A farmer's tractor has gotten stuck in a muddy pasture. To try to free the tractor, the farmer ties a rope to a tree and the front of her tractor, then pulls sideways in the middle of the rope with a force of F = 510 N. Angles of θ = 5 degrees are formed as shown. Find the x and y components of the force applied to the front of the tractor by the rope in this position.
" ... as shown " ????
To find the x and y components of the force applied to the front of the tractor by the rope, we can use trigonometric functions. Let's break down the given information:
Force applied to the middle of the rope (sideways force) = F = 510 N
Angle formed with the x-axis (θ) = 5 degrees
Now, let's calculate the x and y components of the force:
Step 1: Calculate the x-component:
The x-component of the force is given by Fx = F * cos(θ).
Substituting the values: Fx = 510 N * cos(5°).
Step 2: Calculate the y-component:
The y-component of the force is given by Fy = F * sin(θ).
Substituting the values: Fy = 510 N * sin(5°).
Now, let's evaluate these calculations:
Step 1: Calculate the x-component:
Fx = 510 N * cos(5°) ≈ 509.84 N
Step 2: Calculate the y-component:
Fy = 510 N * sin(5°) ≈ 44.66 N
Therefore, the x-component of the force applied to the front of the tractor is approximately 509.84 N, and the y-component is approximately 44.66 N.