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.
Law of sines:
R^2=22^2+35^2-2*22*35*cos52
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|
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.