Prelim2SolS06 - g(s)=mgs sin θ U s(s)=k(s-s 2/2;U(s)=U g(s...

Info icon This preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
Solutions: Prelim 2, Spring 2006 1. F=16 N 2. N=3 3. G [2 points for A, 3 for H] 4.(a) W=0J (b) W=-686 J 5. A 6. I=I COM +Md 2 ; d 2 =R 2 /2; I=2MR 2 /3 7.(a) Conservation of Energy: E=mgH=mgD+mv 2 /2 Normal force vanishes at top: W=mv 2 /r Solve for H: H=D+r/2 (b)1. (c) In rolling only a fraction of the potential energy is transformed to translational kinetic energy, so more initial potential energy is needed to end up with the same speed. (d) 2 (e) The hollow ball has a larger moment of inertia so more of the potential energy is turned into rotational kinetic energy. More initial potential energy is therefore needed to end up with the same speed. 8. (a) U
Image of page 1
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: g (s)=mgs sin( θ ); U s (s)=k(s-s ) 2 /2;U(s)=U g (s)+U s (s) S [m] U g (s) [J] U s (s) [J] U(s) [J] 0.00 4.5 4.5 0.15 1.5 1.125 2.625 0.30 3 3 0.90 9 9 (b) There is one point of equilibrium and it is stable. To find it we set: 0=F= -dU ds =-W sin( θ ) − k(s-s ), which gives s=0.2m. It is stable because d 2 U ds 2 =k>0 (c) 9.(a) v Ai = 8.8cm 0.4s =22cm/s v Af = 6cm 0.3s =20cm/s (c) v cm = 7.2cm 0.4s =18cm/s (d)Momentum is conserved so the COM velocity is constant (e) v Bi = 5.9cm 0.4s =15cm/s v Bf = 3.3cm 0.2s =16.5cm/s (f) K f K i = v Af 2 +v Bf 2 v Ai 2 +v Bi 2 =0.96...
View Full Document

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern