anonymous
  • anonymous
At the instant shown, the rod Ris rotating about its centre of rotation with ω=3.3rad/s. mA=11.7kg; The pulley, with mP=11.6kg and RP=0.2m, may be modelled as a uniform disc. The rod, with mR=6.8kg and L=0.8m, may be modelled as a thin beam rotating about one end. g=9.8m/s ². a)What is the magnitude of the acceleration of point B at this instant?
Physics
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SOLVED
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katieb
  • katieb
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anonymous
  • anonymous
Here is diagram:
1 Attachment
IrishBoy123
  • IrishBoy123
|dw:1446382739643:dw| that's your FBD. do you agree? i've done a Euler Lagrange so we can compare answers when you are done.... use the velocity/acceleration of the box as you reference coordinate and convert the angular motion of the pulley and rod accordingly.
ganeshie8
  • ganeshie8
does this work \(|a| = \sqrt{{a_t}^2 + {a_r}^2}=\sqrt{0+(\omega^2r)^2} = 3.3^2\times 0.8=8.7\)

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IrishBoy123
  • IrishBoy123
ganesh, \(a_t \ne 0\), \(a_t = \dot \omega R\) and will be some multiple of g; so you have to work out what it is. but that's a wicked twist you have spotted....point b has tangential *and* radial components to its motion.
anonymous
  • anonymous
What exactly is an Euler Lagrange? Don't exactly get how to sontinue past drawing the FBD's.
anonymous
  • anonymous
I've created 3 equations, one for each FBD (sum of forces in Y direction for first one, sum of moments equals I*angular acceleration for second and sum of moments for third). However, i have 4 unknowns and am confused as how to proceed?
IrishBoy123
  • IrishBoy123
scan your workings ☘
anonymous
  • anonymous
Here's my working out:
IrishBoy123
  • IrishBoy123
at a glance, looks promising you should connect the motion, using \(v = \omega r\) using the varius radii, that will combine \(a\) and \(\alpha\). you should have 2 different \(\alpha\)'s, the rod and the pully, that need to be done separately. PS for the pulley \(\dfrac{1}{4}mr^2\)
anonymous
  • anonymous
thankyou, i was able to solve the problem by inserting the constraints of the different accelerations and then simultaneously equating.

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