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42. A small block of mass m slides without friction around the loop-the-loop apparatus shown below. (a) If the block starts from rest at A, what is its speed at B? (b) What is the force of the track on the block at B? ) 9ggenb

42. A small block of mass m slides without friction around the loop-the-loop apparatus shown below. (a) If the block starts from rest at A, what is its speed at B? (b) What is the force of the track on the block at B? ) 9ggenb

College Physics
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
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Ch.8 Problem #42
### Problem 42 **Question:** A small block of mass \( m \) slides without friction around the loop-the-loop apparatus shown below. (a) If the block starts from rest at point \( A \), what is its speed at point \( B \)? (b) What is the force of the track on the block at \( B \)? **Diagram Description:** The diagram depicts a block sliding down a track in a loop-the-loop configuration. - The initial point \( A \) is at a height of \( 4R \) above the base of the loop. - The loop has a radius \( R \). - Point \( B \) is located at the top of the loop. The block is shown at point \( A \) with an arrow indicating its direction of motion toward the loop. As the block slides, it reaches \( B \) at the top of the circular loop. **Explanation:** 1. **Initial Energy at \( A \):** The block has gravitational potential energy due to its height. Since it starts from rest, its kinetic energy is zero. 2. **Energy Conservation:** As the block slides down to point \( B \), potential energy is converted into kinetic energy due to the absence of friction. 3. **Calculation of Speed:** Using energy conservation principles, the speed of the block at point \( B \) can be derived. 4. **Force on the Block at \( B \):** At point \( B \), centripetal force and gravitational force need to be considered to find the net force exerted by the track on the block. These principles are crucial for solving the motion dynamics of objects in frictionless, loop-the-loop scenarios.
Transcribed Image Text:### Problem 42 **Question:** A small block of mass \( m \) slides without friction around the loop-the-loop apparatus shown below. (a) If the block starts from rest at point \( A \), what is its speed at point \( B \)? (b) What is the force of the track on the block at \( B \)? **Diagram Description:** The diagram depicts a block sliding down a track in a loop-the-loop configuration. - The initial point \( A \) is at a height of \( 4R \) above the base of the loop. - The loop has a radius \( R \). - Point \( B \) is located at the top of the loop. The block is shown at point \( A \) with an arrow indicating its direction of motion toward the loop. As the block slides, it reaches \( B \) at the top of the circular loop. **Explanation:** 1. **Initial Energy at \( A \):** The block has gravitational potential energy due to its height. Since it starts from rest, its kinetic energy is zero. 2. **Energy Conservation:** As the block slides down to point \( B \), potential energy is converted into kinetic energy due to the absence of friction. 3. **Calculation of Speed:** Using energy conservation principles, the speed of the block at point \( B \) can be derived. 4. **Force on the Block at \( B \):** At point \( B \), centripetal force and gravitational force need to be considered to find the net force exerted by the track on the block. These principles are crucial for solving the motion dynamics of objects in frictionless, loop-the-loop scenarios.
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