Trying to study for my physics exam, any help with the justification for these p

Question

Trying to study for my physics exam, any help with the justification for these problems would be greatly appreciated! (showing 10-14)

10. A solid, uniform sphere of mass 2.0 kg and radius 1.7 m rolls without slipping down arn inclined plane of height 7.0 m. What is the angular velocity of the sphere at the bottomm of the inclined plane? 5.8 rad/s 11. A solid disk of radius 1.60 m and mass 2.30 kg rolls without slipping to the bottom of an inclined plane. If the angular velocity of the disk is 5.35 rad/s at the bottom, what is the height of the inclined plane? 5.61 m 12. A steel guitar string with a diameter of 0.300 mm and a length of 70.0 cm is stretched by 0.500 mm while being tuned. How much force is needed to stretch the string by this amount? (Y-2.0x1011 Pa) 10.1 N 13. An irregularly shaped object 10 m long is placed with each end on a scale. If the scale on the right reads 74 N and the scale on the left reads 93 N, how far from the left is the center of gravity? 4.4 m 14. A roller coaster, loaded with passengers, has a mass of 2000 kg; the radius of curvature of the track at the bottom point of the dip is 24 m. If the vehicle has a speed of 18 m/s at this point, what force is exerted on the vehicle by the track? 4.7x104 N

Explanation / Answer

13) x = L N2 / N1 + N2

= 10 * 74 / (74 + 93 )

= 4.4 m

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14) a = v2 / r = 182 / 24 = 13.5 m/s2

Fnet = m g = 2000 * 13.5 = 27000 N

Fgrav = m g = 2000 * 9.8 = 19600 N

Fnorm = 27000 + 19600 = 46600

= 4.7 * 104 N

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