When pulling the rope, two forces are applied: f1=75 and f2, which is 1/3 less than f1. What is the result of this vector addition? Subject: physics
To find the result of the vector addition of f1 and f2, we need to calculate the magnitude and direction of the resultant vector.
Given that f1 = 75, and f2 is 1/3 less than f1, we can calculate f2 as follows:
f2 = f1 - (1/3 * f1)
= f1 - (1/3) * 75
= 75 - 25
= 50
Now, we can calculate the resultant vector using the Pythagorean theorem:
res = √(f1² + f2²)
= √(75² + 50²)
= √(5625 + 2500)
= √8125
≈ 90.140
Therefore, the magnitude of the resultant vector is approximately 90.140.
To determine the direction of the resultant vector, we can use trigonometry.
tan(θ) = f2/f1
θ = arctan(f2/f1)
= arctan(50/75)
= arctan(2/3)
Using a calculator, we find that θ ≈ 33.69°.
Therefore, the result of this vector addition is a resultant vector with a magnitude of approximately 90.140 and a direction of approximately 33.69°.
To find the result of the vector addition, we need to calculate the net force by adding the two forces together.
Given:
f1 = 75 units
f2 = (1 - 1/3) * f1 = (2/3) * f1
To find the net force (Fnet), we add the two forces:
Fnet = f1 + f2
= 75 + (2/3) * 75
= 75 + 50
= 125 units.
Therefore, the result of this vector addition is a net force of 125 units.