So I did in an experiment and the results I got were the potential energy when the spring compresses is 0 and when it stretches is 1.42. This spring is vertical and has a 250 gram weight attached to it. I was very confused when i got these results because I thought the potential energy is higher when a spring compresses and when it stretches the potential energy turns into Kinetic energy.
When there is no compression OR tension on the spring, usually we call the potential energy zero.
If you either compress it or stretch it, the potential energy increases.
U = (1/2)k x^2
that is + for -x and for +x
The kinetic energy is only when the mass is moving
Ke = (1/2)m v^2
So my results are incorrect right? The PE should not be 0 when compressed.
http://www.youtube.com/watch?v=sTsUx-6CflIhttp://www.youtube.com/watch?v=sTsUx-6CflIhttp://www.youtube.com/watch?v=sTsUx-6CflI
250 gram = .25 Kg
weight = m g = .25*9.8 = 2.45 Newtons
That stretched the spring 1.42 cm?
1.42 cm = .0142 meters
so k of spring = force/elongation =2.45/.0142 = 172.5 Newtons/meter
Potential energy stored in spring = (1/2)k x^2
=(1/2)(172.5)(.0142)^2 = .0174 Joules
Potential energy lost by mass going down in gravity field = m g h
= .25*9.8*.0142 = .0348 Joules
The mass lost more potential energy than the spring gained (twice as much)
So we have .0174 Joules left over when the mass stretches the spring. That energy goes into kinetic energy. The mass falls through that .0142 down point and keeps going for another .0142 meters where it comes to a stop, then bounces back up again to the start, again and again :)
The nasty thing about potential energy is that you can define zero anywhere at all. What matters are differences.
Thanks guys info really helped!
It's understandable that you are confused about the results of your experiment. Let me help explain the concept of potential energy in a spring.
In a vertical spring system like the one you described, the potential energy depends on the position of the weight attached to the spring. When the weight is at the equilibrium position (unstretched), the potential energy is considered to be zero. This is because no work is needed to hold the weight at that position.
As the spring starts to compress or stretch, the potential energy increases. When the spring compresses, it stores potential energy, and when it stretches, it converts potential energy into kinetic energy and vice versa.
Now, to calculate the potential energy in this scenario, you'll need to use the equation: Potential Energy (PE) = mass (m) × acceleration due to gravity (g) × height (h).
Given that the weight attached to the spring is 250 grams, we'll need to convert it to kg by dividing by 1000 (since 1 kg = 1000 grams), so the mass (m) is 0.25 kg.
The height (h) mentioned in your experiment is not clear, so we'll assume it means the displacement of the spring from its equilibrium position.
To calculate the potential energy when the spring compresses or stretches, you need to determine the displacement and consider its sign. If the displacement is positive, it means the spring is stretched, and if it's negative, the spring is compressed.
For example, when the spring is compressed and the potential energy is 0, we can assume that the displacement (h) is zero.
So, Potential Energy (PE) = mass (m) × acceleration due to gravity (g) × height (h) = 0.25 kg × 9.8 m/s^2 × 0 m = 0 J
On the other hand, when the spring stretches and the potential energy is 1.42 J, you'll need to determine the displacement (h) for that specific case.
Potential Energy (PE) = mass (m) × acceleration due to gravity (g) × height (h) = 0.25 kg × 9.8 m/s^2 × h = 1.42 J
By rearranging the equation, you can find the displacement (h) as follows: h = 1.42 J / (0.25 kg × 9.8 m/s^2)
Solving this equation will give you the value of the displacement, which represents how much the spring is stretched.
To summarize, the potential energy in a vertical spring system increases when the spring compresses or stretches. However, to calculate the specific values, you need to know the displacement of the spring at each case.