### Additional Problems

The coefficient of static friction between the rubber eraser of the pencil and the tabletop is ${\mathrm{\xce\u013d}}_{s}=0.80.$ If the force $\stackrel{\xe2\u2020\u2019}{F}$ is applied along the axis of the pencil, as shown below, what is the minimum angle at which the pencil can stand without slipping? Ignore the weight of the pencil.

A pencil rests against a corner, as shown below. The sharpened end of the pencil touches a smooth vertical surface and the eraser end touches a rough horizontal floor. The coefficient of static friction between the eraser and the floor is ${\mathrm{\xce\u013d}}_{s}=0.80.$ The center of mass of the pencil is located 9.0 cm from the tip of the eraser and 11.0 cm from the tip of the pencil lead. Find the minimum angle $\mathrm{\xce\xb8}$ for which the pencil does not slip.

A uniform 4.0-m plank weighing 200.0 N rests against the corner of a wall, as shown below. There is no friction at the point where the plank meets the corner. (a) Find the forces that the corner and the floor exert on the plank. (b) What is the minimum coefficient of static friction between the floor and the plank to prevent the plank from slipping?

A 40-kg boy jumps from a height of 3.0 m, lands on one foot and comes to rest in 0.10 s after he hits the ground. Assume that he comes to rest with a constant acceleration opposite to the motion. If the total cross-sectional area of the bones in his legs just above his ankles is $3.0\phantom{\rule{0.2em}{0ex}}{\text{cm}}^{2},$ what is the compression stress in these bones? Leg bones can be fractured when they are subjected to stress greater than $1.7\phantom{\rule{0.2em}{0ex}}\u0102\u2014\phantom{\rule{0.2em}{0ex}}{10}^{8}\phantom{\rule{0.2em}{0ex}}\text{Pa}.$ Is the boy in danger of breaking his leg?

Two thin rods, one made of steel and the other of aluminum, are joined end to end. Each rod is 2.0 m long and has cross-sectional area $9.1\phantom{\rule{0.2em}{0ex}}{\text{mm}}^{2}.$ If a 10,000-N tensile force is applied at each end of the combination, find: (a) stress in each rod; (b) strain in each rod; and, (c) elongation of each rod.

Two rods, one made of copper and the other of steel, have the same dimensions. If the copper rod stretches by 0.15 mm under some stress, how much does the steel rod stretch under the same stress?