The gate in the Figure A is subjected to water pressure on one side and to air pressure on the other side. Determine the value of x for which the gate will rotate counter clockwise if the gate is  rectangular with dimension of 1.5 m  x  1.0 m

Consider the robotic arm shown below, made up of individual arms ?B and ?C. The weight ofthe arms AB and ?C are each 160 N, and the resultant weight force is shown to act through eacharm’s center of gravity as shown. You may assume that the center of gravity is occurring along themidpoint of each arm’s length. The robotic arm is picking up a package that weighs 40 N, and the40 N weight force acts through the package’s center of gravity at the location shown. a) A servomotor at point B is exerting a torque value to resist the rotation inducedby the weight force of the robotic arm BC and the weight force of the 40 N package.Calculate the required torque at point B necessary to resist the moment caused by therobotic arm BC and the 40 N package. Indicate the direction of the required torque (↺ or↻). Report your answer in N-m.b) A servomotor at point C is exerting a torque value to resist the rotation inducedby the weight force of the 40 N package. Calculate the required torque at point C…

find the center of the figure area shown in the image; you must do it with the integral equations described in the figure

Please solve d through g

Please solve this question in fluid mechanics

Problem 3: Let P' (mass 4 m) be an attracting particle acting on the system S. The system S is comprised of the 4 colored particles: â₂ â₁ S1 S₁ S2 S3 S4 P' mass = 2.5 m 2 m 3 m 6m mass= 4 m mass= Then, the system S possesses the following characteristics where the distance of each particle relative to P'is given: mass= S3 mass= S₂ 70₁4 dâ₁-2dâ₂ = 70 7-0 = 11da₁-10d â₂ = 6 dâ₁-5d â₂ 70→² = 14 dâ₁ +5dâ₂ 70 = 15 dâ₁-8 dâ₂ S4 OP

4. The pressure in a stationary liquid depends on the position below the surface z according to p(2) pg2, where p is the density of the liquid and g is the acceleration due to gravity. A planar dam of width w separates water of depth d from air. = (a) The force exerted by the water on the dam. (b) The moment exerted by the water about the central point O of the base of the dam. d Side view 12 Top view W

Find the center of mass of a uniform slice of pizza with radius R and angular width \theta Express your answer in terms of the variables R and \theta .