Physic Labs

Problem 1

A particle of mass mm slides from rest without friction down a plane of length LL inclined at angle α\alpha, then leaves its edge and lands on a floor HH below the edge. With gravitational acceleration gg, find the sliding time, launch speed, and horizontal range from the edge. Model each stage with the appropriate conservation law or equation of motion; quantities stated as constant remain fixed during that stage. (a) Establish the governing physical relation for each stage. (b) Determine the requested observables from the stated initial conditions and constraints. (c) Check signs, dimensions, and the physical limiting behavior of the results.
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L=12ats2,ts=2Lgsin⁡αL=\frac12 a t_s^2,\qquad t_s=\sqrt{\frac{2L}{g\sin\alpha}}
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Starting from rest with constant acceleration, the distance along the plane is ats2/2at_s^2/2. Solve for the positive time. This follows from the chosen physical model and the stated initial conditions; the sign convention must remain consistent throughout. A dimensional check catches algebraic errors before the result is interpreted.

problems.proof.pitfall. Do not mix sign conventions or omit a system constraint; check the sign and units before interpreting the result.