A-ball-of-mass-m-is-moving-with-a-velocity-u-rebounds-from-a-wall-with-same-speed-The-collision-is-assumed-to-be-elastic-and-the-force-of-interaction-between-the-ball-and-the-wall-varies-as-shown-in-

Question Number 20984 by Tinkutara last updated on 09/Sep/17

$$\mathrm{A}\:\mathrm{ball}\:\mathrm{of}\:\mathrm{mass}\:{m}\:\mathrm{is}\:\mathrm{moving}\:\mathrm{with}\:\mathrm{a} \\ $$$$\mathrm{velocity}\:{u}\:\mathrm{rebounds}\:\mathrm{from}\:\mathrm{a}\:\mathrm{wall}\:\mathrm{with} \\ $$$$\mathrm{same}\:\mathrm{speed}.\:\mathrm{The}\:\mathrm{collision}\:\mathrm{is}\:\mathrm{assumed} \\ $$$$\mathrm{to}\:\mathrm{be}\:\mathrm{elastic}\:\mathrm{and}\:\mathrm{the}\:\mathrm{force}\:\mathrm{of}\:\mathrm{interaction} \\ $$$$\mathrm{between}\:\mathrm{the}\:\mathrm{ball}\:\mathrm{and}\:\mathrm{the}\:\mathrm{wall}\:\mathrm{varies}\:\mathrm{as} \\ $$$$\mathrm{shown}\:\mathrm{in}\:\mathrm{the}\:\mathrm{figure}\:\mathrm{given}\:\mathrm{below}.\:\mathrm{The} \\ $$$$\mathrm{value}\:\mathrm{of}\:{F}_{{m}} \:\mathrm{is} \\ $$

Commented by Tinkutara last updated on 09/Sep/17

Answered by dioph last updated on 09/Sep/17

$$\Delta{P}\:=\:\mathrm{2}{mu} \\ $$$$\Delta{P}\:=\:\int_{\mathrm{0}} ^{\:\mathrm{2}{T}} {F}\left({t}\right){dt}\:=\:{F}_{{m}} {T} \\ $$$${F}_{{m}} {T}\:=\:\mathrm{2}{mu} \\ $$$${F}_{{m}} \:=\:\frac{\mathrm{2}{mu}}{{T}} \\ $$

Commented by Tinkutara last updated on 13/Sep/17

$$\mathrm{Thank}\:\mathrm{you}\:\mathrm{very}\:\mathrm{much}\:\mathrm{Sir}! \\ $$

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