Answered

Westonci.ca offers fast, accurate answers to your questions. Join our community and get the insights you need now. Get the answers you need quickly and accurately from a dedicated community of experts on our Q&A platform. Get quick and reliable solutions to your questions from a community of experienced experts on our platform.

Three forces are applied to an object: (34.3 N, 62.0 degrees); (56.2 N, 125 degrees); and (45.4 N, 251 degrees) resulting in a net force of

Sagot :

LammettHash

Write each force in i,j component form and sum them up to get the resultant force.

• (34.3 N, 62.0°) :

F₁ = (34.3 N) (cos(62.0°) i + sin(62.0°) j) ≈ (16.1 i + 30.3 j) N

• (56.2 N, 125°) :

F₂ = (56.2 N) (cos(125°) i + sin(125°) j) ≈ (-32.2 i + 46.0 j) N

• (45.4 N, 251°) :

F₃ = (45.4 N) (cos(251°) i + sin(251°) j) ≈ (-14.8 i - 42.9 j) N

Then the resultant is approximately

∑ F = F₁ + F₂ + F₃ ≈ (-30.9 i + 33.4 j) N

Its magnitude is

|∑ F| = √((-30.9)² + 33.4²) N ≈ 45.5 N

Let θ be the resultant's direction, so that

tan(θ) ≈ 33.4/(-30.9)

Taking the inverse tangent of both sides gives

θ ≈ arctan(33.4/(-30.9)) ≈ -47.2°

but this would mean the resultant points out into the fourth quadrant. However, we found that the i-component is negative and the j-component is positive, so the resultant should actually point out into the second quadrant.

To get the correct direction for the resultant, we use the fact that for any angle θ,

tan(θ) = tan(θ + 180°)

Then

θ ≈ 180° + arctan(33.4/(-30.9)) ≈ 133°

We hope this was helpful. Please come back whenever you need more information or answers to your queries. Thanks for using our platform. We aim to provide accurate and up-to-date answers to all your queries. Come back soon. Get the answers you need at Westonci.ca. Stay informed by returning for our latest expert advice.