(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

A uniform ball of mass m rols down a rough wedge of mass M and angle alpha , which itself can slide on a smooth horizontal table. The whole sytem undergoes planar motion. How many degrees of freedoms does this system have.? Obtain langrange's equations. for special case in which M =3m/2, find (i) the acceleration of the wedge, ii) the acceleration of the ball releative to the wedge.

2. Relevant equations

3. The attempt at a solution

I am not going to derived my Lagrange equations. I just want know if I have calculated to correct kinetic energy for the wedge and ball and the correct potential energy for the wedge and ball.

T_total=T_ball+T_wedge=T_lin+T_rot.+T_wedge

T_wedge=.5*(3m/2)*v_x^2

v_ball=v_xi+(a*cos(alpha)i+a sin(alpha)k)dtheta/dt

T_ball=.5*m*v_ball^2+.5*(2/5*m*a^2)(*v_ball^2)/a^2. They don't actually tell you the radius of the ball, but I assumed they wanted us to assigned the radius of the ball to a letter and I chose my radius to be a. The first term represents the ball's linear motion and the second term represents the ball's rotational motion.

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# Homework Help: Ball rolls down a piece of wedge

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