Force and Translational Dynamics practice quiz

Key ideax_cm = Σm·x / Σm, or ∫x dm / M for a continuous object, with dm = λ dx.

Common mistakeUsing the geometric midpoint when the density is not uniform.

Key ideaDraw a free-body diagram for each object, choose axes, and write ΣF = ma along each axis.

Common mistakeAdding ma to the diagram as if it were a force, or leaving out a force that acts on the object.

Key ideaKinetic friction is μ_k·N. Static friction adjusts as needed, up to μ_s·N. Find N from the perpendicular equation first.

Common mistakeAssuming N = mg when an angled force or an incline changes it.

Key ideaWhen F depends on t, write m dv/dt = F(t) and integrate. The impulse is ∫F dt.

Common mistakeUsing F = ma with a single value of the force when the force changes during the interval.

Key ideaFor an object falling with drag F = −bv, the velocity approaches the terminal velocity mg/b exponentially, with time constant m/b.

Common mistakeThinking the acceleration stays g, or that terminal velocity is reached in a finite time. The acceleration starts at g and decreases toward zero; the net force is zero only at terminal velocity.

Key ideaThe net inward force is mv²/r. For an orbit, gravity provides it: GMm/r² = mv²/r.

Common mistakeAdding a separate “centripetal force” to the free-body diagram, or using the radius from the surface.

Key ideaF = −kx, measured from the spring’s natural length. Springs in series act softer than either spring alone, and springs in parallel act stiffer.

Common mistakeMeasuring x in F = −kx from the hanging-equilibrium position. The spring force uses the stretch from the natural length; only the net force (spring plus gravity) is −k times the displacement from equilibrium.