Addition of cartesian vectors
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The document contains 5 problems about adding Cartesian vectors to find the magnitude and direction angles of resultant forces. Each problem provides some information about 2 or 3 forces acting on an object, and asks to determine properties of one of the forces so that the resultant force has specified characteristics. The problems demonstrate how to use trigonometric relationships and vector addition to solve for unknown force magnitudes and direction angles.
Addition of cartesian vectors
- 1. Addition of Cartesian Vectors
- 2. 1-The shaft S exerts three force components on the die D. Find the magnitude and coordinate direction angles of the resultant force. Force 𝐹2 acts within the octant shown. Magnitude of 𝐹𝑅 = ? Direction angles of 𝐹𝑅 =? (𝐜𝐨𝐬 ⍺) 𝟐+(𝐜𝐨𝐬 𝜷) 𝟐+(𝐜𝐨𝐬 𝜸) 𝟐=1
- 3. 2-Three forces act on the ring. If the resultant force 𝑭 𝑹 has a magnitude and direction as shown, determine the magnitude and the coordinate direction angles of force 𝑭 𝟑. Magnitude of 𝐹3 = ? Direction angles of 𝐹3 =?
- 4. 𝐴 𝑥=Asin ø cos θ 𝐴 𝑦=Asin ø sin θ 𝐴 𝑧=Acos ø A=Asin ø cos θi+Asin ø sin θj+Acos øk
- 5. 3-If the resultant force acting on the bracket is directed along the positive y axis, determine the magnitude of the resultant force and the coordinate direction angles of F so that 𝛽 > 90°. 𝛽 <90 Magnitude of 𝐹 = ? If 𝑭 𝑹 directed along the positive y axis Direction angles of 𝐹 =?
- 6. • 𝐴 𝑥=Asin ø cos 𝜃 • 𝐴 𝑦=Asin ø sin 𝜃 • 𝐴 𝑧=Acos ø • (cos ⍺)2 +(cos 𝛽)2 +(cos 𝛾)2 =1
- 7. 4-Determine the magnitude and coordinate direction angles of 𝑭 𝟐 so that the resultant of the two forces acts along the positive x axis and has a magnitude of 500 N. Magnitude of 𝐹2 = ? if 𝑭 𝑹=500 i Direction angles of 𝐹2 =?
- 8. 5- If the resultant force acting on the bracket is to be 𝐹𝑅 = {800j} N , determine the magnitude and coordinate direction angles of F. Magnitude of 𝐹 = ? if 𝑭 𝑹=800 j Direction angles of 𝐹 =?