a. If the block starts from rest at A, what is its speed at B? Hint for (a) The speed of block at B is vg b. What is the force of the track on the block at B? Hint for (b) The track exerts a force N: on the block. c. What force does the track exert on the block at the top and at the bottom of the loop? Hint for (c) At the top, the track exerts a force Ntop on the block. At the bottom, the track exerts a force Npottom on the block.

College Physics
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ISBN:9781305952300
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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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A small block of mass mm slides without friction around the loop-the-loop apparatus shown below.


Image Description

 

Answer questions below. Give your answer in terms of RR, mm, and/or gravitational acceleration gg.

  1. If the block starts from rest at AA, what is its speed at BB? Hint for (a)
    The speed of block at BB is vB=vB=  
  2. What is the force of the track on the block at BB? Hint for (b)
    The track exerts a force N=N=   on the block.
  3. What force does the track exert on the block at the top and at the bottom of the loop? Hint for (c)
    At the top, the track exerts a force Ntop=Ntop=   on the block.
    At the bottom, the track exerts a force Nbottom=Nbottom=   on the block.
**Image Description:**

A small block of mass \( m \) slides without friction around a loop-the-loop apparatus. The diagram shows a track resembling a loop. The loop has a radius \( R \). The block starts at point \( A \), which is at a height of \( 4R \) above the ground. As it moves from \( A \) to point \( B \) on the loop, it follows a curved path.

**Diagrams:**

1. **Loop-the-loop Diagram:**
   - The track forms a complete loop with a circular shape.
   - The height of point \( A \) from the bottom of the loop is \( 4R \).
   - The center of the circular loop is at a height \( R \) from the bottom.
   - A radial arrow is drawn from the center of the loop to point \( B \).

**Questions:**

Answer the following questions using the given variables: \( R \), \( m \), and gravitational acceleration \( g \).

a. If the block starts from rest at \( A \), what is its speed at \( B \)?

   - **Hint for (a):** 
   - The speed of block at \( B \) is \( v_B = \) [Your answer here]

b. What is the force of the track on the block at \( B \)?

   - **Hint for (b):**
   - The track exerts a force \( N = \) [Your answer here] on the block.

c. What force does the track exert on the block at the top and at the bottom of the loop?

   - **Hint for (c):**
   - At the top, the track exerts a force \( N_{\text{top}} = \) [Your answer here] on the block.
   - At the bottom, the track exerts a force \( N_{\text{bottom}} = \) [Your answer here] on the block.
Transcribed Image Text:**Image Description:** A small block of mass \( m \) slides without friction around a loop-the-loop apparatus. The diagram shows a track resembling a loop. The loop has a radius \( R \). The block starts at point \( A \), which is at a height of \( 4R \) above the ground. As it moves from \( A \) to point \( B \) on the loop, it follows a curved path. **Diagrams:** 1. **Loop-the-loop Diagram:** - The track forms a complete loop with a circular shape. - The height of point \( A \) from the bottom of the loop is \( 4R \). - The center of the circular loop is at a height \( R \) from the bottom. - A radial arrow is drawn from the center of the loop to point \( B \). **Questions:** Answer the following questions using the given variables: \( R \), \( m \), and gravitational acceleration \( g \). a. If the block starts from rest at \( A \), what is its speed at \( B \)? - **Hint for (a):** - The speed of block at \( B \) is \( v_B = \) [Your answer here] b. What is the force of the track on the block at \( B \)? - **Hint for (b):** - The track exerts a force \( N = \) [Your answer here] on the block. c. What force does the track exert on the block at the top and at the bottom of the loop? - **Hint for (c):** - At the top, the track exerts a force \( N_{\text{top}} = \) [Your answer here] on the block. - At the bottom, the track exerts a force \( N_{\text{bottom}} = \) [Your answer here] on the block.
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