(17%) Problem 4: A ball with an initial velocity of 6.8 m/s rolls up a hill with

Question

(17%) Problem 4: A ball with an initial velocity of 6.8 m/s rolls up a hill without slipping Randomized Variables v=6.8 m/s 50% Part (a) Treating the ball as a spherical shell, calculate the vertical height it reaches, in meters. tan0 sinO coso cotan0 asin acos0 atanO acotan0sinh coshO tanhcotanh0+ 4 5 6 0 °Degrees Radians Submit Hint I give up Hints: 4%deduction per hint. Hints remaining: 2 Feedback: deduction per feedback. -a, 50% Part (b) Repeat the calculation for the same ball if it slides up the hill without rolling.

Explanation / Answer

a) From conservation of energy

m g h = 1/2 m v2 + 1/2 I w2

m g h = 1/2 m v2 + 1/2 (2/5 m r2) w2

m g h = 1/2 m v2 + 1/2 (2/5 m r2) (v/r)2

m g h = 1/2 m v2 + 0.2 m v2

m g h = 0.7 m v2

h = 0.7 v2 / g = 0.7 * 6.82 / 9.8

h = 3.30 m

b) without rolling, m g h = 1/2 m v2

h = 0.5 * v2 / g = 0.5 * 6.82 / 9.8

h = 2.36 m

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