Saturday, August 16, 2014

A spring exerts a force when released of 1000 newtons. The spring is pushing a mass of 3 kilograms. The spring fully extends in 1/50 of a second....

Hello!


Denote the starting force as the mass as the stiffness of a spring as and the finish time as The starting time is Also denote the displacement of a mass as let a spring moves to the left and its final position is


Then we know from Newton's Second law that Also we know Hooke's law, (minus sign because acts to the left but...

Hello!


Denote the starting force as the mass as the stiffness of a spring as and the finish time as The starting time is Also denote the displacement of a mass as let a spring moves to the left and its final position is


Then we know from Newton's Second law that Also we know Hooke's law, (minus sign because acts to the left but compresses a spring to the right).


So we obtain a differential equation for



And we know and (a mass starts from rest) and


The general solution is


From the bounding conditions we have and


Because we obtain the first time it is when or  


Our goal is to find


This is the final formula. The magnitude of the velocity in numbers is 4.24 (m/s).

No comments:

Post a Comment