Alicia draws a diagram to represent two forces, F1 and F2, acting on a body. The angle between the directions of the forces is 50° as shown in the diagram. Alicia notices that she can use the Law of Cosines to find the magnitude of the resultant force R in the diagram. What is the value of R?

Question

Mathematics

Nicolas Medina

4 September, 17:18

Alicia draws a diagram to represent two forces, F1 and F2, acting on a body. The angle between the directions of the forces is 50° as shown in the diagram. Alicia notices that she can use the Law of Cosines to find the magnitude of the resultant force R in the diagram. What is the value of R?

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Answers (2)

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Abdiel Chavez · Answer 1

Abdiel Chavez 4 September, 18:58

0

C. 70.7 is my best guess.

Annabel Rodgers · Answer 2

Refer to the diagram shown below.

When the two forces F₁ and F₂ are added vectorially, the resultant force is R.

The angle x = 180° - 50° = 130°.

From the Law of Cosines, obtain

R² = F₁² + F₂² - 2F₁F₂ cos (130°)

Note that 2 cos (130°) = - 1.2856.

Answer:

R = √ (F₁² + F₂² + 1.2856 F₁F₂)