Spring-Block system executing SHM in a freely falling elevator

Thread starter vijaypandey93
Start date Jul 2, 2013
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Elevator Falling Shm System

In summary, the problem involves a block of mass m suspended from the ceiling of a stationary elevator through a spring of spring constant k. When the cable breaks and the elevator starts falling, the block executes simple harmonic motion of amplitude mg/k in the elevator. To solve this problem without applying pseudo forces, one can consider the motion of the block and the ceiling relative to the ground frame. By choosing the origin of the elevator frame as the relaxed length of the spring, one can write out Newton's 2nd law in the ground frame, taking into account the position vectors of the block and the ceiling. The

Jul 2, 2013

WannabeNewton

Science Advisor

You don't have to explicitly solve it if you don't want to; you can tell just by looking at the equation.

<h2>1. What is a spring-block system executing SHM in a freely falling elevator?</h2><p>A spring-block system executing SHM (Simple Harmonic Motion) in a freely falling elevator refers to a setup where a spring and a block are attached to the ceiling of an elevator that is in free fall. The spring and block are able to move up and down due to the force of gravity acting on them, creating a repeating back-and-forth motion known as SHM.</p><h2>2. How does gravity affect the spring-block system in a freely falling elevator?</h2><p>In a freely falling elevator, gravity is the only force acting on the spring-block system. This force causes the block to accelerate towards the ground, stretching the spring and creating potential energy. As the elevator falls, the block will oscillate up and down due to the restoring force of the spring, resulting in SHM.</p><h2>3. What factors affect the frequency of the spring-block system's SHM in a freely falling elevator?</h2><p>The frequency of the spring-block system's SHM in a freely falling elevator is affected by the mass of the block, the stiffness of the spring, and the acceleration due to gravity. As these factors change, the frequency of the SHM will also change accordingly.</p><h2>4. How does the amplitude of the spring-block system's SHM change in a freely falling elevator?</h2><p>The amplitude, or maximum displacement, of the spring-block system's SHM in a freely falling elevator will decrease as the elevator falls. This is because the acceleration due to gravity increases, causing the restoring force of the spring to also increase and pull the block back towards the equilibrium position.</p><h2>5. Can the spring-block system's SHM in a freely falling elevator be used to measure the acceleration due to gravity?</h2><p>Yes, the spring-block system's SHM in a freely falling elevator can be used to indirectly measure the acceleration due to gravity. By measuring the frequency and amplitude of the SHM, along with the mass and stiffness of the system, the acceleration due to gravity can be calculated using the equation a = (4π²k)/m, where a is the acceleration, k is the spring constant, and m is the mass of the block.</p>

FAQ: Spring-Block system executing SHM in a freely falling elevator

1. What is a spring-block system executing SHM in a freely falling elevator?

A spring-block system executing SHM (Simple Harmonic Motion) in a freely falling elevator refers to a setup where a spring and a block are attached to the ceiling of an elevator that is in free fall. The spring and block are able to move up and down due to the force of gravity acting on them, creating a repeating back-and-forth motion known as SHM.

2. How does gravity affect the spring-block system in a freely falling elevator?

In a freely falling elevator, gravity is the only force acting on the spring-block system. This force causes the block to accelerate towards the ground, stretching the spring and creating potential energy. As the elevator falls, the block will oscillate up and down due to the restoring force of the spring, resulting in SHM.

3. What factors affect the frequency of the spring-block system's SHM in a freely falling elevator?

The frequency of the spring-block system's SHM in a freely falling elevator is affected by the mass of the block, the stiffness of the spring, and the acceleration due to gravity. As these factors change, the frequency of the SHM will also change accordingly.

4. How does the amplitude of the spring-block system's SHM change in a freely falling elevator?

The amplitude, or maximum displacement, of the spring-block system's SHM in a freely falling elevator will decrease as the elevator falls. This is because the acceleration due to gravity increases, causing the restoring force of the spring to also increase and pull the block back towards the equilibrium position.

5. Can the spring-block system's SHM in a freely falling elevator be used to measure the acceleration due to gravity?

Yes, the spring-block system's SHM in a freely falling elevator can be used to indirectly measure the acceleration due to gravity. By measuring the frequency and amplitude of the SHM, along with the mass and stiffness of the system, the acceleration due to gravity can be calculated using the equation a = (4π²k)/m, where a is the acceleration, k is the spring constant, and m is the mass of the block.