Class Management I Help Midterm 3 Begin Date: 11/20/2017 12:01:00 AM- Due Date:

Question

Class Management I Help Midterm 3 Begin Date: 11/20/2017 12:01:00 AM- Due Date: 11/20/2017 11:59:00 PM End Date: 11/20/2017 11:59.00 PM (25%) Problem 1: 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 mieters. sinO cosO cotan asin acos0 atanO acotan sinhO cosh0 tan cotanho Degrees Radians Submit Hint Hints: deduction per hint Hints remaining:2 Feedback: deduction per feedback. 50% Part (b) Repeat the calculation for the same ball if it slides up the hill without rolling

Explanation / Answer

Applying conservation of energy:

Energy at lower point with velocity v= Energy at top where velocity is zero

....hollow sphere moment of inertia about center axis =0.66*m*r*r

Rotational energy=0.5*0.66*m*r*r*v*v/(r*r)=0.33m*v*v.....

(0.5+0.33)*m*6.8*6.8=mgh

A) h=0.83x6.8*6.8/9.8=3.916 m

For without rolling: 0.5*m*6.8*6.8=mgh

B) h=2.359 m

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