Please show free body diagram a and b ### Problem StatementA block with mass \( M \) rests on a frictionless surface and is connected to a horizontal spring of force constant \( k \). The other end of the spring is attached to a wall. A second block with mass \( m \) rests on top of the first block. The coefficient of static friction between the blocks is \( \mu_s \).#### Tasks:1. **Draw a free-body diagram.**2. **Find the maximum amplitude of the oscillation such that the top block will not slip on the bottom block.**### Free-Body DiagramBelow is the description of the free-body diagram shown in the image:1. The figure depicts two blocks, one with mass \( M \) (bottom block) and one with mass \( m \) (top block).2. The bottom block \( M \) is connected to a spring with spring constant \( k \).3. The surface on which block \( M \) rests is frictionless.4. The coefficient of static friction between the blocks is denoted by \( \mu_s \).5. The top block \( m \) is subjected to frictional force due to the coefficient of static friction \( \mu_s \), preventing it from slipping off the bottom block during oscillations.### Detailed Explanation of the Diagram:- **Spring:** A horizontal spring is attached to a wall at one end and to the bottom block \( M \) at the other end. The spring is shown in a compressed or stretched state, indicating its oscillatory motion potential.- **Blocks:** The bottom block \( M \) is in direct contact with the frictionless surface, whereas the top block \( m \) is placed on the bottom block \( M \). - **Friction:** The static friction between blocks \( m \) and \( M \) is represented by \( \mu_s \), preventing the top block from slipping when oscillated horizontally.### Mathematical Formulation#### (a) Free-Body Diagram:- **For the top block (m):** - Weight (\( mg \)) acts downward. - Normal force (\( N \)) acts upward. - Frictional force (\( f = \mu_s \cdot N \)) acts horizontally to the left or right, opposing motion relative to the bottom block.- **For the bottom block (M):** - Weight (\( Mg \)) and the normal reaction from

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Description: Please show free body diagram a and b ### Problem StatementA block with mass \( M \) rests on a frictionless surface and is connected to a horizontal spring of force constant \( k \). The other end of the spring is attached to a wall. A second block

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(hw) A block with mass M rests on a frictionless surface and is connected to a horizontal spring of force constant k. The other end of the spring is attached to a wall. A second block with mass m rests on top of the first of the first block. There coefficient of static friction between the blocks is Ms (a) Draw free-body diagram. (b) Find the maximum amplitude of the oscillation such that the top block will not slip on the bottom block. m kummimmi M M

(hw) A block with mass M rests on a frictionless surface and is connected to a horizontal spring of force constant k. The other end of the spring is attached to a wall. A second block with mass m rests on top of the first of the first block. There coefficient of static friction between the blocks is Ms (a) Draw free-body diagram. (b) Find the maximum amplitude of the oscillation such that the top block will not slip on the bottom block. m kummimmi M M

College Physics

10th Edition

ISBN:9781285737027

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter5: Energy

Section: Chapter Questions

Problem 76AP

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Concept explainers

Simple harmonic motion

Simple harmonic motion is a type of periodic motion in which an object undergoes oscillatory motion. The restoring force exerted by the object exhibiting SHM is proportional to the displacement from the equilibrium position. The force is directed towards the mean position. We see many examples of SHM around us, common ones are the motion of a pendulum, spring and vibration of strings in musical instruments, and so on.

Simple Pendulum

A simple pendulum comprises a heavy mass (called bob) attached to one end of the weightless and flexible string.

Oscillation

In Physics, oscillation means a repetitive motion that happens in a variation with respect to time. There is usually a central value, where the object would be at rest. Additionally, there are two or more positions between which the repetitive motion takes place. In mathematics, oscillations can also be described as vibrations. The most common examples of oscillation that is seen in daily lives include the alternating current (AC) or the motion of a moving pendulum.

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Question

Please show free body diagram

a and b

### Problem Statement

A block with mass \( M \) rests on a frictionless surface and is connected to a horizontal spring of force constant \( k \). The other end of the spring is attached to a wall. A second block with mass \( m \) rests on top of the first block. The coefficient of static friction between the blocks is \( \mu_s \).

#### Tasks:
1. **Draw a free-body diagram.**
2. **Find the maximum amplitude of the oscillation such that the top block will not slip on the bottom block.**

### Free-Body Diagram

Below is the description of the free-body diagram shown in the image:

1. The figure depicts two blocks, one with mass \( M \) (bottom block) and one with mass \( m \) (top block).
2. The bottom block \( M \) is connected to a spring with spring constant \( k \).
3. The surface on which block \( M \) rests is frictionless.
4. The coefficient of static friction between the blocks is denoted by \( \mu_s \).
5. The top block \( m \) is subjected to frictional force due to the coefficient of static friction \( \mu_s \), preventing it from slipping off the bottom block during oscillations.

### Detailed Explanation of the Diagram:

- **Spring:** A horizontal spring is attached to a wall at one end and to the bottom block \( M \) at the other end. The spring is shown in a compressed or stretched state, indicating its oscillatory motion potential.
- **Blocks:** The bottom block \( M \) is in direct contact with the frictionless surface, whereas the top block \( m \) is placed on the bottom block \( M \).
- **Friction:** The static friction between blocks \( m \) and \( M \) is represented by \( \mu_s \), preventing the top block from slipping when oscillated horizontally.

### Mathematical Formulation

#### (a) Free-Body Diagram:
- **For the top block (m):**
- Weight (\( mg \)) acts downward.
- Normal force (\( N \)) acts upward.
- Frictional force (\( f = \mu_s \cdot N \)) acts horizontally to the left or right, opposing motion relative to the bottom block.

- **For the bottom block (M):**
- Weight (\( Mg \)) and the normal reaction from

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