Consider a disc of mass M with a radius of 0.5 m that is lying on a slope at a 45-degree angle to the horizontal. It grips the hill well and does not slide. The disc is designed in such a way that its mass per unit area, (r), equals r1/2 kg m2, where r is the disc's radial distance in metres from its axis. Calculate the disk's mass.

A uniform rod (mass = 1.8 kg) is 1.5 m long. The rod is pivoted about a horizontal, frictionless pin through one end. The rod is released from rest in a horizontal position. What is the angular speed of the rod (in rad/s) when the rod makes an angle of 23° with the horizontal?. The moment of inertia of the rod about this axis is given by (1/3)ML2.

A sphere of mass M and radius R is not necessarily solid or hollow. It has moment of inertia I= cMR2. As shown in the figure, the sphere starts from rest and rolls without slipping down a ramp from height H. It then moves back up the other side, but now with no friction at all between the sphere and the ramp. What height does the sphere reach?

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…

A triangular plate with base 6 m and height 2 m is submerged vertically in water such that the highest vertex of the plate is 6 meters below the surface and the base is horizontal to the surface. 6 m 6 m 2 m Express the hydrostatic force against one side of the plate as an integral and evaluate it. (Round your answer to the nearest whole number. Use 9.8 m/s2 for the acceleration due to gravity. Recall that the weight density of water is 1,000 kg/m3.)

A shape that covers an area A and has a uniform height h has a volume V= ah Show that v= ah is dimensionally correct.

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A body weighs 250 lb at the earth's surface. Determine c. The weight of the body on the moon's surface.

A 61.0-kg survivor of a cruise line disaster rests atop a block of Styrofoam insulation, using it as a raft. The Styrofoam has dimensions 2.00 m ✕ 2.00 m ✕ 0.0870 m. The bottom 0.022 m of the raft is submerged. A. Write Newton's second law for the system in one dimension, using B for buoyancy, w for the weight of the survivor, and wr for the weight of the raft. (Set a = 0. Solve for Fy, the y-component of the net force. Let upward be the positive y-direction.) Fy = (     ) = 0 B. Calculate the numeric value for the buoyancy, B. (Seawater has density 1025 kg/m3. Enter the answer to at least the ones digit.) C. Using the value of B and the weight w of the survivor, calculate the weight wr of the Styrofoam. D. What is the density of the Styrofoam? E. What is the maximum buoyant force, corresponding to the raft being submerged up to its top surface? F. What total mass of survivors can the raft support?

Determine the magnitude and direction of the angle theta of the force FAB that must be exerted on bar AB to maintain equilibrium of the system. The suspended mass is 110 kg. Neglect the size of the pulley at A and treat all pulleys as smooth. What should happen to maintain the equilibrium of the system if FAB acts with an angle theta= 0°?Consider g = 9.81 m/s2.