Grade 12 · Week 06 · Wednesday · Day 03

Vector Force Accounting

Learning objective: Compute the signed sums of horizontal and vertical forces and the resulting acceleration.

45–60 min · Offline-capable · No physical apparatus required

Reading & explanation

Signs carry directions

Choose right as +x and up as +y. A 14 N rightward push and a 6 N leftward push give ΣFx=+14−6=+8 N, NOT 20 N, because vector directions oppose. Report both the magnitude and the direction, and use newtons (N) for force.

Vertical and horizontal ledgers are independent

A horizontally supported block may have weight downward and normal upward with a vertical sum of zero while its horizontal net force is nonzero. For no vertical acceleration, N+Fup−Fdown−mg=0. For the supported block in this tool, N=mg+Fdown−Fup, with strictly positive N throughout the allowed settings.

Newton's second law relates the sums

In an inertial frame with constant mass, ΣF=ma. A 4 kg block with +8 N horizontal net force has ax=+2 m/s². For positive mass, acceleration points in the same direction as the net force. It may nevertheless be opposite to the current velocity, causing slowing before possible reversal.

A model is not a complete experimental description

An instantaneous FBD is about interactions. If you predict position after a later interval using constant acceleration, you additionally assume those forces remain constant and the body continues to obey the model. Actual friction, contact changes or collisions may invalidate that extension.

Vocabulary

vector sum
Sum of vector quantities accounting for direction and magnitude.
component
Signed amount of a vector along one coordinate axis.
newton
SI force unit N=kg·m/s².
acceleration
Rate of change of velocity measured in m/s².
mass
Measure of inertia, expressed in kilograms (kg).

Worked example

Mass 4 kg, right 14 N, left 6 N: ΣFx=+8 N, ax=+2 m/s². With weight and normal alone vertically, both forces have magnitude 39.2 N and ΣFy=0.

Show direction, units, body boundaries and your calculations.

Independent science journal

Run a balanced, right-unbalanced and left-unbalanced force case. Compute all vector sums before checking the on-screen ledger.

Browser-local journal only. Export a backup for another device.

Daily · 4 Practice Questions

Public, open-book practice with feedback and an 80% correction target. It is not a supervised final.