% MotionGenesis file: MGRocketSledOnInclinedPlaneStatics.txt % Copyright (c) 2009 Motion Genesis LLC. All rights reserved. %------------------------------------------------------------- NewtonianFrame N % Nx> is directed upward along inclined plane. Particle Q % Rocket sled (modeled as a particle). %------------------------------------------------------------- Variable FThrust, Ffriction, FNormal Constant theta = 30 degs % Angle of inclined plane. Constant mu = 0.115 noUnits % Coefficient of static/kinetic friction. Constant g = 10 m/s^2 % Earth's gravitational acceleration. Q.SetMass( m = 100 kg ) %------------------------------------------------------------- % Relevant forces (gravity, thrust, normal, friction) GravityDirection> = -sin(theta)*Nx> - cos(theta)*Ny> Q.AddForce( m*g*GravityDirection> + FThrust * Nx> + FNormal * Ny> + Ffriction * Nx> ) %------------------------------------------------------------- % Static equilibrium equations. Statics[1] = Dot( Nx>, Q.GetStatics() ) Statics[2] = Dot( Ny>, Q.GetStatics() ) %------------------------------------------------------------- % (a) Find minimum thrust to prevent rocket sled from sliding downhill. StaticsA = Evaluate( Statics, Ffriction = mu*FNormal ) AResultSymbolic = Solve( StaticsA, FThrust, FNormal ) AResultNumeric = EvaluateToNumber( AResultSymbolic ) %------------------------------------------------------------- % (b) Find minimum thrust to move rocket sled uphill at constant speed. StaticsB = Evaluate( Statics, Ffriction = -mu*FNormal ) BResultSymbolic = Solve( StaticsB, FThrust, FNormal ) BResultNumeric = EvaluateToNumber( BResultSymbolic ) %------------------------------------------------------------- Save MGRocketSledOnInclinedPlaneStatics.html Quit