tip In the above figure the block is just on the verge of tipping: W and N act through point A and thus exert zero torque about point A. The incline angle, Otip, is the incline angle beyond which the block will tip, since increasing the angle beyond Orip will move the CG beyond where there is a point of support below it, as in the previous figure. It is not difficult to show, using some geometry and trigonometry, that 0tip is given by Orip = tan' (w/ h) (1) Equation (1) agrees with our intuition: If the block is short and wide (h small, w large) the block will be more difficult to tip (Otip is large) and if the block is tall and narrow (h large, w small) the block will be easier to tip (Otip is small). It is now not difficult to see why the automotive industry defines a safety factor describing how easily a vehicle will rollover as (roughly) vehicle width / vehicle height. The larger this safety factor is, the more resistant the vehicle is to rolling: Short and wide vehicles can take curves at high speeds without rolling, while tall and narrow vehicles cannot. While the torque responsible for tipping a vehicle going around a curve is different than in the case of the block on the incline, the principles involving torques that stabilize and de-stabilize the vehicle to rotation are the same.

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

Find the magnatidue of VB(ft/s): Find the angle of VB(degrees)

show all steps in detail, units and formulas please.

show all steps in detail, units and formulas please.

Many aspects of a gymnast's motion can be modeled by representing the gymnast by four segments consisting of arms, torso (including the head), thighs, and lower legs, as in the figure below. Thigh O Arm Leg 60° 60° Torso a b In the figure, (b) shows arrows of lengths r, locating the center of gravity of each segment. Use the data below and the cg coordinate system shown in figure (b) to locate the center of gravity of the gymnast shown in figure (a). Masses for the arms, thighs, and legs include both appendages. (Enter your answers in m, to at least three significant figures.) Segment Mass (kg) Length (m) (m) Arms 6.89 0.548 0.242 Torso 33.6 0.613 0.337 Thighs 14.1 0.376 0.145 Legs 7.50 0.350 0.227 HINT m %D m y cg E E

See image that is attached. Thank you.

What is the equation of the circle that has radius of 9 and centre at 3 8)2 O (x+3)°+(y-8)°-9 O (x-3)²+(y+8)² – 81 O (x-3)° +(y18)²-9 O (x+3)² + (y-8)²=81 A Moving to another question will save this response.

Please do this carefully.