PHSX 220 Physics I (w/ Calculus) · Unit 1: Kinematics & Newton’s laws · on Exam 1
Ch 5.6–5.7 Common forces and free-body diagrams
Study notes for Common forces and free-body diagrams in PHSX 220 Physics I (w/ Calculus) at Montana State University: the big ideas, key formulas, a worked example, common mistakes and an exam tip. The same topic has endless practice questions and flashcards in StudyCat.
Big ideas
- Normal force $N$: perpendicular to the surface, as large as needed to prevent the object from sinking in. It is not always $mg$: on an incline $N = mg\cos\theta$; in an accelerating elevator $N = m(g + a)$; with an extra downward push it grows.
- Tension $T$: along the rope, same magnitude at both ends of a massless rope, pulls (never pushes). An ideal pulley changes direction, not magnitude.
- Weight $mg$ down; friction parallel to the surface, opposing sliding (or the tendency to slide); spring force $F = -kx$.
- Free-body diagram recipe: isolate one object as a dot; draw every force on it with a label and agent; choose axes (along the acceleration is smartest, tilted for inclines); resolve; write $\sum F_x = ma_x$ and $\sum F_y = ma_y$.
- Equilibrium means $\vec a = 0$: every component sum is zero. This is how you solve for tensions in hanging signs and cables.
Key formulas
Incline (tilted axes)
$$N = mg\cos\theta,\qquad \text{along the slope: } mg\sin\theta$$
Elevator / apparent weight
$$N - mg = ma_y \Rightarrow N = m(g + a_y)$$
Hooke’s law
$$F_{\text{spring}} = -kx$$
Worked example
A 20 kg traffic light hangs from two cables that each make $30^\circ$ with the horizontal. Find the tension.
Show the solution
Vertical equilibrium: $2T\sin30^\circ = mg = 196$ N, so $T = 196$ N. (The horizontal components cancel by symmetry.)
Common mistakes
- Drawing the normal force vertical on an incline. It is perpendicular to the surface.
- Putting forces on the diagram that the object exerts on other things.
- Choosing horizontal axes on an incline, which drags trig into every equation.
Exam tipA correct free-body diagram is worth most of the credit on an exam problem and makes the algebra almost automatic. Never skip it.
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