hw36 - 1 x C = F m t- gt M C = I C f R = mR 2 2 C mgR = mR...

Info iconThis preview shows pages 1–4. Sign up to view the full content.

View Full Document Right Arrow Icon
TAM212 Introductory Dynamics Spring 2005 S. Balachandar Homework 36 (4.62, 4.78) 4.62 N f mg y x Equations of motion F x = m ¨ x C mg sin β - f = m ¨ x C M c = I C α fr = 2 5 mr 2 ¨ θ f = 2 5 mr ¨ θ ¨ x C = r ¨ θ Solving the three equations, we get ¨ θ = 5 g sin β 7 r ¨ x C = 5 g sin β 7 1
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Integrating ¨ x C , we get ˙ x C = 5 g sin β 7 t + a a A 0 C 1 Integrating again, x C = 5 g sin β 14 t 2 + a a A L C 2 x C ( t ) = 5 g sin β 14 t 2 + L 4.78 (a) F 0 C mg f N Assume rolling; the equations of motion are then F x = m ¨ x C F 0 - f = m ¨ x C M C = I C α f R = mR 2 2 ¨ θ C f = mR 2 ¨ θ C ¨ x C = R ¨ θ Solving, the three equations, we get F 0 = 3 mR ¨ θ C 2 F 0 = 3 f 2
Background image of page 2
For rolling, 0 f μ N f μ mg F 0 3 μ mg F 0 mg 3 μ So, if F 0 mg > 3 μ , it will slip (b) Assume slipping, i.e. f = μ N . So the equations for motion become, F x = m ¨ x C F 0 - μ N = m ¨ x C F 0 - μ mg = m ¨ x C Integrating, m ˙ x C = F 0 t - μ mgt + a a A 0 C
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 4
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: 1 x C = F m t- gt M C = I C f R = mR 2 2 C mgR = mR 2 2 C C = 2 g R Integrating, C = 2 g R t + a a A C 2 Now, velocity of point B, x B = x C-R = F m t- gt-R 2 g R t = F m t- gt-2 gt = F m t-3 gt 3 If cylinder is slipping, then the point B is dragging and hence, its velocity is to the right x B > F m t-3 gt > F mg > 3 4...
View Full Document

This note was uploaded on 05/24/2010 for the course TM 212 taught by Professor Richard during the Spring '10 term at University of Illinois, Urbana Champaign.

Page1 / 4

hw36 - 1 x C = F m t- gt M C = I C f R = mR 2 2 C mgR = mR...

This preview shows document pages 1 - 4. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online