A force Farrowbold1 of magnitude 5.00 units acts on an object at the origin in a direction θ = 34.0° above the positive x-axis. (See the figure below.) A second force Farrowbold2 of magnitude 5.00 units acts on the object in the direction of the positive y-axis. Find graphically the magnitude and direction of the resultant force Farrowbold1 + Farrowbold2.
magnitude units
direction ° counterclockwise from the +x axis
9.23
To find the magnitude and direction of the resultant force, we can use graphical methods. Here's how you can find it:
1. Draw a coordinate system with the x-axis and y-axis.
2. Locate the point (0,0) at the origin, which represents the position of the object where the forces act.
3. Draw a vector for Farrowbold1 by measuring an angle of 34.0° above the positive x-axis and a magnitude of 5.00 units. The vector should start at the origin.
4. Draw a vector for Farrowbold2 by measuring a direction along the positive y-axis and a magnitude of 5.00 units. The vector should start at the origin as well.
5. To find the resultant force Farrowbold1 + Farrowbold2 graphically, add the vector Farrowbold2 to the tip of the vector Farrowbold1.
6. Draw a vector from the origin to the tip of the resultant vector. This vector represents the magnitude and direction of the resultant force.
7. Measure the length of the resultant vector. The length represents the magnitude of the resultant force. In this case, the length should be around 7.07 units.
8. Measure the angle between the positive x-axis and the resultant vector. This angle represents the direction of the resultant force. In this case, the angle should be around 45.0° counterclockwise from the positive x-axis.
Therefore, the magnitude of the resultant force Farrowbold1 + Farrowbold2 is approximately 7.07 units, and its direction is approximately 45.0° counterclockwise from the positive x-axis.