1. A child slides across a floor in a pair of rubber-soled shoes. The friction force acting on each foot is 20 N, the footprint area of each foot is 14 cm2, and the thickness of the soles is 5.0 mm. Find the horizontal distance travelled by the sheared face of the sole. The shear modulus of the rubber is 3.0 × 106 Pa.
2. A high-speed lifting mechanism supports an 800-kg object with a steel cable that is 25.0 m long and 4.00 cm2 in cross-sectional area.
(a) Determine the elongation of the cable.
(b) By what additional amount does the cable increase in length if the object is accelerated upwards at a rate of 3.0 m/s2?
(c) What is the greatest mass that can be accelerated upwards at 3.0 m/s2 if the stress in the cable is not to exceed the elastic limit of the cable, which is 2.2 × 108 Pa?
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