A solid block in the shape of a cube is sliding on a horizontal table with negligible friction at a speed v, as shown in figure (a) below. The block's mass is M, and the length of each side of the block is 2a. When it reaches the edge of the table, it strikes a small protruding "lip" that causes it to rotate about its lower right corner, as shown in figure (b). The collision when the block strikes the lip is inelastic. What is the minimum speed v that the block must have in order to just barely tip over and fall off the table? Use only the following symbols in your answer as necessary: M, a, and g.
A solid block in the shape of a cube is sliding on a horizontal table with negligible friction at a speed v, as shown in figure (a) below. The block's mass is M, and the length of each side of the block is 2a. When it reaches the edge of the table, it strikes a small protruding "lip" that causes it to rotate about its lower right corner, as shown in figure (b). The collision when the block strikes the lip is inelastic. What is the minimum speed v that the block must have in order to just barely tip over and fall off the table? Use only the following symbols in your answer as necessary: M, a, and g.
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Chapter1: Units, Trigonometry. And Vectors
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A solid block in the shape of a cube is sliding on a horizontal table with negligible friction at a speed v, as shown in figure (a) below. The block's mass is M, and the length of each side of the block is 2a. When it reaches the edge of the table, it strikes a small protruding "lip" that causes it to rotate about its lower right corner, as shown in figure (b). The collision when the block strikes the lip is inelastic. What is the minimum speed v that the block must have in order to just barely tip over and fall off the table? Use only the following symbols in your answer as necessary: M, a, and g.
Transcribed Image Text:The image consists of two diagrams labeled (a) and (b), depicting the motion of a block on a table.
Diagram (a):
- A block with mass \( M \) is resting on a table.
- The block has a width of \( 2a \).
- An arrow labeled \( \vec{v} \) points horizontally to the right, indicating velocity.
Diagram (b):
- The block on the table is now depicted at an angle, showing rotation as it moves.
- A curved arrow labeled \( \omega \) encircles the tilted block, indicating angular velocity or rotational motion.
These diagrams illustrate the transition from linear motion to rotational motion of a block initially with horizontal velocity.
![### Scenario Description
A solid block in the shape of a cube is sliding on a horizontal table with negligible friction at a speed \( v \), as shown in figure (a). The block's mass is \( M \), and the length of each side of the block is \( 2a \). When it reaches the edge of the table, it strikes a small protruding "lip" that causes it to rotate about its lower right corner, as shown in figure (b). The collision when the block strikes the lip is inelastic.
**Problem:** What is the minimum speed \( v \) that the block must have in order to just barely tip over and fall off the table? Use only the following symbols in your answer as necessary: \( M \), \( a \), and \( g \).
### Figures and Explanation
**Figure (a):**
- Depicts a cube-shaped block sliding to the right with velocity \( v \) on a flat table.
- The block is labeled with mass \( M \) and has side length \( 2a \).
**Figure (b):**
- Shows the block after it has hit the lip, beginning to tip over the edge.
- The block is rotating about its lower right corner, indicated by a curved arrow labeled \( \omega \), demonstrating rotational motion initiated by the collision.
**Equation:**
\[ v = \]
This problem requires finding the expression for \( v \), ensuring that the block tips over successfully using given parameters.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb3965d5f-cca3-4ea0-89ca-4efc2bdd21b8%2F074ef8e6-5dbf-4fbb-8c55-3b51c05b8cbf%2Fvcwinkv_processed.png&w=3840&q=75)
Transcribed Image Text:### Scenario Description
A solid block in the shape of a cube is sliding on a horizontal table with negligible friction at a speed \( v \), as shown in figure (a). The block's mass is \( M \), and the length of each side of the block is \( 2a \). When it reaches the edge of the table, it strikes a small protruding "lip" that causes it to rotate about its lower right corner, as shown in figure (b). The collision when the block strikes the lip is inelastic.
**Problem:** What is the minimum speed \( v \) that the block must have in order to just barely tip over and fall off the table? Use only the following symbols in your answer as necessary: \( M \), \( a \), and \( g \).
### Figures and Explanation
**Figure (a):**
- Depicts a cube-shaped block sliding to the right with velocity \( v \) on a flat table.
- The block is labeled with mass \( M \) and has side length \( 2a \).
**Figure (b):**
- Shows the block after it has hit the lip, beginning to tip over the edge.
- The block is rotating about its lower right corner, indicated by a curved arrow labeled \( \omega \), demonstrating rotational motion initiated by the collision.
**Equation:**
\[ v = \]
This problem requires finding the expression for \( v \), ensuring that the block tips over successfully using given parameters.
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