# Work-Energy Scaling

 P: 142 A particle of mass $$M$$ moves along a straight line with initial speed $$v_i$$. A force of magnitude $$F$$pushes the particle a distance $$D$$ along the direction of its motion. assume that the particle's mass is increased to 3M. B.)By what multiplicative factor $$R_k$$ does the initial kinetic energy increase, and by what multiplicative factor $$R_w$$ does the work done by the force increase (with respect to the case when the particle had a mass $$M$$) If one of the quantities doubles, for instance, it would increase by a factor of 2. If a quantity stays the same, then the multiplicative factor would be 1. You should enter the two factors separated by a comma. $$R_k,R_w = ___________$$ this is what i think: to find $$R_k$$ i must use this formula: 1/2*m*v^2 to find $$R_W$$, i must use this formula: W=f*d okay, now to find r_k: 1/2*M*v^2 = 3M (cancel everything and get only 3) now to find r_w: $$W = 1/2*M*v_i^2+F*D -1/2*M*v_i^2 = 1/2*3M*v_i^2+F*D -1/2*3M*v_i^2$$ <-- i get 0, is this correct? i'm pretty sure i'm doing it incorrectly, but i dont know how to correct it. can someone help?