at position \( x = 0 \), the spring is at its unstretched length. The block is pulled to position \( x = +x_0 \), as shown above, and released from rest. The block then travels to the left and passes through \( x = 0 \) before coming momentarily to rest at position \( x = -\frac{x_0}{2} \).**Diagram Explanation**The diagram shows a mass \( m \) attached to a spring on a horizontal surface. The spring is fixed at one end, and the other end is attached to the mass. The positions along the horizontal axis are marked with \( +x_0 \), \( 0 \), and \(-\frac{x_0}{2}\). The mass is initially at \( x = +x_0 \) and moves left toward \( x = 0 \).**Problem Statement**Which of the following is a correct expression for the kinetic energy of the block as it first travels through position \( x = 0 \)?A) \( 0 \)B) \( \frac{kx_0^2}{2} \)C) \( \frac{kx_0^2}{2} - \mu mgx_0 \)D) \( \frac{kx_0^2}{2} + \mu mgx_0 \) A block of mass \( m \) is on a rough horizontal surface and is attached to a spring with spring constant \( k \). The coefficient of kinetic friction between the block and surface is \( \mu \). The block is initially at position \( x = +x_0 \), as shown above, and released from rest. The block then travels to the left and passes through \( x = 0 \) before coming momentarily to rest.Which of the following is a correct expression for the kinetic energy of the block as it first travels through position \( x = 0 \)?- **A**: \( 0 \)- **B**: \( \frac{kx_0^2}{2} \)- **C**: \( \frac{kx_0^2}{2} - \mu mg x_0 \)- **D**: \( \frac{\frac{3\mu mg x_0}{2}}{2} \)- **E**: \( \frac{kx_0^2}{2} - 2\mu mg x_0 \)

Given, From Newton's second law, applying along the vertical axis on the block of mass m.…

m ell +Xo 2 A block of mass m is on a rough horizontal surface and is attached to a spring with spring constant k. The coefficient of kinetic friction between the surface and the block is u. When the block is at position z 0, the spring is at its unstretched length. The block is pulled to position z= +zo, as shown above, and released from rest. The block then travels to the left and passes through z=0 before coming momentarily to rest at position a- Which of the following is a correct expression for the kinetic energy of the block as it first travels through position z =0?

m ell +Xo 2 A block of mass m is on a rough horizontal surface and is attached to a spring with spring constant k. The coefficient of kinetic friction between the surface and the block is u. When the block is at position z 0, the spring is at its unstretched length. The block is pulled to position z= +zo, as shown above, and released from rest. The block then travels to the left and passes through z=0 before coming momentarily to rest at position a- Which of the following is a correct expression for the kinetic energy of the block as it first travels through position z =0?

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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Concept explainers

Spring Potential Energy

The potential energy is the energy possessed by a body by virtue of its position or the energy held by the object due to its position relative to other objects, its force like stresses, charge, and other factors affecting the particles of the body. The potential energy is the measure of the net work done by or on the body. The spring potential energy is the potential energy stored due to the deformation of an elastic spring and this elasticity is due to the stretched spring. The elasticity is the ability of a solid-state matter to come back to its equilibrium position or original position after any kind of external force is acted on it. It is also known as Elastic potential energy. The potential energy here is caused due to the displacement of the spring from its equilibrium position to another position and this potential energy is equal to the net work done due to the stretching of the spring. It also resembles the same mechanics of the oscillation of a simple pendulum, where due to the external force, the object moves from its equilibrium position to its maximum ends and the periodic motion continues till it comes back to the equilibrium position to rest. 

Question

A block of mass \( m \) is on a rough horizontal surface and is attached to a spring with spring constant \( k \). The coefficient of kinetic friction between the block and surface is \( \mu \). The block is initially at position \( x = +x_0 \), as shown above, and released from rest. The block then travels to the left and passes through \( x = 0 \) before coming momentarily to rest.

Which of the following is a correct expression for the kinetic energy of the block as it first travels through position \( x = 0 \)?

- **A**: \( 0 \)

- **B**: \( \frac{kx_0^2}{2} \)

- **C**: \( \frac{kx_0^2}{2} - \mu mg x_0 \)

- **D**: \( \frac{\frac{3\mu mg x_0}{2}}{2} \)

- **E**: \( \frac{kx_0^2}{2} - 2\mu mg x_0 \)

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