The 42nd Period | STEM Education Hub

Your teacher will assign you two forces — a magnitude and an angle for each. From here, the whole project is: calculate the third force that balances them, then prove your math right on the actual table.

🎯 Goals

Add two known force vectors using components to find their resultant.
Calculate the equilibrant that would balance those two forces on a force table.
Set up and test your predicted third force on the real apparatus.
Compare your predicted balancing force to what you actually measured, and explain any gap.

🧰 Materials

⚙️Force table apparatus with pulleys, string, and a ring

🪝Hanging weight sets for all three strings

📐Protractor (for confirming pulley angles)

🧮Calculator

📓Physics notebook

DAY 1

Learn to Add Force Vectors

Section 1 of 5

Build the New Skill

Work through the Deep Dive before touching any real numbers.

Adding vectors with components is the entire foundation of this project — rushing this step will cost you more time later, not less.

Practice with the Force Vector Adder using made-up numbers first.

Get comfortable with the tool and the pattern (components → sum → resultant → equilibrant) before your real assigned values are on the line.

DAY 2

Calculate Your Prediction

Section 2 of 5

Your Assigned Forces

Record your two assigned forces exactly as given.

Double-check both the magnitude (from the hanging weight) and the angle (from the pulley position) before you calculate anything.

Fill out the prediction table below by hand, then check it against the Deep Dive's tool.

Show your work for each step — components, sums, resultant, and equilibrant — not just final numbers.

⚠️ If your calculated equilibrant angle doesn't match the quadrant your components suggest, you likely need to add 180° to your calculator's raw inverse-tangent answer.

	Magnitude (N)	Angle (°)	Fx (N)	Fy (N)
Force 1 (given)
Force 2 (given)
Sum (ΣFx, ΣFy)	—	—
Resultant			—	—
Equilibrant (your prediction)			—	—

DAY 3

Test It For Real

Section 3 of 5

Set Up the Force Table

Set your third string to your predicted angle, and hang your predicted weight.

Set up all three strings, release the ring, and watch what happens.

If the ring isn't centered, make small adjustments and record what you changed.

A slightly-off ring usually means a small adjustment to weight or angle — record your final adjusted values as your 'measured' result.

Section 4 of 5

Compare and Explain

Fill in the comparison table below.

Calculate the difference between your predicted and measured values for both magnitude and angle.

Quantity	Predicted	Measured	Difference
Equilibrant magnitude (N)
Equilibrant angle (°)

Section 5 of 5

Draw Your Free-Body Diagram

Sketch the ring with all three forces drawn to scale and correctly labeled.

Include magnitude and angle labels for each of the three forces, and show that they sum to (approximately) zero.

Sketch your free-body diagram here (or attach a separate sheet)

📊 What Gets Graded

Vector math — correct components, sums, resultant, and equilibrant, with work shown
Prediction — a specific, calculated magnitude and angle for the third force
Comparison — an honest predicted-vs-measured table with a reasonable explanation for any gap
Free-body diagram — all three forces drawn to scale, correctly labeled

📤 Turn In

Completed prediction table showing your full vector-addition work
Completed predicted-vs-measured comparison table
Free-body diagram of the ring showing all three forces in equilibrium

← Back to Project 2-1-4 Overview Review the Deep Dive →Next up: Lesson 2-2-1, Friction — Static vs. Kinetic.