PHYS_2014_Exam_3_soln

# PHYS_2014_Exam_3_soln - PHYS2014/Fall 2010/Exam No 3 Name...

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Unformatted text preview: PHYS2014/Fall 2010/Exam No. 3 Name:___________________________________ OSU Physics Dept./Benton Recitation TA _________Recitation Time:_______ 1 Physics 2014: General Physics I Solutions to Exam No. 3 16 November 2010 1. A 4.8 kg weight, m w , slides down a frictionless ramp that is at an angle of θ = 22 ° with respect to the horizontal. The weight is attached to a massless string, which in turn is threaded over a pulley (solid disk) of radius r p = 4.5 cm and mass m p = 0.55 kg. The string is then wound around a thin hollow metal cylinder (hoop) of radius r c = 9.4 cm and mass m c = 8.6 kg. Assuming the wheel starts from rest, find its velocity after it has traveled a distance s = 15 cm down the ramp. Solution: (Hopefully) this problem reminds you of a number of similar problems we’ve already seen. In that case, let’s adopt the same approach to solving this problem, i.e. Conservation of Energy. 2 2 2 2 2 2 2 2 2 2 2 2 2 1 1 1 2 2 2 sin 1 2 1 1 sin 2 4 g w Rp Rc w w p p c c p p p p p c c c c c w w p p U K K K m gh m v I I h s I m r v r I m r v r m g s m v m r ω ω θ ω ω θ = + + = + + = Δ = = = = Δ = + 2 2 p v r 2 1 2 c c m r + 2 2 c v r ( ) 2 2 2 2 1 1 1 sin 2 4 2 1 1 sin 2 2 w w p c w w p c m g s m v m v m v m g s m m m v θ θ Δ = + + Δ = + + θ =22 r c =9.4 cm, m c =8.6 kg r p =4.5 cm, m p =0.55kg m w =4.8 kg PHYS2014/Fall 2010/Exam No. 3 Name:___________________________________ OSU Physics Dept./Benton Recitation TA _________Recitation Time:_______ 2 ( ) ( ) 2 2 sin 1 2 m 2 4.8kg 9.80 0.15m sin 22 s 1 4.8kg 0.55kg 8.6kg 2 m 0.62 s w w p c m g s v m m m v v θ Δ = + + ⋅ ⋅ ⋅ ⋅ = + + = r Alternatively, you can solve this problem using torques and forces. First consider just the mass, m w , and solve for the tension in the string between the mass and the pulley, T w . Rotate the coordinate system m w for by 22 ° clockwise....
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PHYS_2014_Exam_3_soln - PHYS2014/Fall 2010/Exam No 3 Name...

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