Calculating useful force or force at an angle

  • #1
richard9678
79
4

Homework Statement



I don't understand my textbook.

Homework Equations



Fh = Fa Cos θ

Where Fa is some pulling force applied, in-between horizontal and vertical.

Where Fh is force in the horizontal.

The Attempt at a Solution



Intuitively, if the angle of the force applied is at 45°, then the force in the horizontal and vertical is the same, and half of Fa.

Cos θ for 45° is 0.707. I was expecting 0.5.

What am I getting wrong? Thanks.
 

Answers and Replies

  • #2
Doc Al
Mentor
45,410
1,845
Intuitively, if the angle of the force applied is at 45°, then the force in the horizontal and vertical is the same, and half of Fa.
You are correct that the horizontal and vertical components must be the same, but that doesn't mean that they are each half the total force. Realize that they are perpendicular. Imagine a 45°-45° right triangle with sides of 1 unit length. What's the hypotenuse equal?
 
  • #3
gneill
Mentor
20,945
2,886

Homework Statement



I don't understand my textbook.

Homework Equations



Fh = Fa Cos θ

Where Fa is some pulling force applied, in-between horizontal and vertical.

Where Fh is force in the horizontal.

The Attempt at a Solution



Intuitively, if the angle of the force applied is at 45°, then the force in the horizontal and vertical is the same, and half of Fa.

Cos θ for 45° is 0.707. I was expecting 0.5.

What am I getting wrong? Thanks.

Force components sum the way the legs of a right triangle "sum" to find the hypotenuse.

As you noted, if the angle is 45° then cos(θ) is 1/√2. But sin(θ) is also 1/√2, so the vertically directed force component is indeed equal to the horizontally directed component. But neither one is half of the net force!

For a right triangle with side lengths A and B, the hypotenuse C is given by the relationship:

C2 = A2 + B2

Force components add in the same fashion.

EDIT: Doc Al beat me to it!
 
  • #4
grzz
998
15
... if the angle of the force applied is at 45°, then the force in the horizontal and vertical is the same, and half of Fa...

Yes, at that angle, the two components of the original force have the same magnitude.

BUT since these two components are not in the same direction the magnitude of each of them is not half the magnitude of the original force.

Two forces, each of magnitude F/2, can only give a resultant of magnitude F if these two forces are in the same direction.
 

Suggested for: Calculating useful force or force at an angle

Replies
10
Views
2K
  • Last Post
Replies
1
Views
1K
Replies
11
Views
32K
  • Last Post
Replies
5
Views
3K
  • Last Post
Replies
1
Views
12K
  • Last Post
Replies
8
Views
3K
Replies
4
Views
2K
  • Last Post
Replies
5
Views
6K
Replies
3
Views
5K
Top