Meriam, Kraige & Bolton — Statics of Particles: Problem 2_106

⚡ Mecademy AIENG정역학 · ch2  Problem Statement 2/106 Determine the -, -, and -components of force which acts on the tetrahedron as shown. The quantities , and are known, and is the midpoint of edge . Problem 2/106 ● 1. Identify the coordinates of the key points From the given figure, we can determine the coordinates of the vertices of the tetrahedron relative to the origin : Point lies on the -axis at distance : Point lies on the -axis at distance : Point lies on the -axis at distance : Point is defined as the midpoint of the edge . We calculate its coordinates using the midpoint formula: ● 2. Determine the position vector The force acts along the line from point to point . The position vector is given by: ● 3. Calculate the magnitude of the position vector The distance between and is the magnitude of vector : xyzF a,b,cFMAB O(0,0,0) AxaA=(a,0,0) BybB=(0,b,0) CzcC=(0,0,c) MAB M= , , = ( 2 x +x AB 2 y +y AB 2 z +z AB ) , , = ( 2 a+0 2 0+b 2 0+0 ) , ( 2 a 2 b r CM FCMr CM r = CM r − M r = C −0 i+ ( 2 a ) −0 j+ ( 2 b )(0−c)k r = CM i+ 2 a j− 2 b ck CMr CM ∣r ∣= CM = + +(−c) ( 2 a ) 2 ( 2 b ) 2 2 + + c 4 a 2 4 b 2 2 Simplifying the expression by finding a common denominator: ● 4. Express the force as a vector The force vector is the product of its magnitude and the unit vector along its line of action : ● 5. Extract the scalar components From the vector expression, we can identify the -, -, and -components: The scalar components of the force are: ✨ Final Answer Summary Mecademy AI