Answered

Westonci.ca is the ultimate Q&A platform, offering detailed and reliable answers from a knowledgeable community. Find reliable answers to your questions from a wide community of knowledgeable experts on our user-friendly Q&A platform. Join our Q&A platform to connect with experts dedicated to providing accurate answers to your questions in various fields.

A particle at the origin is experiencing three forces. The first one has a magnitude of 57 lb and is directed towards (2,-4,5), while the second one has a magnitude of 32 lb and is directed towards (-1,-2,-8). If the net force is 41 lb in the direction of (-5,-1,4), what is the x-component of the third force acting on the particle (in lb)?

Sagot :

onyebuchinnaji

The x-component of the third force acting on the particle is 41.2 lb.

The given parameters;

  • (2, -4, 5) = 57 lb
  • (-1, -2, -8) = 32 lb
  • (-5, -1, 4) = 41 lb

The vector components of the forces is calculated as;

[tex]F_1 = 57, (2,-4, 5) = 57\times \frac{2i -4j+ 5k}{\sqrt{2^2 + 4^2 + 5^2} } = 8.5(2i -4j+ 5k)\\\\F_1 = (17 i -34j + 42.5k)lb\\\\\\ F_2 = 32, (-1, -2, -8) = 32\times \frac{-i -2j-8k}{\sqrt{1^2 + 2^2 + 8^2} } = 8.3(-i-2j-8k)\\\\ F_2 = (-8.3i - 16.6j - 66.4k)lb\\\\\\ F_{net}= 41, (-5, -1, 4) = 41\times \frac{-5i -j+ 4k}{\sqrt{5^2 + 1^2 + 4^2} } = 6.5(-5i-j+ 4k)\\\\ F_{net} = (-32.5i -6.5j+ 24k)lb[/tex]

The x-component of the third force is calculated from the resultant of the forces;

[tex]F_1+F_2 + F_3 = F_{net}\\\\F_3 = F_{net} - (F_1 + F_2)\\\\F_3 = (-32.5i -6.5j + 24k) - (17i -34j + 42.5k) - (-8.3i -16.6j -66.4k)\\\\F_3 = (-32.5 -17 + 8.3)i +(-6.5 + 34+ 16.6)j + (24 -42.5+66.4)k\\\\F_3=(-41.2 i) +(44.1)j + (47.9)k\\\\F_3 = (-41.2i + 44.1 j + 47.9k)lb[/tex]

Thus, the x-component of the third force acting on the particle is 41.2 lb.

Learn more here:https://brainly.com/question/11558676

We hope this was helpful. Please come back whenever you need more information or answers to your queries. We appreciate your time. Please come back anytime for the latest information and answers to your questions. We're here to help at Westonci.ca. Keep visiting for the best answers to your questions.