Trying to study for my physics exam any help with the justif

Trying to study for my physics exam, any help with the justification for these problems would be greatly appreciated! (showing 15-19)

15. A 1,500 kg car rounds an unbanked (completely horizontal) curve with a radius of 52 m, at a speed of 12 m/s. What minimum coefficient of friction must exist between the road and the tires to prevent the car from slipping? 0.28 16. A metal rod that is 4.00 m long and 0.50 cm2 in cross-section area is found to stretch 0.20 cm under a tension of 5000 N. What is the Young modulus for this material? 2.0x1011 Pa 17. A specimen of oil having an initial volume of 600 cm3 is subjected to a pressure increase of 3.6x106 Pa, and the volume is found to decrease 0.45 cm3. What is the compressibility of the material? 2.1x1010 Pa1 18. In a materials testing laboratory, metal wire made from a new alloy is found to break when a tensile force of 90.8 N is applied perpendicular to each end. If the diameter of the wire is 1.84 mm, what is the breaking stress of the alloy? 3.41x107 Pa 19. A certain gyroscope consists of a uniform disk with a 50 cm radius mounted at the center of an axle that is 11 cm long and of negligible mass. The axle is horizontal and supported at one end. If the disk is spinning around the axle at 1000 rev/min, what is the precession rate? 0.041 rad/s

Solution

15) mu = v² / R g

= 12² / (52 * 9.8)

= 0.28

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16) Young’s modulus for this metal = l₀ F / A * delta l

= (4 * 5000) / (0.5 * 10^-4 * 0.2 * 10^-2)

= 2 * 10¹¹ Pa