1.2 - Resolution of Forces

Two Perpendicular Components

• Resolution of forces separates a single force into components. Use two perpendicular components, usually horizontal and vertical.
• In tarik upih, an inclined pull has a horizontal component that overcomes friction and a vertical component that helps balance weight together with the normal reaction.
• For force $F$ at angle $\theta$ above the horizontal, the force is the diagonal of a rectangle with sides $F_x$ and $F_y$:

• $F_x$ acts horizontally and $F_y$ vertically. Identify the angle’s reference direction before choosing sine or cosine.

Pushing and Weight on an Incline

• When mopping a floor, a 32 N pushing force at $60^{\circ }$ below the horizontal has a horizontal component along the floor and a vertical component downwards.
• A child of weight 300 N on a slide inclined at $50^{\circ }$ experiences weight vertically downwards. Resolve it into components parallel and perpendicular to the slide.
• For a plane inclined at $\theta$ to the horizontal:

• The angle between the weight and its perpendicular component equals the plane’s angle of inclination.

Worked Example: Inclined Pull on a Block

• A 2.4 kg block experiences pull $T=36\mathrm{N}$ at $30^{\circ }$ above the horizontal, weight $W=24\mathrm{N}$, normal reaction $R=6\mathrm{N}$ and opposing friction $F_R=20\mathrm{N}$.

• Combine forces separately along each direction:

• Resultant force: 11.18 N to the right. Acceleration:

Worked Example: Smooth Inclined Plane

• A 2.4 kg block slides down a smooth plane inclined at $60^{\circ }$. Its weight is 24 N and normal reaction is 12 N.

• Perpendicular forces balance: $R-W_y=12-12=0$.
• The resultant is 20.78 N down the plane: