**Title:** Simple Harmonic Motion of a Block and Bullet System**Overview:**A massless spring with a spring constant \( k = 25 \, \text{N/m} \) is attached to a block of mass \( M = 3.0 \, \text{kg} \) on a frictionless horizontal table. The other end of the spring is fixed to a wall. A bullet with mass \( m_b = 0.3 \, \text{kg} \) is fired into the block from the left at a speed \( v_0 = 200 \, \text{m/s} \) and comes to rest in the block instantaneously.**Diagrams:**1. **Initial Setup:** - The spring is stretched between the wall and the block (\( M = 3.0 \, \text{kg} \)). - The bullet (\( m_b = 0.3 \, \text{kg} \)) is approaching with velocity \( v_0 = 200 \, \text{m/s} \).2. **Impact and Motion:** - After the bullet embeds in the block, the combined mass (\( M + m_b \)) moves to the right with velocity \( v_x \).3. **Simple Harmonic Motion:** - The block and bullet system enters simple harmonic motion around the equilibrium position \( x = 0 \).**Problems to Solve:**a. **Find the amplitude of the resulting simple harmonic motion.**b. **Determine the time it takes for the block to first return to the position \( x = 0 \).**

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Description: **Title:** Simple Harmonic Motion of a Block and Bullet System**Overview:**A massless spring with a spring constant \( k = 25 \, \text{N/m} \) is attached to a block of mass \( M = 3.0 \, \text{kg} \) on a frictionless horizontal table. The other en

spring constant (k) = 25 N/m M = 3 kg mb = 0.3 kg vo = 200 m/s Using conservation of momentum : mb×vo = (mb + M)×V0.3×200 = (0.3+3)×V 60 = 3.3×V 18.1818 ms = V A) using the conservation of energy : initial kinetic energy = spring potential energy 12×(mb + M)×V2 = 12×k×A2(0.3+3)×(18.1818)2 = 25×A21090.909 = 25×A243.636 = A26.606 m = A Amplitude of the motion = 6.606 m B) using the formula : k = (M+m)×ω225 = (3+0.3)×(2πT)22.752 = 2πTT = 2.2828 sec time taken by the block to first return to the position x = 0 = T2= 2.28282 sec = 1.1414 sec

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A massless spring with spring constant k = 25 N/m is attached at one end of a block of mass M = 3.0 kg that is resting on a frictionless horizontal table. The other end of the spring is fixed to a wall. A bullet of mass m = 0.3 kg is fired into the block from the left with a speed vo = 200 m/s and comes to rest in the block (assume that this happens instantaneously). m₂ M x=0 x=0 M+ m₂ o ⁰ ⁰ ⁰ ⁰ ⁰ ⁰ ⁰ ⁰ o o o o o o o o The resulting motion of the block and bullet is simple harmonic motion. M+ 000000000 Find the amplitude of the resulting simple harmonic motion. b. How long does it take the block to first return to the position x = = 0?

A massless spring with spring constant k = 25 N/m is attached at one end of a block of mass M = 3.0 kg that is resting on a frictionless horizontal table. The other end of the spring is fixed to a wall. A bullet of mass m = 0.3 kg is fired into the block from the left with a speed vo = 200 m/s and comes to rest in the block (assume that this happens instantaneously). m₂ M x=0 x=0 M+ m₂ o ⁰ ⁰ ⁰ ⁰ ⁰ ⁰ ⁰ ⁰ o o o o o o o o The resulting motion of the block and bullet is simple harmonic motion. M+ 000000000 Find the amplitude of the resulting simple harmonic motion. b. How long does it take the block to first return to the position x = = 0?

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

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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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

**Title:** Simple Harmonic Motion of a Block and Bullet System

**Overview:**
A massless spring with a spring constant \( k = 25 \, \text{N/m} \) is attached to a block of mass \( M = 3.0 \, \text{kg} \) on a frictionless horizontal table. The other end of the spring is fixed to a wall. A bullet with mass \( m_b = 0.3 \, \text{kg} \) is fired into the block from the left at a speed \( v_0 = 200 \, \text{m/s} \) and comes to rest in the block instantaneously.

**Diagrams:**

1. **Initial Setup:**
- The spring is stretched between the wall and the block (\( M = 3.0 \, \text{kg} \)).
- The bullet (\( m_b = 0.3 \, \text{kg} \)) is approaching with velocity \( v_0 = 200 \, \text{m/s} \).

2. **Impact and Motion:**
- After the bullet embeds in the block, the combined mass (\( M + m_b \)) moves to the right with velocity \( v_x \).

3. **Simple Harmonic Motion:**
- The block and bullet system enters simple harmonic motion around the equilibrium position \( x = 0 \).

**Problems to Solve:**

a. **Find the amplitude of the resulting simple harmonic motion.**

b. **Determine the time it takes for the block to first return to the position \( x = 0 \).**

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