Two children, Roberto (mass 35.0 kg) and Mary (mass 30.0 kg), go out sledding one winter day. Roberto sits on the sled of mass 5.00 kg, and Mary gives the sled a forward push. The coefficients of friction between Roberto and the upper surface of the sled are μs=0.300 and μk=0.200; the friction force between the sled and the icy ground is so small that we can ignore it. Mary finds that if she pushes too hard on the sled, Roberto slides towards the back of the sled. What is the maximum pushing force she can exert without this happening? Ok so for this problem I actually got the final answer correct (118 N) but was wondering if the way I attempted the problem is correct since my textbook did it differently. So the way my textbook went through the problem was consider Roberto by himself first, and then Roberto and the sled as one unit, two objects all together. To solve they went through this lengthy process first finding Roberto's maximum acceleration then substituting the acceleration expression into the x component expression of the sled and Roberto as one unit, ending up with the final equation FMary on unit=munitμsg. The way I attempted the problem is a lot easier imo. I treated Roberto and the sled as one single unit from the get go. I basically only used two equations: ∑Fext,y= normal force -392N= 0 with -392N being the magnitude of the weight in the negative y direction. From this I solved for n (normal force) and plugged the value into the static friction equation, fs,max=μsn= (0.300)(392N)=118N. From this value i concluded that the force cannot be larger than maximum static friction value, or else Roberto would begin to slip back, so 118N is the correct answer. Both ways of doing it lead to the right answer, but is my way of going about the problem correct or did I just coincidentally get the correct answer? Is it necessary to go back and try the problem using the book's method?