Torque Calculations for Problems 5 and 6
Question:
What is the torque for the following problems?
- Problem 5: A force of 60 N is applied at a distance of 3 m from the axis of rotation, making an angle of 125° with the lever arm.
- Problem 6: A force of 90 N is applied at a distance of 6 cm (i.e., 0.06 m) from the axis of rotation, making an angle of 50° with the lever arm.
Answer:
Torque Formula
Torque (also known as moment) is calculated using the formula:
τ = F × r × sin(θ)
- τ is the torque in Newton-meters (N·m)
- F is the force applied (in Newtons)
- r is the distance from the pivot point (in meters)
- θ is the angle between the force vector and lever arm (in degrees)
Problem 5
Given:
- F = 60 N
- r = 3 m
- θ = 125°
Step-by-step Calculation:
sin(125°) ≈ 0.8192
τ = 60 × 3 × sin(125°)
τ = 60 × 3 × 0.8192 = 147.456 N·m
τ = 60 × 3 × sin(125°)
τ = 60 × 3 × 0.8192 = 147.456 N·m
✔ Torque for Problem 5 = 147.5 N·m (Counterclockwise)
Problem 6
Given:
- F = 90 N
- r = 6 cm = 0.06 m
- θ = 50°
Step-by-step Calculation:
sin(50°) ≈ 0.7660
τ = 90 × 0.06 × sin(50°)
τ = 90 × 0.06 × 0.7660 = 4.133 N·m
τ = 90 × 0.06 × sin(50°)
τ = 90 × 0.06 × 0.7660 = 4.133 N·m
✔ Torque for Problem 6 = 4.13 N·m (Counterclockwise)