Masses m and 2m are joined by a light inextensible string which runs without slipping over a uniform circular pulley of mass 2m and radius a. Using the angular position of the pulley as generalized coordinate, write down the Lagrangian function and Lagrange's equation. Find the acceleration of the masses.​

Masses M And 2m Are Joined By A Light Inextensible String Which Runs Without Slipping Over A Uniform

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Answer 1

Answer:   the acceleration of the masses is given by = 0, which means the angular acceleration of the pulley is zero. This implies that the masses m and 2m move with constant velocity,  they are in equilibrium.


Related Questions

When a piece of wood is put in a graduated cylinder containing water the level of water rises from 17.7cm cubic to 18.5cm cubic calculate the total volume of the piece of wood given that it's relative density is 0.60

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The total volume of the piece of wood is 1.33[tex]cm^3[/tex].

To calculate the total volume of the piece of wood, we can use the principle of displacement.

1. First, we need to find the difference in volume between the two water levels. The initial volume is 17.7 [tex]cm^3[/tex], and the final volume is 18.5 cm^3. The difference is 18.5 [tex]cm^3[/tex] - 17.7 [tex]cm^3[/tex] = 0.8 [tex]cm^3[/tex].

2. Now, we need to find the volume of water displaced by the piece of wood. Since the relative density of the wood is 0.60, it means that the wood is 0.60 times denser than water.

3. The volume of water displaced by the wood is equal to the difference in volume divided by the relative density of the wood. So, the volume of water displaced is 0.8 cm^3 / 0.60 = 1.33 [tex]cm^3[/tex].

4. Finally, the total volume of the piece of wood is equal to the volume of water displaced. Therefore, the total volume of the piece of wood is 1.33 [tex]cm^3[/tex].

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