A door of rectangular shape is hinged along the axis whose direction lies in the xz plane. The door is supported by a cable that has a tensile force of F = 100N. Determine the moment of F about the origin.
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- BUESTION 5 Tit x- aund Use parametric expresion fra oly differentiat on aud find au m its simplest form.Determine the DE for: Straight lines at a fixed distance P from the origin. a. (xy" – y)? = P²[1+ (y')²] %3D b. (xy' – y)? = p2[1+ (y')²] c. (xy' – y)3 = p3[1+ (y')³] d. (xy" – y)3 = p³[1 + (y')³] e. none of theseIf a vector force F = -7 i +10 j +4 k [kN], what will be the coordinate direction angle with the Y-axis: Select one: Oa. B = 83.875° Ob.B= 141.125° Oc. B = 45° O d. B= 38.875°
- Given: F₁ = + < -13.6, 15.6,07 [N] 1₂= 20.1[N] 8 = 45° witch w = 1.875 m Height = 1.875m h h L 144 ( force would need to act ? Y W 1644 11. X 154 varhar is X-dorance from the origin The resultantConsider the robotic arm placed on the zy-place as shown below. Let O be the origin and assume that joint A is on the y-axis. It is given that |OA|-0.6 m. |AB|-1.3 m, IBC) - 1.7 m, ICD-1.2 m, [DE] -0.4 m, ZOAB 160°, ZABC-43° and ZBCD-120°. It is also given that DE || OA. Answer the following. a. Find the direction angle of CD in standard position. Direction angle b. Find ZCDE. ZCDE- c. Find the horizontal distance h and the vertical distance e between O and E. Round your answers to at least 2 decimal places. h- ******** m mh ALL R Y 147 Iwould need to act ? 2x TUL Crven: Force vector F₁ = 20.1 N F₂ = ± L-13.6 ₁13.6, 0) N 2 angle = 0 = 45° width = w 1.875 m height = h = 1.875 m = W = what is x-distance from the origin the resultant force unit [m].
- For the given Two Link Manipulator (Fig 1), If 11-1m and 12=1m 01-40° and 02-10° Calculate the coordinates of the end effector (x,y)Vectors A, Band C are defined as follows: A = 7.5i + 7j - 4.3k; B = 2.5i – 8.3j + 7k; C = 4.8i + 2.9k. Determine the magnitude of vector A [units]. Answer: Determine the magnitude of vector B [units]. Answer: Determine the dot product of vectors A and B. Answer: Determine the angle between vectors A and B in degrees. Answer: Determine the magnitude of the vector (cross) product between vectors A and C. Answer: Determine AxB.C Answer: Determine A (BxC) Answer:It's shown in Fig. 1 that the coordinate frame 0₁X₁Y₁Z₁ is oriented at an angle 0 = 30° with respect to 0oXoyozo, and p¹ = []. Find rotation matrices R and R, and show that RR = 1, where I is an identity matrix. F3 49 F4 H ------- % Yo 00, 01 H Q Search F5 p Q cos A 6 F6 8=30° ** F7 & 7 -40 sin 0 PrtScn F8 Home H F9 End F10 PgUp F
- 2) The vertices of a wedge are given in the matrix show below. Rotate the wedge 30* CCW around the x-axis and then 45° CW around the y-axis. r0 0 0 0 0 11 4 0 0 [P] 4 0 2 0 3 o 3 0.5. वो D 10' F is the orange arrow C 10' B 45* 1000lbs Find FAD, FBC, FCD FAB FAC -7The state of stress at a point in an engine piston is given in the x-y-z coordinates by: 90 180 xx ху XZ [6]=0, |180 240 0 MPa ух yy yz 120 ZX zy Using the matrix transformation law, determine the state of stress at the same point for an element rotated about the x-axis (in the y-z plane) 60° clockwise from its original position. Calculate the stress invariants and write the characteristic equation for the original state of stress, Calculate the deviatoric invariants for the original state of stress, Calculate the principal stresses and the absolute maximum shear stress at the point. What are the stress invariants and the characteristic equation for the transformed state of stress, а. b. С. d. BRE