1. The problem statement, all variables and given/known data A car attempts to accelerate up a hill at an angle θ to the horizontal. The coefficient of static friction between the tires and the hill is µ > tan θ. What is the maximum acceleration the car can achieve (in the direction upwards along the hill)? Neglect the rotational inertia of the wheels. #8 on this website: https://www.aapt.org/physicsteam/2010/upload/2010_Fma.pdf 2. Relevant equations ΣF = ma f_k = μN 3. The attempt at a solution I first started by drawing a free-body diagram. I knew that there had to be a weight force on the car acting downward, so I drew it. The other obvious force is the normal force, which acts perpendicular to the surface. Now, I first thought that there should also be an external applied force on the car acting in the direction upwards along the hill. I also reasoned that in the direction of motion is upwards along the hill, then there should be a friction force in the direction directly opposite the driving force. I tried solving for a, the maximum acceleration of the car, but I couldn't because I didn't have enough information: N-mgcos(θ) = 0 ⇒ N = mgcos(θ) f_k = μN ⇒ f_k = μ(mgcos(θ)) (F_applied) - mgsin(θ) - μ(mgcos(θ)) = ma a = ((F_applied) - mgsin(θ) - μ(mgcos(θ)))/(m) The above equation for a is simply incorrect; even if I found out the value of (F_applied) or if I found out (F_applied) in terms of some other variables, the answer would be incorrect. Because of this, i suspected that perhaps the applied force of the engine is for some reason some internal force of the system that cancels out with another force to become zero. Then, I considered the possibility of friction acting in the direction of motion, opposite the direction of mgsin(θ). One reason why I thought kinetic friction would act in the direction of motion is that the rear tire has a tendency to rotate clockwise. I then tried solving the problem again with these new forces, and I got the correct answer: N = mgcos(θ) f_k = μ(mgcos(θ)) μ(mgcos(θ)) - mgsin(θ) = ma a = (μ(mgcos(θ)) - mgsin(θ))/(m) ⇒ a = g(µ cos(θ) − sin(θ)) Although this is the correct answer, I still am not sure if my second approach to the problem is correct. If it is the correct attempt, I still don't conceptually understand why there is no applied force in the free body diagram. Also, I don't exactly fully understand why the friction is propelling the car forward; it would make more intuitive sense to me if friction were to be in the opposite direction of the car's motion. How can I fully conceptually understand how the forces act on this system?