If a force of 15 N is applied at an angle of 30 degrees to the lever arm of leng

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Question: If a force of 15 N is applied at an angle of 30 degrees to the lever arm of length 1.5 m, what is the torque about the pivot?

Options:

Correct Answer: 7.5 Nm

Solution:

Torque (τ) = F × r × sin(θ) = 15 N × 1.5 m × sin(30°) = 15 × 1.5 × 0.5 = 11.25 Nm.

If a force of 15 N is applied at an angle of 30 degrees to the lever arm of length 1.5 m, what is the torque about the pivot?

If a force of 15 N is applied at an angle of 30 degrees to the lever arm of length 1.5 m, what is the torque about the pivot?

Correct Answer: 11.25 Nm

Step 1: Identify the force applied, which is 15 N.
Step 2: Identify the length of the lever arm, which is 1.5 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 (θ)).
Step 5: Substitute the values into the formula: τ = 15 N × 1.5 m × sin(30°).
Step 6: Calculate sin(30°), which is 0.5.
Step 7: Multiply the values: τ = 15 N × 1.5 m × 0.5.
Step 8: Calculate the result: τ = 15 × 1.5 × 0.5 = 11.25 Nm.

Torque Calculation – Torque is calculated 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 – Understanding how to use sine in the context of angles is crucial for calculating torque correctly.
Units of Measurement – Recognizing that torque is measured in Newton-meters (Nm) and ensuring that all units are consistent in calculations.