Physic Labs

Problem 1

A mass mm slides from rest without friction down an incline of angle alpha and vertical height hh. Find its speed at the bottom. Assume ideal objects and components, neglect unstated losses, and use SI units. (a) Derive the primary requested quantity from the appropriate law. (b) Analyze quantitatively how the result depends on the given parameters. (c) Check a physically meaningful limiting case and explain its meaning. State sign conventions, show reasoning, and check dimensions. (a) Calculate the requested quantity from the data. (b) Give the law or expression showing parameter dependence. (c) Examine a limit consistent with the model. The incline ends in a rough horizontal patch of length d and kinetic-friction coefficient mu, followed by a spring of stiffness k.
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v0=2gh,v1=2g(h−μd),xmax⁡=2mg(h−μd)/k,h≥μd\boxed{v_0=\sqrt{2gh},\quad v_1=\sqrt{2g(h-\mu d)},\quad x_{\max}=\sqrt{2mg(h-\mu d)/k},\quad h\ge\mu d}
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The boxed results answer each part in order and satisfy the assumptions and dimensional requirements.