PHYS 1003 Lecture Notes - Lecture 9: Integral, Gravity Well
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17 Oct 2016
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So far, we only looked over work done with constant forces . As the spring is compressed or stretched, the force changes too. There are many diff. materials which act like springs, so this example is useful to study. ** the minus sign indicates that the internal spring force and displacement are always in opposite directions. The variable k , constant of proportionality, is known as the spring constant. Measure of how stiff a spring is. The higher the value of k, the stiffer the spring. Higher k = more resistance to compression or stretch. To solve this problem, we must use integral calculus. We calculate the work done for a very small displacement. Force to be constant over that small distance x . An integral with the limits specified is known as a definite integral. An integral specified without limits is known as an indefinite integral. The integrand is the function being integrated (f(x))