Finding the resultant of coplanar forces problem

In summary: F2 is 10 degrees from the horizontal, the angle between R2 and the vertical must be 10 degrees as well.Ahh I think I see now. Given that R2 is 100 degrees from the... vertical line, and F2 is 10 degrees from the horizontal, the angle between R2 and the vertical must be 10 degrees as well.
  • #1
Theodore Hodson
24
0

Homework Statement


A uniform ladder of weight W rests with its top against a rough wall and its foot on rough ground which slopes down from the base of the wall at 10 degrees to the horizontal. Resolve, horizontally and vertically, each of the forces acting on the ladder.

2P2cHlT3Aq0c.jpg


Homework Equations

The Attempt at a Solution



Okay so I'm just having some difficulty following this example about coplanar forces from my book.

Looking at the smaller diagrams they drew for splitting R2 and F2 into their perpendicular components, I can't seem to figure out how they knew that those angles would be 10 degrees. I know I need to go back to the original diagram and employ some basic geometrical reasoning, starting from the fact that the ground is inclined at 10 degrees. However, I've been fiddling about with this for a while (drawing on the components on the main diagram, forming right triangles, looking for any parallel lines etc) to try and figure out how those angles would be 10 degrees myself but haven't made any headway. So I'm think I'm going about this the wrong way/not noticing something important.

Any hints/tips to help me on this one would be much appreciated :)
 
Physics news on Phys.org
  • #2
Theodore Hodson said:

Homework Statement


A uniform ladder of weight W rests with its top against a rough wall and its foot on rough ground which slopes down from the base of the wall at 10 degrees to the horizontal. Resolve, horizontally and vertically, each of the forces acting on the ladder.

2P2cHlT3Aq0c.jpg


Homework Equations

The Attempt at a Solution



Okay so I'm just having some difficulty following this example about coplanar forces from my book.

Looking at the smaller diagrams they drew for splitting R2 and F2 into their perpendicular components, I can't seem to figure out how they knew that those angles would be 10 degrees. I know I need to go back to the original diagram and employ some basic geometrical reasoning, starting from the fact that the ground is inclined at 10 degrees. However, I've been fiddling about with this for a while (drawing on the components on the main diagram, forming right triangles, looking for any parallel lines etc) to try and figure out how those angles would be 10 degrees myself but haven't made any headway. So I'm think I'm going about this the wrong way/not noticing something important.

Any hints/tips to help me on this one would be much appreciated :)
Turn the first of the two triangles they drew around. ##R_2## is normal to the ladder, so a vertical line starting from the bottom of the ladder makes an angle of 10° with ##R_2##. Once you see that, getting the two sides of the triangle are pretty straightforward.
 
  • #3
Mark44 said:
Turn the first of the two triangles they drew around. ##R_2## is normal to the ladder, so a vertical line starting from the bottom of the ladder makes an angle of 10° with ##R_2##. Once you see that, getting the two sides of the triangle are pretty straightforward.

Thanks for the response - I think I can see now how the smaller diagrams fit in with the bigger one. The only thing is I don't get how they knew that the angle between R2 and the vertical line drawn is 10 degrees. How?
 
  • #4
Theodore Hodson said:
Thanks for the response - I think I can see now how the smaller diagrams fit in with the bigger one. The only thing is I don't get how they knew that the angle between R2 and the vertical line drawn is 10 degrees. How?
The vertical line is perpendicular to the horizon, right? Through what angle would you have to rotate another vertical line to get one that is perpendicular to the sloping ground? Where you end up is ##R_2##, the hypotenuse of that right triangle.
 
  • #5
Theodore Hodson said:
Thanks for the response - I think I can see now how the smaller diagrams fit in with the bigger one. The only thing is I don't get how they knew that the angle between R2 and the vertical line drawn is 10 degrees. How?
What angle is F2 to the horizontal? What angle is R2 to F2? What angle does that make R2 to the horizontal?
 
  • #6
haruspex said:
What angle is F2 to the horizontal? What angle is R2 to F2? What angle does that make R2 to the horizontal?

F2 is 10 degrees to the horizontal. R2 and F2 are perpendicular so 90 degrees. So does that mean that R2 to the horizontal is 100 degrees?
 
  • #7
Theodore Hodson said:
F2 is 10 degrees to the horizontal. R2 and F2 are perpendicular so 90 degrees. So does that mean that R2 to the horizontal is 100 degrees?
Yes. So what is the angle of R2 to the vertical?
 
  • #8
haruspex said:
Yes. So what is the angle of R2 to the vertical?

Ahh I think I see now. Given that R2 is 100 degrees from the horizontal, and drawing in a vertical line perpendicular to the horizontal at the foot of ladder, its clear that the angle R2 to the vertical will be given by 100-90 .So R2 to the vertical is 10 degrees and that's where the 10 degrees comes from in the component diagrams. Thank-you very much for the hints :)
 

What is meant by "resultant" in the context of coplanar forces?

The resultant of coplanar forces refers to the single force that has the same effect on an object as all the individual forces acting on it combined. It is the vector sum of all the forces and takes into account both the magnitude and direction of each force.

How do you find the resultant of coplanar forces?

To find the resultant of coplanar forces, you need to first determine the magnitude and direction of each force. Then, you can use the parallelogram or triangle method to add the forces together and find the resultant. Alternatively, you can use trigonometric functions and vector components to calculate the resultant.

What is the difference between the parallelogram and triangle method for finding the resultant?

The parallelogram method involves drawing a parallelogram using the forces as adjacent sides and the diagonal of the parallelogram represents the resultant. The triangle method, on the other hand, involves drawing a triangle with the forces as sides and the direction of the resultant is determined by the angle opposite the longest side.

What happens if the resultant of coplanar forces is zero?

If the resultant of coplanar forces is zero, it means that the forces are balanced and cancel each other out. In other words, the net force acting on the object is zero and the object will remain at rest or continue moving at a constant velocity.

Can the resultant of coplanar forces ever be greater than the sum of the individual forces?

Yes, it is possible for the resultant of coplanar forces to be greater than the sum of the individual forces. This can happen when the forces are acting in different directions and the resultant is at an angle between them, resulting in a larger magnitude. This is known as the principle of the parallelogram of forces.

Similar threads

  • Introductory Physics Homework Help
Replies
2
Views
731
  • Introductory Physics Homework Help
Replies
5
Views
2K
  • Introductory Physics Homework Help
Replies
5
Views
2K
  • Introductory Physics Homework Help
Replies
10
Views
1K
  • Introductory Physics Homework Help
Replies
2
Views
1K
  • Introductory Physics Homework Help
Replies
5
Views
687
  • Introductory Physics Homework Help
Replies
2
Views
3K
  • Introductory Physics Homework Help
Replies
4
Views
394
  • Introductory Physics Homework Help
Replies
3
Views
1K
  • Introductory Physics Homework Help
Replies
4
Views
1K
Back
Top