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Law of sines:
R^2=22^2+35^2-2*22*35*cos52
Two forces act on a point. One force is 35 newtons. The other is 22 newtons. The angle between the two forces is 52degrees. Find the magnitude of the resultant force in newtons.
bobpursley
answered8 years ago
Steve
answered8 years ago
actually, if you draw the parallelogram, you will see that you have the wrong diagonal.
R^2=22^2+35^2-2*22*35*cos(180-52)
If the vectors are u and v, you want |u+v|, not |u-v|
Explain Bot
answered11 months ago
To find the magnitude of the resultant force, we can use the concept of vector addition. Here's how you can calculate it step by step:
1. Split each force into its horizontal and vertical components. We need to do this because the given forces are not parallel or collinear.
Force 1 (35 newtons):
- Horizontal component: 35 * cos(0°) = 35 * 1 = 35 newtons
- Vertical component: 35 * sin(0°) = 0 newtons
Force 2 (22 newtons):
- Horizontal component: 22 * cos(52°)
- Vertical component: 22 * sin(52°)
2. Add up the horizontal and vertical components of the two forces separately:
Horizontal component of the resultant force = sum of horizontal components of Force 1 and Force 2
Vertical component of the resultant force = sum of vertical components of Force 1 and Force 2
Horizontal component of the resultant force = 35 newtons + (22 newtons * cos(52°))
Vertical component of the resultant force = 0 newtons + (22 newtons * sin(52°))
3. Use Pythagoras' theorem to find the magnitude of the resultant force:
Magnitude of the resultant force = square root of [(horizontal component)^2 + (vertical component)^2]
Magnitude of the resultant force = √[(35 + 22cos(52°))^2 + (22sin(52°))^2]
Evaluating this expression will give you the magnitude of the resultant force in newtons.