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

a)

The moment of a spherical shell is I = (2/3)mr^2

where r is radius.

The initial KE of the sphere is (1/2)mv^2 + (1/2)Iw^2

where w = v/r is the angular velocity

Using conservation of energy, PE gained = KE lost

mgh = (1/2)mv^2+(1/2)Iw^2

mhg = (1/2)mv^2 + (1/2)(2/3)mr^2(v/r)^2

mgh = (1/2)mv^2 + (1/3)mv^2

mgh = (5/6)mv^2

h = 5v^2/6g

h = [5 x (6.80 m/s)^2] / (6 x 9.81 m/s^2)

h = 3.93 m

b)

If instead the ball slides without rolling then w = 0 so

mgh = (1/2)mv^2

h = v^2/2g.

h = (6.80 m/s)^2 / (2 x 9.81 m/s^2)

h = 2.357 m

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