Physic Labs

Problem 2

A mass mm slides from rest down an incline at angle θ\theta with kinetic friction coefficient μ\mu. Find its acceleration and speed after distance LL. The block slides with constant kinetic-friction coefficient μ\mu and constant acceleration; take downhill along the plane as positive. (a) Find the normal force NN. (b) Find acceleration along the incline. (c) Find the speed after distance LL and state the condition for downhill sliding. Express each answer in terms of the supplied parameters, using SI units for any numerical evaluation. State the assumptions used, check dimensions at each result, and compare with the governing law to catch a sign error or a missing condition.
problems.proof.stepOf
problems.proof.prevStepproblems.proof.nextStep
a=g(sin⁡θ−μcos⁡θ),N=mgcos⁡θ,v=2gL(sin⁡θ−μcos⁡θ),sin⁡θ>μcos⁡θ\boxed{a=g(\sin\theta-\mu\cos\theta),\quad N=mg\cos\theta,\quad v=\sqrt{2gL(\sin\theta-\mu\cos\theta)},\quad \sin\theta>\mu\cos\theta}
problems.proof.analysis

The final expressions are collected in the order requested and must satisfy the equations used above. Checking dimensions, signs, and limiting conditions catches algebra errors or omitted constraints.