Prove that a force F(x, y, z) is conservative if, and only if, the following relations are satisfied:
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Vector Mechanics for Engineers: Statics and Dynamics
- E:17 EV N 35.4i – 35.4j –- 86.6k 35.4i - 35.4j + 86.6k 35.4i + 35.4j + 86.6k Determine the magnitude of the projection of the vector force F = 100N, onto u axis, from the figure * given below fe 100N 450 70.7N O 100N 60N 96.6Narrow_forwardQ11/ Determine the magnitude of the resultant force acting on the plate and its direction, measured counterclockwise from the positive x axis? Ans: R 1955 N, 0=4.12° F, 650 N F2 750 N 450 00 F 900 N 601arrow_forwardA force is an agent that destroys or tends to destroy motion. Select one: True Falsearrow_forward
- The forces acting on a tripod carrying camera is an example of system of forces. Coplanar Non concurrent Non coplanar Non concurrent O Coplanar concurrent Non coplanar concurrentarrow_forwardThe vertical reaction at support O is directed to the positive direction of the x axis y 3 ft 5 ft 3 ft В 6 ft 60 lb 250 lb 175 lb 5 ft O True O Falsearrow_forwardQ1: Determine the Moment of the Force 800N shown in Fig, about point O By at least 3 ways. 875 mm 625 mm 30 F = 800 N Q2: The effect or two forces FA,FB is (5 KN) and acting along u axis, determine the value of FB by parallelogram method (nun perpendicular coordinate) 00 FA-3 kN 00 00 00 #六女女六六☆☆☆会☆☆女☆☆女☆六☆☆☆☆☆女☆☆☆六☆☆☆☆女☆☆六六☆哈如セ4 位信名 8883 ******** ****** *******arrow_forward
- Assume the following force vectors. These are the only forces acting on the object. Cable AB: F A B = A B k Cable AC: F A C = − 0.55 ⋅ A C i − 0.50 ⋅ A C j + 0.85 ⋅ A C k Cable AD:F A D = 0.25 ⋅ A D i − 0.45 ⋅ A D j + 0.85 ⋅ A D k Applied force 1 (weight): P 1 = − 25 k Applied force 2: P 2 = 12 j a) correct equation for equilibrium in the x-direction? b) correct equation for equilibrium in the y-direction? c) correct equation for equilibrium in the z-direction?arrow_forwardQ.4) A moment and four forces are applied to a two-dimensional frame as shown in figure below. Replace the given force system by a resultant force system acting at point A. Then replace the resultant force system by the simplest resultant and find x and y intercepts of its line of action. 70 lb с 12 in 100 lb 18 in. 90 lb y 14 in. ↓ A B D K E 120 lb-in. - X 15 in. 16 in → G 15 in.- F 80 lbarrow_forwardentalsOfBiomechanics.pdf - Adobe Acrobat Reader DC (32-bit) Sign Window Help Sign 2017 Book_Funda. x 124% 32 (46 of 459) Problem 2.3 Consider the two forces, F, and F2, shown in Fig. 2.17. Assume that these forces are applied on an object in the xy-plane. The first force has a magnitude F1 = 15 N and is applied in a direction that makes an angle a = positive x axis, and the second force has a magnitude F2 = 10 N and is applied in a direction that makes an angle B = 45° with the negative x axis. FR 30° with the (a) Calculate the scalar components of F, and F2 along the x and directions. Fig. 2.17 Problem 2.3 (b) Express F, and F2 in terms of their components. (c) Determine an expression for the resultant force vector, FR. (d) Calculate the magnitude of the resultant force vector. (e) Calculate angle 0 that FR makes with the positive y axis. Answers:arrow_forward
- Consider three forces P1, P2, and P3, where P1 = 165 lb, P2 = 135 Ib, and P3 = 95 Ib. Determine the x and y components of each of the forces shown. %3D |y 30° 40° 45° P3 P1 P2 | lb. |lb. | lb. The x component of force P1 is The y component of force P1 is The x component of force P2 is The y component of force P2 is The x component of force P3 is The y component of force P3 i Ib. Ib. Ib.arrow_forwardQ2. Determine the resultant force and angle of the two forces as shown in figure by (components method the x-horizontal component and y-vertical components)? 60 600 N 400 N 03. Determine the resultant force and angle of the two forces as shown in figure by (Pythagorean law) and (components method the x-horizontal component and y-vertical components)? 3N 60 04. The resultant force equal to 1000N Determine the angle between the two forces as shown in figure by (Pythagorean law)? 1400 N 800 Narrow_forward4) A ring fastened to a beam has two ropes attached. These two ropes exert forces on the ring. F₁ is applied at an angle of 20° from vertical. F₂ is applied at an angle of 0° from vertical. It is desired that the combined force on the ring is 1000N straight down. If 8° = 30°, then what are the forces, F₁ and F₂, in each rope? F2 0 8-300 20° F₁arrow_forward
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