Barron's 2nd Edition PT1 Q23

Barron's Book

23) This problem wants us to find the net acceleration of the 5-kilogram mass. To simplify the problem, we can draw out a free body diagram of all the forces acting on the mass.

Where F[N] is normal force, T is tension force, F[g] is gravitational force, and f is friction force

Since F[g] and F[N] are equal in magnitude but opposite in direction, we only need to take into account the forces in the x-direction.

Looking at the x-direction forces, I see one problem we need to solve: we don't know the magnitude of the friction force. We are given the coefficient of friction, so we can solve for the friction force.

Where f is friction force, μ is coefficient of friction, F[N] is normal force, F[g] is gravitational force, m is mass, and g is acceleration of gravity

Finally, we only have two steps left: we need to sum the forces and use Newton's 2nd Law to find the acceleration.

Where T is tension force, f is friction force, F[Net] is the net force, m is mass, and a is acceleration

Answer: E