Learning Goal: To understand the concept of moment of a force and how to calculate it using a vector formulation. Part A A man wishes to spin a merry-go-round in the x-y plane centered at the origin (0.000, 0.000, 0.000). (Figure 1) Because he must pull upward and cannot stand on the merry-go-round, he must apply a force in the direction of the unit vector u = (-1/3)i+ (2/3)j + (2/3)k. He pulls with a force F = 36.0 Ib from point A [(3.00, 4.00, 0.000) ft]. What are the x, y, and z components of the resulting moment acting on the merry-go-round about the origin? Express your answers numerically in pound-feet to three significant figures separated by commas. М. М,, М, - 96,-72, 120 1b -ft Submit Previous Answers Completed Part B Figure < 1 of 1> Find the magnitude of the moment, and e, the angle between r and the force F. Express your answers in pound-feet and degrees to three significant figures separated by a comma. Πνα ΑΣΦ ve M,0 = lb ft,degrees Submit Request Answer

Learning Goal: To understand the concept of moment of a force and how to calculate it using a vector formulation. A man wishes to spin a merry-go-round in the x-y plane centered at the origin (0.000, 0.000, 0.000). (Figure 1) Because he must pull upward and cannot stand on the merry-go-round, he must apply a force in the direction of the unit vector u = (-1/3)i+(2/3)j+(2/3) k. He pulls with a force F = 47.0 lb from point A[(3.00, 4.00, 0.000) ft]. Part A What are the x, y, and z components of the resulting moment acting on the merry-go-round about the origin? Express your answers numerically in pound-feet to three significant figures separated by commas. ► View Available Hint(s) VE ΑΣΦ Mz, My, M₂ = Submit Part B Complete previous part(s) Provide Feedback vec ? lb-ft

A vector B is 10 cm. long and has a direction – sense of 45°. Vector C is 15 cm. long and has a direction sense of 150°, Find the vector sum or resultant magnitude and its direction by; y 1. Mathematical Solution, 2. Graphical Solution. Scale: 1:1 cm. 3. Draw the position of resultant. 1500 e 450

Learning Goal: To gain insight into the independence of the scalar triple product from the point on the line chosen as the reference point of the calculation. The magnitude of a moment about a line segment connecting points P and Q due to a force F applied at point R (with R not on the line through P and Q) can be calculated using the scalar triple product, MPQ = = upq r x F, where r is a position vector from any point on the line through P and Q to R and up is the unit vector in the direction of line segment PQ. The unit vector upq is then multiplied by this magnitude to find the vector representation of the moment. As shown in the figure, the member is anchored at A and section AB lies in the x-y plane. The dimensions are x₁ = 1.2 m, y₁ = 1.8 m, and z1₁ = 1.6 m. The force applied at point C is F = [-170 i +105 j + 110 k] N. Figure B 1 of 1 Using the position vector from A to C, calculate the moment about segment AB due to force F. Express the individual components to three…