Four forces (measured in Newtons) act on a crate. The forces are given by the vectors: F₁ = 2121-136j+241k N, F₂ = 108i + 144j+ 189k N. F₂ = -400i + 180j + 240k N, and F₁ = -270€ N a) What is the resultant, R = F₁+F₂ +F3 + F4, of the four forces? What is the magnitude of the resultant force? b) If the displacement of the crate is given by d = 0.5f-0.1j+2.7k m What is the contribution by the first force F₁ to the work done, i.e. W = F₁.d? c) If the third force, F3, acts at the point (0.5, 0.8,0.1) m, what is the moment, M = r X F3, at the point (-0.5,0.8,0.7) m?
Four forces (measured in Newtons) act on a crate. The forces are given by the vectors: F₁ = 2121-136j+241k N, F₂ = 108i + 144j+ 189k N. F₂ = -400i + 180j + 240k N, and F₁ = -270€ N a) What is the resultant, R = F₁+F₂ +F3 + F4, of the four forces? What is the magnitude of the resultant force? b) If the displacement of the crate is given by d = 0.5f-0.1j+2.7k m What is the contribution by the first force F₁ to the work done, i.e. W = F₁.d? c) If the third force, F3, acts at the point (0.5, 0.8,0.1) m, what is the moment, M = r X F3, at the point (-0.5,0.8,0.7) m?
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Chapter1: Units, Trigonometry. And Vectors
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Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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![Question
Four forces (measured in Newtons) act on a crate. The forces are given by the vectors:
F₁ = 212i-136j + 241k N,
F₂ =
= 108i + 144j+ 189k N.
F₂ = -400 + 180j + 240k N, and F₂ = -270€ N
a) What is the resultant, R = F₁+F₂ + F3 + F4, of the four forces? What is the magnitude
of the resultant force?
b) If the displacement of the crate is given by
d = 0.5i - 0.1j + 2.7k m
What is the contribution by the first force F₁ to the work done, i.e. W = F₁. d?
c) If the third force, F3, acts at the point (0.5, 0.8,0.1) m, what is the moment, M = r X F3,
at the point (-0.5,0.8,0.7) m?
d) What is the angle (in degrees to 2 decimal places) between the force vectors F₂ and
F3?
e) What is the force vector, F, that acts in the opposite direction to the force F₂ and has
magnitude of 203 Newtons?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd054b33a-21e3-45de-bc4b-e34888cb542c%2F84729c97-1561-4c9b-b839-16723675a879%2Fxg8f0e_processed.png&w=3840&q=75)
Transcribed Image Text:Question
Four forces (measured in Newtons) act on a crate. The forces are given by the vectors:
F₁ = 212i-136j + 241k N,
F₂ =
= 108i + 144j+ 189k N.
F₂ = -400 + 180j + 240k N, and F₂ = -270€ N
a) What is the resultant, R = F₁+F₂ + F3 + F4, of the four forces? What is the magnitude
of the resultant force?
b) If the displacement of the crate is given by
d = 0.5i - 0.1j + 2.7k m
What is the contribution by the first force F₁ to the work done, i.e. W = F₁. d?
c) If the third force, F3, acts at the point (0.5, 0.8,0.1) m, what is the moment, M = r X F3,
at the point (-0.5,0.8,0.7) m?
d) What is the angle (in degrees to 2 decimal places) between the force vectors F₂ and
F3?
e) What is the force vector, F, that acts in the opposite direction to the force F₂ and has
magnitude of 203 Newtons?
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