Suppose that F1 = 850 N and F2 = 425 N . Determine the magnitude of the resultant force.
session.masteringengineering.com/problemAsset/2086561/6/Hibbeler14.ch2.p43.jpg
I think i need to draw a line from F1 to F2 on the figure and work out the problem. Not sure whaat to do . I forgot what the resutant force is.
?? Usually a resultant is just the sum of the two forces.
Just add F1 and F2. You just have to break them down into i and j components first, which you have shown you can do.
Or, use the law of cosines. The angle between F1 and F2 is 105°, so the length of F1+F2 is just the diagonal of the parallelogram formed by them. That is,
d^2 = 850^2 + 425^2 - 2*850*425 cos75°
To determine the magnitude of the resultant force, you need to understand that the resultant force is the vector sum of F1 and F2. In other words, you need to add these two forces together as vectors.
To visualize this, you can draw a vector diagram. Start by drawing a line to represent F1 and label its magnitude, which is 850 N. Then, draw another line to represent F2 and label its magnitude, which is 425 N. The lines should originate from the same point, representing the point of application of the forces.
Next, draw a third vector to represent the resultant force. To do this, you need to connect the initial and final points of F1 and F2 with a straight line. The length of this line will represent the magnitude of the resultant force.
Finally, use a ruler or a protractor to measure the length of the line representing the resultant force. The magnitude of the resultant force will be equal to the length you measure.
Alternatively, if you are unable to physically measure the diagram, you can use the Pythagorean theorem to find the magnitude of the resultant force. The Pythagorean theorem states that in a right-angled triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
In this case, F1 and F2 form right-angled sides of a triangle, with the resultant force as the hypotenuse. You can calculate the magnitude of the resultant force using the following formula:
Resultant force magnitude (FR) = sqrt(F1^2 + F2^2)
Substituting the given values, we have:
FR = sqrt(850^2 + 425^2)
Compute the square of each term, add them together, and take the square root to find the magnitude of the resultant force, FR.
I hope this helps!