I am taking the basic physics class thru Udacity. This blog is my scratch pad and results as I work my way thru the class. In addition, I am refreshing myself on basic calculus
Tuesday, July 17, 2012
Unit 4 - Problem 8 ==> Challenge with a spring
Given:
The mass of an object is compressed into the spring for a distance of delta x.
mass = 500 grams = 0.5 kilograms
delta x = 10 cm = 0.1 meters
The spring has a spring constant of 500 newtons/meter
There is a resistance section:
Whose length is 0.8 meters
And which exerts a force of 1 newton
The mass moves up a curving ramp that is 0.5 meters high
Two questions
Where does the mass eventually come to rest on the resistance section as measured from the spring?
What is the maximum height above the ramp achieved by the mass?
Calculate: Initial energy stored by the mass compressing the spring
E_{initial} = \frac{1}{2} k {\Delta{x}}^2
E_{initial} = 0.5 * 500 * 0.1^2 = 2.5\;{joules}
Calculate: Energy dissipated traveling over the friction
E_{friction} = F_{friction} L_{friction}
E_{friction} = 1 * 0.8 = 0.8\;{joules}
Calculate: Cycles over the friction to dissipate the initial energy
A full cycle entails two passes over the friction.
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