18) A uniform ball is released from rest on a no-slip surface, as shown in the figure. After reaching its lowest point, the ball begins to rise again, this time on a frictionless surface. When the ball reaches its maximum height on the frictionless surface, it is No slip Frictionless A) higher than when it was released. B) lower tha C) at the same height from which it was released. D) It is impossible to tell without knowing the mass of the ball. E) It is impossible to tell without knowing the radius of the ball. when it was released. Explain why.

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**Transcription for Educational Website:**

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**Problem Statement:**

18) A uniform ball is released from rest on a no-slip surface, as shown in the figure. After reaching its lowest point, the ball begins to rise again, this time on a frictionless surface. When the ball reaches its maximum height on the frictionless surface, it is:

A) higher than when it was released.

B) lower than when it was released.

C) at the same height from which it was released.

D) It is impossible to tell without knowing the mass of the ball.

E) It is impossible to tell without knowing the radius of the ball.

Explain why.

**Diagram Explanation:**

The diagram shows a track with two sections. On the left, the section is labeled "No slip" and features a concave surface. On the right, it transitions into a "Frictionless" surface, also shown as concave. The ball is depicted at various points to illustrate its motion, starting from the no-slip section and moving onto the frictionless section.

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**Analysis and Explanation:**

When a ball is released from rest on a no-slip surface, it will begin to roll downwards due to gravity. Once it moves to the frictionless surface, the ball will continue to move without any frictional forces acting against it. Due to the conservation of mechanical energy (kinetic and potential energy), the maximum height the ball reaches on the frictionless section will be equal to the height from which it was initially released, assuming no energy losses.

Thus, the correct choice is:

C) at the same height from which it was released.

This conclusion is reached because, on a frictionless surface, there are no external forces doing work on the system, so the mechanical energy remains constant.

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Transcribed Image Text:**Transcription for Educational Website:** --- **Problem Statement:** 18) A uniform ball is released from rest on a no-slip surface, as shown in the figure. After reaching its lowest point, the ball begins to rise again, this time on a frictionless surface. When the ball reaches its maximum height on the frictionless surface, it is: A) higher than when it was released. B) lower than when it was released. C) at the same height from which it was released. D) It is impossible to tell without knowing the mass of the ball. E) It is impossible to tell without knowing the radius of the ball. Explain why. **Diagram Explanation:** The diagram shows a track with two sections. On the left, the section is labeled "No slip" and features a concave surface. On the right, it transitions into a "Frictionless" surface, also shown as concave. The ball is depicted at various points to illustrate its motion, starting from the no-slip section and moving onto the frictionless section. --- **Analysis and Explanation:** When a ball is released from rest on a no-slip surface, it will begin to roll downwards due to gravity. Once it moves to the frictionless surface, the ball will continue to move without any frictional forces acting against it. Due to the conservation of mechanical energy (kinetic and potential energy), the maximum height the ball reaches on the frictionless section will be equal to the height from which it was initially released, assuming no energy losses. Thus, the correct choice is: C) at the same height from which it was released. This conclusion is reached because, on a frictionless surface, there are no external forces doing work on the system, so the mechanical energy remains constant. ---
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