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Question Number 20984 by Tinkutara last updated on 09/Sep/17
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 the figure given below. The  value of F_m  is
$$\mathrm{A}\:\mathrm{ball}\:\mathrm{of}\:\mathrm{mass}\:{m}\:\mathrm{is}\:\mathrm{moving}\:\mathrm{with}\:\mathrm{a} \\ $$$$\mathrm{velocity}\:{u}\:\mathrm{rebounds}\:\mathrm{from}\:\mathrm{a}\:\mathrm{wall}\:\mathrm{with} \\ $$$$\mathrm{same}\:\mathrm{speed}.\:\mathrm{The}\:\mathrm{collision}\:\mathrm{is}\:\mathrm{assumed} \\ $$$$\mathrm{to}\:\mathrm{be}\:\mathrm{elastic}\:\mathrm{and}\:\mathrm{the}\:\mathrm{force}\:\mathrm{of}\:\mathrm{interaction} \\ $$$$\mathrm{between}\:\mathrm{the}\:\mathrm{ball}\:\mathrm{and}\:\mathrm{the}\:\mathrm{wall}\:\mathrm{varies}\:\mathrm{as} \\ $$$$\mathrm{shown}\:\mathrm{in}\:\mathrm{the}\:\mathrm{figure}\:\mathrm{given}\:\mathrm{below}.\:\mathrm{The} \\ $$$$\mathrm{value}\:\mathrm{of}\:{F}_{{m}} \:\mathrm{is} \\ $$
Commented by Tinkutara last updated on 09/Sep/17
Answered by dioph last updated on 09/Sep/17
ΔP = 2mu  ΔP = ∫_0 ^( 2T) F(t)dt = F_m T  F_m T = 2mu  F_m  = ((2mu)/T)
$$\Delta{P}\:=\:\mathrm{2}{mu} \\ $$$$\Delta{P}\:=\:\int_{\mathrm{0}} ^{\:\mathrm{2}{T}} {F}\left({t}\right){dt}\:=\:{F}_{{m}} {T} \\ $$$${F}_{{m}} {T}\:=\:\mathrm{2}{mu} \\ $$$${F}_{{m}} \:=\:\frac{\mathrm{2}{mu}}{{T}} \\ $$
Commented by Tinkutara last updated on 13/Sep/17
Thank you very much Sir!
$$\mathrm{Thank}\:\mathrm{you}\:\mathrm{very}\:\mathrm{much}\:\mathrm{Sir}! \\ $$

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