Meriam, Kraige & Bolton — Statics of Particles: Problem 2_2

⚡ Mecademy AIENG정역학 · ch2  Problem Statement 2/2 The magnitude of the force F is 400 lb. Express F as a vector in terms of the unit vectors i and j. Identify both the scalar and vector components of F. Problem 2/2 ● 1. Analysis of the Force Direction From the provided diagram for Problem 2/2, we can observe the following: The magnitude of the force is given as . The force vector F is directed towards the lower-left (the third quadrant relative to the origin). The angle is specified between the force vector and the horizontal axis (- axis). Because the vector points into the third quadrant, both its and components will be negative. ● 2. Expressing F as a Vector We use trigonometric functions to resolve the force into its rectangular components based on the given angle with the horizontal: 1. Calculate the x-component: 2. Calculate the y-component: F=400 lb θ=30 ∘ x xy F = x −Fcos(30) ∘ F = x −400×cos(30) ∘ F = x −400×0.8660≈−346.4 lb F = y −Fsin(30) ∘ F = y −400×sin(30) ∘ F = y −400×0.5=−200 lb 3. Vector Expression: Combining these into vector notation using unit vectors and : ● 3. Identifying Scalar and Vector Components Scalar components: These are the signed magnitudes along each axis. Vector components: These are the actual vector vectors acting along each axis. Final Result: Vector Expression: Scalar Components: Vector Components: (Note: Results are rounded to three significant figures.) ✨ Final Answer Summary Force Vector: Scalar Components: , Vector Components: , Mecad