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HW 10 Question 9

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A block of mass m1 = 1.60 kg and a block of mass m2 = 6.35 kg are connected by a massless string over a pulley in the shape of a solid disk having radius R = 0.250 m and mass M = 10.0 kg. The fixed, wedge-shaped ramp makes an angle of θ = 30.0° as shown in the figure. The coefficient of kinetic friction is 0.360 for both blocks.

image

(b) Determine the acceleration of the two blocks. (Enter the magnitude of the acceleration.)


(c) Determine the tensions in the string on both sides of the pulley.

asked Oct 25, 2013 in Others by tatooine (280 points)

1 Answer

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The blocks are going to slide with acceleration to the right and down the ramp. 

Do free body diagrams for the two blocks and the pulley. Define the positive direction being clock wise for the rotation and towards right and down the ramp. 

two block pulley ramp

For block 1, you would have 4 forces with ||N_1=m_1g|| and ||f_1=\mu m_1 g||. $$T_1-f_1=m_1a$$

For block 2, we have ||N_2 =m_2 gcos\theta|| and ||f_2=\mu m_2gcos\theta||. $$m_2gsin\theta -T_2-f_2=m_2a$$

For the pulley, we have ||I=\frac 1 2 MR^2||. $$T_2R-T_1R=I\alpha$$

And ||\alpha R=a||.

Solve for ||a||, ||T_1|| and ||T_2||. 

 

answered Oct 25, 2013 by PhysicsDude (21,750 points)
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