Spanner Torque Calculation Explained

This solution details the process of calculating the torque applied when a force acts on a spanner. Torque is fundamentally a rotational or twisting force.

Understanding Torque: Force and Lever Arm

Torque ($\tau$) is generated when a force ($F$) is applied at a distance ($r$) from a pivot point. The magnitude of the torque depends on the force applied and the perpendicular distance from the pivot to the line of action of the force. This distance is often referred to as the lever arm.

The formula for calculating torque is:

$ \tau = F \times r $

In this formula:

• $ \tau $ represents the torque, measured in Newton-meters (N-m).
• $ F $ is the magnitude of the applied force, measured in Newtons (N).
• $ r $ is the length of the lever arm, measured in meters (m).

Given Force and Spanner Length

The problem provides the following information:

• Applied Force ($F$): 300 N
• Effective Length of the Spanner ($r$): 15 cm

Unit Conversion: Centimeters to Meters

To ensure accuracy in the calculation, the effective length of the spanner must be converted from centimeters (cm) to meters (m), the standard SI unit for length.

Since $ 1 \, \text{meter} = 100 \, \text{centimeters} $, the conversion is as follows:

$ r = \frac{15 \, \text{cm}}{100 \, \frac{\text{cm}}{\text{m}}} = 0.15 \, \text{m} $

Applying the Torque Formula: Step-by-Step

Now, substitute the values of the force and the converted effective length into the torque formula:

$ \tau = F \times r $

Substitute the given values:

$ \tau = 300 \, \text{N} \times 0.15 \, \text{m} $

Calculate the result:

$ \tau = 45 \, \text{N-m} $

Final Torque Result and Options Analysis

The calculated torque applied to the spanner is 45 Newton-meters (N-m).

Let's review the provided options:

• 1. 20 N-m
• 2. 90 N-m
• 3. 45 N-m
• 4. 11.25 N-m

The computed value of 45 N-m corresponds to Option 3.