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Use Lagrangian formalism to solve the following problem: A block of mass m is held motionless on a frictionless plane of mass M and angle of inclination @ (see Figure below). Here x1 and x2 are the horizontal positions of the plane and block respectively. The plane rests on a frictionless horizontal surface. The block is released. a) What is the change in the vertical height of the block when the plane and the block moved horizontally x1 and x2 distances respectively? b) Write the Lagrangian for the system. c) Derive the Euler-Lagrangian equations for the x1 and x2. ftho plane?

Use Lagrangian formalism to solve the following problem: A block of mass m is held motionless on a frictionless plane of mass M and angle of inclination @ (see Figure below). Here x1 and x2 are the horizontal positions of the plane and block respectively. The plane rests on a frictionless horizontal surface. The block is released. a) What is the change in the vertical height of the block when the plane and the block moved horizontally x1 and x2 distances respectively? b) Write the Lagrangian for the system. c) Derive the Euler-Lagrangian equations for the x1 and x2. ftho plane?

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Use Lagrangian formalism to solve the following problem: A block of mass m is held motionless on a frictionless plane of mass M and angle of inclination @ (see Figure below). Here x1 and x2 are the horizontal positions of the plane and block respectively. The plane rests on a frictionless horizontal surface. The block is released. a) What is the change in the vertical height of the block when the plane and the block moved horizontally x1 and x2 distances respectively? b) Write the Lagrangian for the system. c) Derive the Euler-Lagrangian equations for the x1 and x2. b) What is the horizontal acceleration of the plane?
Transcribed Image Text:Use Lagrangian formalism to solve the following problem: A block of mass m is held motionless on a frictionless plane of mass M and angle of inclination @ (see Figure below). Here x1 and x2 are the horizontal positions of the plane and block respectively. The plane rests on a frictionless horizontal surface. The block is released. a) What is the change in the vertical height of the block when the plane and the block moved horizontally x1 and x2 distances respectively? b) Write the Lagrangian for the system. c) Derive the Euler-Lagrangian equations for the x1 and x2. b) What is the horizontal acceleration of the plane?
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