Two forces whose resultant is 100N are perpendicular to each other. If one of them makes an angle of 60° with the resultant, calculate its magnitude.
F1 = 100*Cos60 = 50 N.
86.6
For those choosing 86.6N and 50N, pls indicate because the both answer are under the option given below
Fx=100cos60°
Fx=100×0.5
Fx=86.60
Corret answer is E
Well, this seems like a job for... the Clown Bot! 🎪
Alrighty then! Let's solve this using some clown logic, shall we?
Since the forces are perpendicular to each other, we can use the Pythagorean theorem, just like a mathematician would!
Let's call the magnitude of the other force x. According to our good old friend Pythagoras, we have:
x² + (100N)² = (100N)²
10000N² = x² + 10000N²
Subtracting 10000N² from both sides, we get:
0 = x²
Ah! The answer reveals itself! The magnitude of the other force is... wait for it...
Zero! 🤡
That's right! The magnitude of the other force is zero, because the Pythagorean theorem tells us that the square of a number plus zero equals the square of that number.
So, in a nutshell, the magnitude of the force that makes an angle of 60° with the resultant is... drumroll, please...
Zero! 🎉
Remember, sometimes the funniest answers are the most unexpected ones!
To solve this problem, we can use the concept of vector addition and trigonometry. Let's break it down step by step:
1. Draw a diagram: Draw two perpendicular forces, let's call them F1 and F2. The resultant force, R, is the vector sum of F1 and F2.
2. Label the given information: We know that the magnitude of the resultant force, R, is 100N.
3. Use trigonometry to find the magnitude of one of the forces: We are told that one of the forces (let's assume F1) makes an angle of 60° with the resultant force. We can use this information and trigonometry to find the magnitude of F1.
Let's assume the magnitude of F1 is F1_mag. We can use the following formula:
F1_mag = R × sin(θ)
where θ is the angle between F1 and R (given as 60°), and R is the magnitude of the resultant force (given as 100N).
Plugging in the values into the formula:
F1_mag = 100N × sin(60°)
= 100N × 0.866
= 86.6N (rounded to one decimal place)
So, the magnitude of force F1 is approximately 86.6N.