A 49-N force is applied perpendicular to the portion BC of the bent bar. Determine the moment of P about point B and about point A.
The image shows a bar that is straight from point A to B but then bends at a 42 degree angle to the left from point B to point C. The distance from A to B and B to C is 2.0m.
I determined the moment at point B (before the bend) as the simple calculation 2*49 and got 98.
My question is about the moment about point A. What steps should I take to figure this out?
To determine the moment of a force about a point, we need to calculate the cross product of the position vector from the point to the line of action of the force and the force vector.
In this case, the force of 49 N is applied perpendicular to the portion BC of the bent bar. To determine the moment of P about point A, we need to find the position vector from point A to the line of action of the force.
Here's how you can proceed:
1. Draw a diagram of the bent bar and label the relevant points and distances.
2. Identify the position vector from point A to point C. In this case, it is the sum of vectors AC and AB. Since AB is straight, it is simply 2 m in length along the x-axis. To find AC, the vertical component, we can use the sine rule: AC = AB / sin(CAB). Since the angle CAB is 42 degrees, AC = 2 m / sin(42°).
3. Calculate the position vector from point A to the line of action of the force. This is a vector from point A along the line BC, perpendicular to BC. This can be found by subtracting the vector BC from AC.
4. Calculate the moment about point A using the cross product formula: moment = force magnitude * position vector magnitude * sin(angle between force and position vector). In this case, the force magnitude is 49 N.
5. Calculate the angle between the force vector and the position vector using the dot product formula: cosine(angle) = (force vector * position vector) / (force magnitude * position vector magnitude). Since the force vector is perpendicular to the position vector, the angle will be 90 degrees.
6. Plug in the values into the formula: moment = 49 N * position vector magnitude * sin(90°).
7. Calculate the magnitude of the position vector from point A to the line of action of the force.
8. Finally, calculate the moment about point A by multiplying the force magnitude by the magnitude of the position vector calculated in the previous step.
Following these steps will allow you to determine the moment of the force about point A. Remember to check the direction of your answer, as moments can be either clockwise or counterclockwise.