Period, velocity, acceleration of a spring

AI Thread Summary
The discussion focuses on calculating the force constant, period, maximum velocity, and maximum acceleration of a spring with a suspended mass. The force constant is determined to be 28.6 N/m using the formula F=ky. The period of the motion is calculated as 0.734 seconds. The maximum velocity is found to be 0.300 m/s, and the maximum acceleration is 2.57 m/s², both using the correct amplitude of 35.0 mm. The calculations are confirmed to be accurate, with the amplitude being the initial displacement when the mass is released.
lilkrazyrae
Messages
64
Reaction score
0
A .390kg mass is suspended from a spring. A force of 1.00N stretches it an additional 35.0mm. Find the force constant of the spring, the period of the motion which results when the mass is released, the maximum acceleration, and the maximum velocity.

Ok so the force constant is F=ky therefore F/y=k and k=1.00/.035=28.6 N/m
The period is T=2pi(sqrt(m/k))
=2pi(sqrt(.390/28.6))
=.734m
That is pretty straightforward but the velocity and the acceleration is what I have a problem with, I don't know if 35.0mm is the amplitude or if you have to find the amplitude.

I used v=(sqrt(k/m))(A)
=(sqrt(28.6/.390))(.0350)
=.300m/s

and for acceleration a=(k/m)(A)
=(28.6/.390)(.0350)
=2.57m/s^2

Are these methods right or should a different amplitude be used? Please help asap!
 
Physics news on Phys.org
I didn't check your arithmetic, but your methods look good to me. And yes, you are using the correct amplitude. (When the mass is hanging undisturbed, it rests at the equilibrium position. When the mass is then given a displacement and released, it will oscillate about the equilibrium position with an amplitude equal to the initial displacement.)
 
I multiplied the values first without the error limit. Got 19.38. rounded it off to 2 significant figures since the given data has 2 significant figures. So = 19. For error I used the above formula. It comes out about 1.48. Now my question is. Should I write the answer as 19±1.5 (rounding 1.48 to 2 significant figures) OR should I write it as 19±1. So in short, should the error have same number of significant figures as the mean value or should it have the same number of decimal places as...
Thread 'Collision of a bullet on a rod-string system: query'
In this question, I have a question. I am NOT trying to solve it, but it is just a conceptual question. Consider the point on the rod, which connects the string and the rod. My question: just before and after the collision, is ANGULAR momentum CONSERVED about this point? Lets call the point which connects the string and rod as P. Why am I asking this? : it is clear from the scenario that the point of concern, which connects the string and the rod, moves in a circular path due to the string...
Thread 'A cylinder connected to a hanging mass'
Let's declare that for the cylinder, mass = M = 10 kg Radius = R = 4 m For the wall and the floor, Friction coeff = ##\mu## = 0.5 For the hanging mass, mass = m = 11 kg First, we divide the force according to their respective plane (x and y thing, correct me if I'm wrong) and according to which, cylinder or the hanging mass, they're working on. Force on the hanging mass $$mg - T = ma$$ Force(Cylinder) on y $$N_f + f_w - Mg = 0$$ Force(Cylinder) on x $$T + f_f - N_w = Ma$$ There's also...
Back
Top