Question
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
Answers
GPT 3.5
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°.
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°.