You are pulling a heavy trunk of mass m along a level floor in which the
coefficient of sliding is μ_{k}. You can pull with a force of
fixed magnitude F.

* Question: * What direction should you
pull to accelerate as quickly as possible?

- Diagram and coordinate systems
- Isolate the systems
- Draw all forces acting
- Take components
- Apply
**F**=m**a**and constraints - Solve
- Check!

Steps 1-4: See transparency

Step 5: Apply Newton's 2nd law

y-component: F sin θ + N =
mg x-component: F
cosθ - μ_{k}N = ma_{x}

Step 6: Solve

The y equation gives: N = mg - F sin θ.

Substitute into the x equation to give:

ma_{x} = Fcosθ - μ_{k}(mg -
F sin θ) = F(μ_{k}sin θ + cosθ) -
μ_{k}mg.

Maximize a_{x}. Compute da_{x}/dθ and set it to zero.
This gives: tan θ_{c} =
μ_{k}.

Finally, determine (a_{x})_{max} by evaluating at the
critical angle.