Question

Experiment 1

Rupert finds that if he attaches a 430.0  gram mass to the hook, and then very slowly lowers the mass with his hand until the force on the mass by the spring is as large as the weight of the mass, that the spring stretches by 39.0  cm

A Second Experiment with the Vertical Mass-Spring System

Rupert now plans to try a second experiment. He will use the same mass, and once again the experiment will begin with the mass hanging at rest at the end of the stretched spring, with the mass hanging 39.0  cm below the position of the free end when the spring is unstretched. He wishes to grasp the hanging mass with his hand and to pull it downwards and release it from rest as before, but this time he wishes the mass to have a maximum speed of 1.780  m/s as it vibrates up and down at the end of the vertical spring. But Rupert doesn't know how far downwards to pull the mass in order to acheive this maximum speed. It is your task to calculate the necessary downward distance over which Rupert must pull.

You are required to do the calculation in two different coordinate systems. First, you are required to use a vertical y coordinate system with y = 0 at the location of the unstretched position of the free end of the hanging spring, with UP as the positive y direction. In this coordinate system, the necessary position of release will be negative, and Rupert's required distance will be gotten by finding the absolute value of that negative number and then subtracting 39.0  cm . Using this y coordinate system, you must arrive at a quadratic equation which can be solved for the position of release. Your quadratic equation must be of the form:

Ax2 + Bx + C = 0

and it must be derived directly from Conservation of Mechanical Energy applied to this physical situation, and using the y coordinate system described here. Each term in your equation must therefore have units of Joules; do not multiply or divide your equation by any constants; the value of the coefficient A must be greater than zero.

a) Enter your values for A, B, and C for the required quadratic equation.

b) Enter the solutions to your quadratic equation, largest first.

Answer 1

Answer 2

A problem on mass spring system