What is the Torque?
Question:
A force is applied at two different points along a lever arm: one at 3 cm and another at 4 cm from a pivot point. The same force is applied at both points and at an angle of 100° from the lever. Calculate the total torque produced about the pivot.
A force is applied at two different points along a lever arm: one at 3 cm and another at 4 cm from a pivot point. The same force is applied at both points and at an angle of 100° from the lever. Calculate the total torque produced about the pivot.
📘 Step-by-Step Explanation:
🔹 Understanding Torque:
Torque (
Where:
Torque (
τ) is the measure of the rotational effect of a force about a pivot point and is calculated using the formula:τ = r × F × sin(θ)Where:
ris the distance from the pivot (in meters)Fis the applied force (in Newtons)θis the angle between the force and lever arm
🔹 First Torque Calculation (3 cm):
Convert distance to meters:
Given:
Convert distance to meters:
r₁ = 3 cm = 0.03 mGiven:
θ = 100° → sin(100°) ≈ 0.9848τ₁ = 0.03 × F × sin(100°) = 0.03 × F × 0.9848 = 0.029544 × F
🔹 Second Torque Calculation (4 cm):
Convert distance to meters:
Convert distance to meters:
r₂ = 4 cm = 0.04 mτ₂ = 0.04 × F × sin(100°) = 0.04 × F × 0.9848 = 0.039392 × F
🔹 Total Torque:
τ_total = τ₁ + τ₂ = (0.029544 + 0.039392) × F = 0.068936 × F
✅ Final Answer:
The total torque produced is:
(where
The total torque produced is:
τ = 0.068936 × F(where
F is the applied force in Newtons)