Child pulling 9 kg sled: finding friction and reaction force

[BoogieBot]

1. A child pulls a sled with mass 9.0kg through the snow(note: no coefficient of friction given, but there _is_ friction between sled & snow). The sled accelerates at 1.0 m/s². The rope exerts 27Nt on the sled in the forward direction.

a) what force must the rope exert on the child (magnitude & direction)?

b) What is the magnitude of the frictional force on the sled (hint: it's in the opposite direction of the sled's motion)?

Homework Equations

F=ma

The Attempt at a Solution

a) 27 Nt, due to Newton's 3rd law, in the opposite direction of the child/sled's motion.


b)
F_rope - F_k = F_total = ma

F_rope = F_k + ma

27 = F_k + (9 * 1)

18Nt = F_k


are my answers correct? Should their signs be negative, because they are in the opposite direction of the sled's motion? Have I made any glaring omissions regarding the rope's tension?

 

[Doc Al]

Looks good to me. Magnitudes are always positive. (The abbreviation for Newton is N, not Nt.)