A force of 30 N is applied at an angle of 60 degrees to a lever arm of length 2

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Question: A force of 30 N is applied at an angle of 60 degrees to a lever arm of length 2 m. What is the torque about the pivot?

Options:

Correct Answer: 52 Nm

Solution:

Torque (τ) = F × r × sin(θ) = 30 N × 2 m × sin(60°) = 30 × 2 × (√3/2) = 30√3 Nm ≈ 51.96 Nm.

A force of 30 N is applied at an angle of 60 degrees to a lever arm of length 2 m. What is the torque about the pivot?

A force of 30 N is applied at an angle of 60 degrees to a lever arm of length 2 m. What is the torque about the pivot?

Step 1: Identify the force applied. In this case, the force (F) is 30 N.
Step 2: Identify the length of the lever arm. Here, the length (r) is 2 m.
Step 3: Identify the angle at which the force is applied. The angle (θ) is 60 degrees.
Step 4: Use the formula for torque (τ): τ = F × r × sin(θ).
Step 5: Calculate sin(60 degrees). The value of sin(60 degrees) is √3/2.
Step 6: Substitute the values into the torque formula: τ = 30 N × 2 m × (√3/2).
Step 7: Simplify the calculation: τ = 30 × 2 × (√3/2) = 30√3 Nm.
Step 8: If needed, calculate the approximate value of 30√3 Nm. This is about 51.96 Nm.

Torque Calculation – Understanding how to calculate torque using the formula τ = F × r × sin(θ), where F is the force, r is the lever arm length, and θ is the angle between the force and the lever arm.
Trigonometric Functions – Applying the sine function to find the effective component of the force that contributes to torque.
Units of Measurement – Recognizing that torque is measured in Newton-meters (Nm) and ensuring unit consistency in calculations.