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?

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**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) \( \frac{kx_0^2}{2} + \mu mgx_0 \)
Transcribed Image Text:**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**: \( \frac{kx_0^2}{2} - 2\mu mg x_0 \)
Transcribed Image Text: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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