A force of 50 N is applied at an angle of 30 degrees to the lever arm of length

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Question: A force of 50 N is applied at an angle of 30 degrees to the lever arm of length 2 m. What is the torque about the pivot?

Options:

Correct Answer: 86.6 N·m

Solution:

Torque (τ) = F × r × sin(θ) = 50 N × 2 m × sin(30°) = 50 N × 2 m × 0.5 = 50 N·m.

A force of 50 N is applied at an angle of 30 degrees to the lever arm of length 2 m. What is the torque about the pivot?

A force of 50 N is applied at an angle of 30 degrees to the lever arm of length 2 m. What is the torque about the pivot?

Step 1: Identify the force applied, which is 50 N.
Step 2: Identify the length of the lever arm, which is 2 m.
Step 3: Identify the angle at which the force is applied, which is 30 degrees.
Step 4: Use the formula for torque: Torque (τ) = Force (F) × Length of lever arm (r) × sin(angle).
Step 5: Substitute the values into the formula: τ = 50 N × 2 m × sin(30°).
Step 6: Calculate sin(30°), which is 0.5.
Step 7: Substitute sin(30°) into the equation: τ = 50 N × 2 m × 0.5.
Step 8: Perform the multiplication: 50 N × 2 m = 100 N·m.
Step 9: Now multiply 100 N·m by 0.5 to get the final torque: 100 N·m × 0.5 = 50 N·m.

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