How do you find amplitude if you have the height measured. We are doing a spring lab and we are trying to find the Spring constant using Hooke's Law. We hung a spring and put a mass on it and measured how far the bottom of the mass hanger was from the table. The height was .511 m and the mass was .21 kg.
2007-02-06 03:17:05 · 5 answers · asked by Anonymous in Science & Mathematics ➔ Physics
If I understand correctly, then you need another piece of information such as the height of the hangar without a weight in it. Then you would be able to tell how far the spring stretched, and knowing the force that stretched it (.21 kg acted on by gravity) you could calculate k.
2007-02-06 03:25:28 · answer #1 · answered by Grizzly B 3 · 0⤊ 0⤋
Hooke's law - F=kx, and you're searching for K. You measured the height, and you have the mass. You need to convert Mass to force - by using F=ma (in this case a = the gravitational constant g - look up the value ~ 9.81 m/s^2). So, now you've got F. What you need for x isn't the distance from the table, but the difference between the distance of the stretched and unstretched spring - that's x. Once you have that (assuming k is linear) you can solve for it easily.
2007-02-06 11:37:56 · answer #2 · answered by Jeffrey S 1 · 0⤊ 0⤋
If the object is hanging at rest from a spring then the net force acting on the object is zero (it is not accelerating).
There are two forces acting on the spring (in opposite directions and with equal magnitude).
There is the force of gravity acting on the mass (its weight).
There is also the spring force acting on the mass due to the fact that the block is stretching out the spring.
Weight = mass * gravity
W = mg
Spring Force = Spring constant * Stretch distance
F_s = kx
The force is directed in the opposite direction of the displacement (meaning that if you pull it out, the spring will want to compress and if you compress it, the spring will want to expand).
In order for the mass to be hanging in equilibrium, these two forces must be pulling on the mass with an equal magnitude but in opposite directions to cancel each other out.
If we set the forces equal to each other,
Weight = spring force
mg = kx
We can solve for k, the spring constant.
k = mg/x
We know the mass of the object (.21 kg), we can measure the stretch distance, x, and we are assumed to know the gravitational acceleration on the surface of the Earth (9.81 m/s^2).
Plugging these values in,
k = (.21 kg)(9.81 m/s^2) / x
k =
(We are assuming the spring has a negligible mass)
The stretch distance, x, can be measured as the length of the stretched out spring minus the length of the un-stretched spring (i.e. how far you pull it out).
Once you know this value you can plug it in and find the spring constant.
2007-02-06 11:26:49 · answer #3 · answered by mrjeffy321 7 · 0⤊ 0⤋
I believe the amplitude would be the difference between the height of the mass hanger with no load applied (mass=0) and the height with the load applied.
So if you measure the height with the load removed, the amplitude would be h(no load) - 0.511.
Three significant figures is probably too precise for the error involved here though.
2007-02-06 11:22:19 · answer #4 · answered by gebobs 6 · 0⤊ 0⤋
Well, if I understand you correctly, the stretched amount IS the amplitude.
2007-02-06 11:20:57 · answer #5 · answered by Anonymous · 0⤊ 0⤋