Mastering Physics: Static Equilibrium, Torque, Tension, and a subtle point about Friction!

3 Mastering Physics problems: 1) You open a restaurant and hope to entice customers by hanging out a sign (Figure 1). The uniform horizontal beam supporting the sign is 1.60 m long, has a mass of 17.0 kg , and is hinged to the wall. The sign itself is uniform with a mass of 33.0 kg and overall length of 1.20 m . The two wires supporting the sign are each 35.0 cm long, are 90.0 cm apart, and are equally spaced from the middle of the sign. The cable supporting the beam is 2.20 m long. a) What minimum tension must your cable be able to support without having your sign come crashing down? b) What minimum vertical force must the hinge be able to support without pulling out of the wall? 2) A uniform ladder with mass m2 and length L rests against a smooth wall (Figure 1). A do-it-yourself enthusiast of mass m1 stands on the ladder a distance d from the bottom (measured along the ladder). The ladder makes an angle theta with the ground. There is no friction between the wall and the ladder, but there is a frictional force of magnitude f between the floor and the ladder. N1 is the magnitude of the normal force exerted by the wall on the ladder, and N2 is the magnitude of the normal force exerted by the ground on the ladder. Throughout the problem, consider counterclockwise torques to be positive. None of your answers should involve T (i.e., simplify your trig functions). a) What is the minimum coefficient of static friction mu_min required between the ladder and the ground so that the ladder does not slip? b) Suppose that the actual coefficient of friction is one and a half times as large as the value of mu_min . That is, Hs = (3/2)µmin . Under these circumstances, what is the magnitude of the force of friction f that the floor applies to the ladder? Express your answer in terms of m1, m2, d, L, g, and theta. 3) A Bar Suspended by Two Vertical Strings. The figure (Figure 1) shows a model of a crane that may be mounted on a truck. A rigid uniform horizontal bar of mass m1 = 85.0 kg and length L = 5.70 m is supported by two vertical massless strings. String A is attached at a distance d = 1.50 m from the left end of the bar and is connected to the top plate. String B is attached to the left end of the bar and is connected to the floor. An object of mass m2 = 2000 kg is supported by the crane at a distance x = 5.50 m from the left end of the bar. Throughout this problem, positive torque is counterclockwise and use 9.80 m/s^2 for the magnitude of the acceleration due to gravity. a) Find T_A, the tension in string A. Express your answer in Newtons using the three significant figures. b) Find T_B, the magnitude of the tension in string B. Express your answer in Newtons using three significant figures. c) If the bar and block are too heavy the strings may break. Which of the two identical strings will break first? d) If the mass of the block is too large and the block is too close to the left end of the bar (near string B) then the horizontal bar may become unstable (i.e., the bar may no longer remain horizontal). What is the smallest possible value of x such that the bar remains stable (call it x_critical)? Express your answer for x_critical in terms of m1, m2, d, and L. Facebook: www.facebook.com/nike.dattani LinkedIn:   / nike-dattani   Google Scholar: https://scholar.google.com/citations?...   / ndattani   https://github.com/ndattani Stack Exchange: https://stackexchange.com/users/13271... https://hpqc.org/ https://hpqc.org/college