An object is tied using three wires. The object is extremely small and lightweight and is in static equilibrium. Using the given figure calculate the third wire's tension (magnitude and direction).

A cylindrical object with a mass of 25 kg is positioned on a sloping surface that forms a 32° angle with the horizontal as shown in the figure. The cylindrical object remains at rest on the 32° incline. Determine the magnitude of static friction that prevents the cylindrical object from rolling down the inclined surface.

A vending machine that forms a perfect rectangular prism and stands upright with dimensions of height 2.0 meters, width 1.2 meters, and depth 0.6 meters. This machine is loaded onto a van with the side measuring 1.2 meters aligned with the vehicle's forward motion. Given that friction between the machine and the van's floor prevents sliding, determine the highest possible acceleration of the van that would not cause the vending machine to fall over. Hint: Analyze the situation by considering the action of the normal force at the critical edge along the base of the machine.