Problems(1)
A simplified model of a bicycle of mass M has two tires that each comes into contact with the ground at a point. The wheelbase of this bicycle (the distance between the points of contact with the ground) is w, and the center of mass of the bicycle is located midway between the tires and a height h above the ground. The bicycle is moving to the right, but slowing down at a constant rate. The acceleration has a magnitude a. Air resistance may be ignored.
[asy]
size(175);
pen dps = linewidth(0.7) + fontsize(4); defaultpen(dps);
draw(circle((0,0),1),black+linewidth(2.5));
draw(circle((3,0),1),black+linewidth(2.5));
draw((1.5,0)--(0,0)--(1,1.5)--(2.5,1.5)--(1.5,0)--(1,1.5),black+linewidth(1));
draw((3,0)--(2.4,1.8),black+linewidth(1));
filldraw(circle((1.5,2/3),0.05),gray);
draw((1.3,1.6)--(0.7,1.6)--(0.7,1.75)--cycle,black+linewidth(1));
label("center of mass of bicycle",(2.5,1.9));
draw((1.55,0.85)--(1.8,1.8),BeginArrow);
draw((4.5,-1)--(4.5,2/3),BeginArrow,EndArrow);
label("h",(4.5,-1/6),E);
draw((1.5,2/3)--(4.5,2/3),dotted);
draw((0,-1)--(4.5,-1),dotted);
draw((0,-5/4)--(3,-5/4),BeginArrow,EndArrow);
label("w",(3/2,-5/4),S);
draw((0,-1)--(0,-6/4),dotted);
draw((3,-1)--(3,-6/4),dotted);
[/asy]
Case 1 (Questions 28 - 29): Assume that the coefficient of sliding friction between each tire and the ground is μ, and that both tires are skidding: sliding without rotating. Express your answers in terms of w, h, M, and g.What is the maximum value of a so that both tires remain in contact with the ground?<spanclass=′latex−bold′>(A)</span> hwg<spanclass=′latex−bold′>(B)</span> 2hwg<spanclass=′latex−bold′>(C)</span> 2whg<spanclass=′latex−bold′>(D)</span> 2wgh<spanclass=′latex−bold′>(E)</span> none of the above