Physic Labs

Problem 1

A particle of mass mm is attached to a light string of length LL and moves in a vertical circle. Its speed at the lowest point is v0v_0. Find its speed at the highest point and the string tension at both points; assume the string remains taut. (a) State the assumptions and establish the governing equation for the requested quantity. (b) Solve it in terms of the given symbols, identifying the direction, sign, or physical nature of the result. (c) Check a simple limiting case and state when the model remains valid. Use SI units consistently, retain the symbols in the setup, and enforce all geometric constraints and initial conditions.
problems.proof.stepOf
problems.proof.prevStepproblems.proof.nextStep
12mv02=12mvt2+2mgL,vt2=v02−4gL,Tb−mg=mv02L⇒Tb=m(v02L+g),Tt+mg=mvt2L⇒Tt=m(v02L−5g)\boxed{\frac12mv_0^2=\frac12mv_t^2+2mgL,\quad v_t^2=v_0^2-4gL,\quad T_b-mg=\frac{mv_0^2}{L}\quad\Rightarrow\quad T_b=m(\frac{v_0^2}{L}+g),\quad T_t+mg=\frac{mv_t^2}{L}\Rightarrow T_t=m(\frac{v_0^2}{L}-5g)}
problems.proof.analysis

The results are listed in the order requested and use one consistent sign convention. Their dimensions, initial conditions, and model constraints must all agree.