1. Radio engineers are erecting a communications tower that is 16.0 m high. During the installation they stabilize the tower with 32.0 m long cables running from the top of the tower to the ground. The anchors consist of concrete blocks to which the cables can be secured. Each block weighs 1590 N. If the coefficient of static friction between a block and the ground is 0.800, what is the maximum tension that can exist in a cable before that cable's anchor is in danger of moving?
hint: you don't know the friction force at this point, so that doesn't necessarily help you immediately. You must write balance of forces equations in both the x and y directions. You have the x equation already. For the y equation, remember that there are three contributions: the weight of the block, the normal force on the block, and the vertical component of the tension on the cable. You will have to combine the x and y equations algebraically to find the result, also using the condition that friction = mu*(normal force) when the block is about to slide.
2. An airplane traveling at 529 km/hr needs to reverse its course. The pilot decides to accomplish this by banking the wings at an angle of theta = 41.0 degree.
a) Find the time needed to reverse course.
b) How heavy would a 56 kg passenger feel during the turn? In other words, what would be the magnitude of the total force exerted on the passenger by the airplane seat?
Hint: This is a banked turn problem. The force responsible for the turning (centripetal force) comes entirely from the horizontal component of the lift force. Note that the pilot will fly through half a circle while making the turn. You'll have to figure out the turning radius first, then the time to complete half a circle (not a whole circle!).
For part b) Your weight is what a scale would read if you were standing on it during the turn. This is equal to the normal force of the plane holding you "up", in the direction of the lift force on the banked plane.
These two problems on friction and banking angle of airplane have been solved step by step duly illustrated with figs.