W=m[v22]uv=12mv2−12mu2cap W equals m open bracket the fraction with numerator v squared and denominator 2 end-fraction close bracket sub u to the v-th power equals one-half m v squared minus one-half m u squared W=ΔKcap W equals cap delta cap K 2. Potential Energy of a Spring The restoring force of an ideal spring is

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0=u2sin2θ−2gH⟹H=u2sin2θ2g0 equals u squared sine squared theta minus 2 g cap H ⟹ cap H equals the fraction with numerator u squared sine squared theta and denominator 2 g end-fraction Horizontal Range (

v2rg=sinθ+μcosθcosθ−μsinθthe fraction with numerator v squared and denominator r g end-fraction equals the fraction with numerator sine theta plus mu cosine theta and denominator cosine theta minus mu sine theta end-fraction Dividing the numerator and denominator by gives the maximum safe speed ( vmaxv sub max of end-sub

Total Energy = K.E. + P.E. Speed of Transverse Waves on a String: Derive Tips to Master Physics Derivations

.Work done by an external agent to stretch the spring by a distance