A block of mass m is on a frictionless track, initially at a height h above the ground. The block slides down the track and collides at the bottom with a larger block of mass 3m. The two blocks stick together and move off to the right. Finally they are brought momentarily to rest by a spring with spring constant k. Fnd the maximum amount by which the spring will be compressed in stopping the combined blocks. [Ans: d = mgh/(2k)]I h 3m M Problem 4 Problem 5 E
A block of mass m is on a frictionless track, initially at a height h above the ground. The block slides down the track and collides at the bottom with a larger block of mass 3m. The two blocks stick together and move off to the right. Finally they are brought momentarily to rest by a spring with spring constant k. Fnd the maximum amount by which the spring will be compressed in stopping the combined blocks. [Ans: d = mgh/(2k)]I h 3m M Problem 4 Problem 5 E
Related questions
Question
![**Problem 4 Description:**
A block of mass \( m \) is on a frictionless track, initially at a height \( h \) above the ground. It slides down the track and collides at the bottom with a larger block of mass \( 3m \). The two blocks stick together and move off to the right. They are momentarily brought to rest by a spring with a spring constant \( k \). The task is to find the maximum compression of the spring (denoted as \( d \)) when stopping the combined blocks.
**Equation Provided:**
\[ d^2 = \frac{mgh}{2k} \]
**Diagram Explanation:**
- The diagram shows a frictionless curved track starting from a height \( h \) on the left with a block of mass \( m \) at the top.
- At the bottom of the track, there is a larger block of mass \( 3m \).
- To the right of this setup, a spring with spring constant \( k \) is depicted, indicating where the blocks eventually come to rest after sticking together.
**Concepts Involved:**
- Gravitational potential energy conversion to kinetic energy.
- Inelastic collision (the blocks stick together).
- Energy conservation involving kinetic energy and elastic potential energy of the spring.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd767e2f1-cca9-465a-901b-5ef8f3218e51%2F2ba1c326-a606-46c6-9f50-805fac0dc93a%2Fxnce8h_processed.png&w=3840&q=75)
Transcribed Image Text:**Problem 4 Description:**
A block of mass \( m \) is on a frictionless track, initially at a height \( h \) above the ground. It slides down the track and collides at the bottom with a larger block of mass \( 3m \). The two blocks stick together and move off to the right. They are momentarily brought to rest by a spring with a spring constant \( k \). The task is to find the maximum compression of the spring (denoted as \( d \)) when stopping the combined blocks.
**Equation Provided:**
\[ d^2 = \frac{mgh}{2k} \]
**Diagram Explanation:**
- The diagram shows a frictionless curved track starting from a height \( h \) on the left with a block of mass \( m \) at the top.
- At the bottom of the track, there is a larger block of mass \( 3m \).
- To the right of this setup, a spring with spring constant \( k \) is depicted, indicating where the blocks eventually come to rest after sticking together.
**Concepts Involved:**
- Gravitational potential energy conversion to kinetic energy.
- Inelastic collision (the blocks stick together).
- Energy conservation involving kinetic energy and elastic potential energy of the spring.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 2 steps
