Consider a rigid rod AB acted upon by a force F at point A, inclined as shown. What is the perpendicular distance of the force from the fixed point P? *1 point

To find the perpendicular distance of the force $F$ from the fixed point $P$ on a rigid rod $AB$, we follow these steps:

1. ### Break Down the Problem

• Identify the angle $\theta$ at which force $F$ is inclined with respect to the horizontal or vertical.
• Determine the length of the rod $L$.
• Locate the fixed point $P$ on the rod.

2. ### Relevant Concepts

• The perpendicular distance ($d$) from point $P$ to the line of action of force $F$ can be expressed using trigonometry. Specifically, we can use the relationship:

$d = L \cdot \sin(\theta)$

where $L$ is the distance from point $P$ along the length of the rod to the point of application of force $F$, and $\theta$ is the angle between the force direction and the line connected to point $P$.

3. ### Analysis and Detail

• If the distance from $P$ to $A$ is known, you can calculate the total length $L = PA$.
• By substituting the known values into the identified formula, we can calculate the perpendicular distance.

4. ### Verify and Summarize

• Check that the angle and lengths used are correct, ensuring measurements are taken from point $P$ to point $A$.
• Confirm the calculations follow the $\sin$ function correctly.

Final Answer

The perpendicular distance of the force $F$ from point $P$ is given by:

$d = L \cdot \sin(\theta)$

where $L$ is the length from point $P$ to point $A$, and $\theta$ is the angle of force $F$. (Values for $L$ and $\theta$ must be substituted as per the problem's specifics to compute a numeric result.)