What is the moment caused by the force, F = 116 lbf, on the wrench with length, L = 6 in,
around the bolt as shown if θ = 43° ? Report your answer in ft-lbs with the direction of the
moment.*

The moment \( M \) caused by a force \( F \) acting on a wrench is given by the formula:

\[
M = F \cdot L \cdot \sin(\theta)
\]

Where:
- \( F = 116 \, \text{lbf} \) is the force applied,
- \( L = 6 \, \text{inches} \) is the length of the wrench,
- \( \theta = 43^\circ \) is the angle between the force and the wrench,
- \( \sin(\theta) \) is the sine of the angle, which adjusts for the effective perpendicular component of the force.

We need to convert the length of the wrench from inches to feet because the final moment needs to be in ft-lbs. Since \( 1 \, \text{ft} = 12 \, \text{in} \), we convert \( L = 6 \, \text{inches} \) as:

\[
L = \frac{6}{12} = 0.5 \, \text{ft}
\]

Now, substituting values into the moment formula:

\[
M = 116 \cdot 0.5 \cdot \sin(43^\circ)
\]

Let me calculate that for you.The moment caused by the force on the wrench is approximately \( 39.56 \, \text{ft-lbs} \).

### Direction of the Moment:
- Since the force is applied at an angle \( \theta = 43^\circ \), assuming the force tends to rotate the wrench counterclockwise around the bolt, the moment would be **counterclockwise**.

Would you like more details on how moments work, or do you have any other questions?

### Related Questions:
1. How would the moment change if the angle \( \theta \) were increased to 60°?
2. What would happen to the moment if the force was applied in the opposite direction?
3. How does the moment vary if the wrench length \( L \) was doubled?
4. Can you calculate the moment in Nm instead of ft-lbs?
5. How would the moment be affected if the force was applied perpendicular to the wrench?

### Tip:
When calculating moments, always consider the perpendicular component of the force acting relative to the lever arm.

What is the moment caused by the force, F = 116 lbf, on the wrench with length, L = 6 in, around the bolt as shown if θ = 43°? Report your answer in ft-lbs with the direction of the moment.

Learn how to calculate the moment of a force of 116 lbf acting on a wrench with length 6 inches at an angle of 43°. This problem covers key trigonometric and physics concepts, such as force, moment calculation, and sine rule. Suitable for students in Grades 10-12.

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