Forces and Newton's laws (SACE Stage 2 Physics)

What this dot point is asking

You need to state and apply Newton's three laws, draw free-body diagrams, resolve forces (including on inclined planes), and calculate acceleration from the net force on an object or connected system.

The three laws

The second law is the workhorse. "Net force" means the vector sum of all forces acting on the object. If the net force is zero the object is in equilibrium (first law); if not, it accelerates in the direction of the net force, with $a = F_\text{net}/m$.

Free-body diagrams

A free-body diagram shows one object as a point (or simple shape) with every force on it drawn as an arrow from that point. Typical forces are:

• Weight $W = mg$, always vertically down.
• Normal force $N$, perpendicular to the surface.
• Tension $T$, along a rope or cable, pulling away from the object.
• Friction $f$, parallel to the surface, opposing relative motion.
• Applied force $F$, whatever pushes or pulls.

Once drawn, resolve the forces into perpendicular axes (usually horizontal and vertical, or along and across an incline) and apply $\vec{F}_{\text{net}} = m\vec{a}$ to each axis separately.

Forces on an inclined plane

For an object on a frictionless incline at angle $\theta$, choose axes along and perpendicular to the slope. The weight resolves into:

Perpendicular to the slope there is no acceleration, so $N = mg\cos\theta$. Along the slope, $mg\sin\theta$ produces an acceleration $a = g\sin\theta$ (frictionless). If friction acts, subtract $f$ from $mg\sin\theta$ before dividing by the mass.

Connected systems

For objects joined by a rope (e.g. a trolley pulled by a hanging mass over a pulley), treat the whole system to find the common acceleration, then isolate one object to find the tension. For the whole system:

Then apply Newton's second law to a single object to get the internal tension. The rope tension is an internal force for the system but an external force for each block, which is why isolating one block reveals it.

Equilibrium

When $\vec{F}_{\text{net}} = 0$ the object is in equilibrium (at rest or constant velocity). Then the components of all forces balance in each direction. This is how you find unknown tensions in a hanging sign or the friction holding a box still on a slope. Set the sum of components to zero along each axis and solve.