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 ofinclination @ (see Figure below).Here x1 and x2 are the horizontal positions of the plane andblock 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 blockmoved 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?

Given data: mass of block=m, mass of plane=M, the angle of inclination=θ, a) change in vertical…

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Three forces of magnitudes F₁ = 4.0 N, F₂ = 6.0 N, and F3 = 8.0 N are applied to a block of mass = m = 2.0 kg, initially at rest, at angles shown on the diagram. (Figure 1) In this problem, you will determine the resultant (net) force by combining the three individual force vectors. All angles should be measured counterclockwise from the positive x axis (i.e., all angles are positive). Figure 325° F₁ 25° F₂ 1 of 1 X What is the direction of a? In other words, what angle does this vector make with respect to the positive x axis? Express your answer in degrees to two significant figures. ——| ΑΣΦ Submit Part E d = Request Answer Submit = How far (in meters) will the block move in 5.0 s? Recall that it starts from rest. Express the distance d in meters to two significant figures. ΠΙ ΑΣΦ Request Answer ? degrees ? m
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