# 2題普通物理求解 20點

1.A 5.0-m-long ladder leans against a smooth wall at a point 4.0 m above a cement floor. The ladder is uniform and has mass m = 10kg. Assuming the wall is frictionless, but us=0.5 for the floor. What is the maximum distance along the ladder a person of mass 50kg can climb before the ladder start to slip?

2.A solid cylinder of mass m and radius r (I=1/2 mr2) which rolls without slipping down an incline and then up along a vertical circular track of radius R. What is the minimum height H from which the ball must start so that it barely stays in contact at the top of the circle? Assume r<<H and r<<R

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1.A 5.0m ladder leans against a smooth wall at a point 4.0 m above a cement floor. The ladder is uniform and has mass m=10kg. Assum us=0.5 for the floor. What is the maximum distance along the ladder a person of mass M=50kg can climb before the ladder start to slip?Ans:ΣFy=N1-(M+m)g=0 => N1=60gΣFx=N2-u*N1=0 => N2=0.5*60g=30gΣM(N2)=3N1-4Fr-3mg/2-M*g*x=0x=(3N1-4Fr-3mg/2)/Mg=(3*60g-4*30g-15g)/50g=(180-120-15)/50=45/50=0.9m.....ans

2.A solid cylinder of mass m and radius r (I=1/2 mr2) which rolls without slipping down an incline and then up along a vertical circular track of radius R. What is the minimum height H from which the ball must start so that it barely stays in contact at the top of the circle? Assume r<<H and r<<R Ans:Energy Equation at top: m*g*H=m*V^2/2+mg(2R-r) => V^2=2g(H-2R+r)Ball weight=Centrifugal force at top:m*g=m*V^2/(R-r) => V^2=(R-r)*g=2g(H-2R+r)R-r=2H-4R+2r => H=(5R-3r)/2lim(r->0)H≒5R/2.....ans