Resultant Force of two vectors

In summary, the conversation discussed finding the resultant force of two forces, one at a 30 degree angle and one at a 45 degree angle. There was confusion about the coordinate angles and the angles between the forces and the axes. The interpretation of the figure was discussed, with some disagreement about the angles involved. Ultimately, the conversation concluded that the force F2 makes an angle of 45 degrees with the x-y plane and its projection onto the x-y plane makes an angle of 30 degrees with the y-axis and 60 degrees with the x-axis.
  • #1
Hr0427
2
0
Hibbler.ch2.p69.jpg


Find the result force of the two forces.
This problem seemed easy at first, but I think I'm confused as to how to find the coordinate angle (gamma) . For the ( i,j,k) components of F1, I got (300cos(30)i, 0j, 300sin(30)k) I don't understand the function of the 45 degree angle, either. What am i doing wrong? Is the 45 degrees the angle between the y-axis and F2? and also would that make 135 degrees the angle between F2 and Z? then that would make 60 degrees the angle between the x-axis and F2. However, the answer for the resultant force is 733... and i got a number close to 900.
 
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  • #2
Interpretation of the figure seems pretty straight-forward to me. F2 is 30 degrees down from the y-axis on the yz plane and if you create a plane that is perpendicular to the yz plane and contains the F2 vector, F2 is out 45 degrees put on that plane from the line it makes with the yz plane. F1 is obviously 30 degrees down from the x-axis on the xz plane.
 
  • #3
Please post HW-type problems like this in the appropriate HW forum. Also, please use the HW template.
 
  • #4
New to this site, Sorry.
 
  • #5
phinds said:
Interpretation of the figure seems pretty straight-forward to me. F2 is 30 degrees down from the y-axis on the yz plane and if you create a plane that is perpendicular to the yz plane and contains the F2 vector, F2 is out 45 degrees put on that plane from the line it makes with the yz plane. F1 is obviously 30 degrees down from the x-axis on the xz plane.
I look at it from a different, but equivalent, perspective. The force F2 makes an angle of 45 degrees with the x-y plane. Its projection onto the x-y plane makes an angle of 30 degrees with the y-axis and 60 degrees with the x axis.

Chet
 
  • #6
Chestermiller said:
I look at it from a different, but equivalent, perspective. The force F2 makes an angle of 45 degrees with the x-y plane. Its projection onto the x-y plane makes an angle of 30 degrees with the y-axis and 60 degrees with the x axis.

Chet

HA ... you are right of course. An optical illusion, sort of. Seems totally open to interpretation.
 

What is the definition of the resultant force of two vectors?

The resultant force of two vectors is the single vector that represents the combined effect of the two original vectors.

How is the resultant force of two vectors calculated?

The resultant force can be calculated using the Pythagorean theorem and trigonometric functions. The magnitude of the resultant force is equal to the square root of the sum of the squares of the individual vectors' magnitudes. The direction can be determined using inverse trigonometric functions.

What is the difference between the resultant force and the net force?

The resultant force is a single vector that represents the combined effect of two or more vectors, while the net force is the sum of all the forces acting on an object in a specific direction. The net force can be calculated using the same methods as the resultant force, but it takes into account all forces acting on the object, not just two.

Can the resultant force be negative?

Yes, the resultant force can be negative if the two vectors are pointing in opposite directions. This indicates that the object will experience a force in the opposite direction of the resultant force vector.

How does the angle between two vectors affect the resultant force?

The angle between two vectors can affect the magnitude and direction of the resultant force. If the angle is 0 degrees, the resultant force will be the sum of the two vectors. If the angle is 90 degrees, the resultant force will be the square root of the sum of the squares of the individual vectors' magnitudes. The direction of the resultant force will depend on the angle between the two vectors.

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