Two ropes attached to a young tree are pulled by two landscapers. Rope 1 is pulled with 267 N of force at an angle of 23 degrees north of east and Rope 2 is pulled with 377 N of force due west.
To find the resultant, resolve forces into x (due east) and y (due north) components and add.
Use a diagram to help you understand the angles.
To find the net force on the tree, we need to break down the forces into their horizontal and vertical components and then add them together.
Let's start with Rope 1. The force is 267 N and it is at an angle of 23 degrees north of east. To find the horizontal component of this force, we need to find the cosine of the angle:
Horizontal component = 267 N * cos(23°)
Next, let's find the vertical component of Rope 1. To do this, we need to find the sine of the angle:
Vertical component = 267 N * sin(23°)
Next, let's move on to Rope 2. The force is 377 N and it is due west. Since there is no vertical component for this force, we only need to consider the horizontal component:
Horizontal component = 377 N
Now, let's add up the horizontal components of both ropes:
Net horizontal force = Horizontal component of Rope 1 + Horizontal component of Rope 2
To find the net vertical force, we add up the vertical components of Rope 1:
Net vertical force = Vertical component of Rope 1
Finally, we can find the net force by combining the horizontal and vertical forces:
Net force = √(Net horizontal force^2 + Net vertical force^2)
By plugging in the values and performing the calculations, we can find the net force on the tree.