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Let's break down and solve the given problem step by step.

### Part (a): **Find the moment applied to the bolt at A as a result of the force at point B.**

The **moment** or **torque** \( M \) applied at point A is given by the formula:

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

Where:
- \( F \) is the force applied (50 lbs),
- \( d \) is the perpendicular distance from the point where the force is applied to the pivot (A),
- \( \theta \) is the angle between the force and the lever arm.

Here, \( F = 50 \, \text{lbs} \), the **effective distance** from point A to B is the horizontal distance (10 inches), and \( \theta = 60^\circ \).

Now, we can compute:

\[
M = 50 \cdot 10 \cdot \sin(60^\circ)
\]

We'll calculate this next.

### Part (b): **What orientation of the force at point B would create the maximum moment?**

The moment is maximized when \( \sin(\theta) \) is maximized. The sine function reaches its maximum value when \( \theta = 90^\circ \). Hence, the force should be applied perpendicular to the wrench to create the maximum moment.

### Part (c): **What other change to the setup could increase the moment?**

To increase the moment, either:
1. Increase the length of the wrench, which would increase the distance \( d \),
2. Increase the magnitude of the applied force \( F \), or
3. Ensure the angle \( \theta \) is as close to \( 90^\circ \) as possible to maximize \( \sin(\theta) \).

Let me now compute the moment for part (a).The moment applied to the bolt at point A, as a result of the force at point B, is approximately **433.01 inch-lbs**.

Would you like any further details or have additional questions?

Here are some related questions for further practice:
1. How would the moment change if the force were applied at a 90-degree angle?
2. What would happen to the moment if the length of the wrench was increased to 12 inches?
3. If the force was increased to 60 lbs, what would the new moment be?
4. How does the moment change if the angle decreases to 45 degrees?
5. Can you think of a scenario where decreasing the distance \(d\) might be beneficial?

**Tip**: Always ensure that the angle used in torque calculations is between the direction of the force and the lever arm.

A wrench is used to tighten bolts onto a plate as shown. a) Find the moment applied to the bolt at A as a result of the force at point B. b) What approximate orientation of the force at point B would create the maximum moment, assuming all else stayed the same? Show some math to prove your answer. c) What other change to the setup shown could also increase the moment?

Solve a problem involving torque applied to a bolt using a wrench. Learn how to calculate the moment given force, distance, and angle, and explore how to maximize the moment by changing the orientation of the force or other setup parameters.

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