Assignment 1 Engineering Mechanics 1. A uniform log of length L is incline 30° from the horizontal when supported by a frictionless rock located 0.6L from its left end. The mass of the log is 200 kg. an engineer with a mass of 53.5 kg walks along the log from the left to the right until the log is balanced horizontally. How far from the left end of the log is the engineer when the log is horizontal?
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Base on the illustration. What must be true of all these force for the body to
be in equilibrium?
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- The drag on an airplane wing in flight is known to be a function of the density of air (), the viscosity of air(), the free-stream velocity (U), a characteristic dimension of the wing (s), and the shear stress on the surface of the wing (s). Show that the dimensionless drag, sU2, can be expressed as a function of the Reynolds number, Us.A differential equation encountered in the vibration of beams is d4ydx4=2D where x = distance measured along the beam; [x]=[L] y = displacement of the beam; [y]=[L] = circular frequency of vibration; []=[T1] = mass of the beam per unit length; []=[ML1] D = bending rigidity of beam; [D]=[FL2] Show that the equation is dimensionally homogeneous. Note that [F]=[MLT2] see Eq. (1.21:).• A uniform aluminum beam 9.00 m long, weighing 300 N, rests symmetrically on two supports 5.00 m apart (Fig. E11.14). A boy weighing 600 N starts at point A and walks toward the right. (a) In the same diagram construct two graphs showing the upward forces FA and FB exerted on the beam at points A and B, as functions of the coordinate x of the boy. Let 1 cm = 100 N vertically and 1 cm = 1.00 m horizontally. (b) From your diagram, how far beyond point B can the boy walk before the beam tips? (c) How far from the right end of the beam should support B be placed so that the boy can walk just to the end of the beam
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- A 45 grams (0.045 kg) golf ball of diameter equal to 43 mm fell into a 2m deep lake. Neglect inertia at the moment of impact. Assume viscosity of 1.12x10-3 Ns/m2 , water density of 1,000 kg/m3 and Cd=0.5. Sphere volume equals 4π r³ /3. 1. How long will it take from the moment it hits the surface until it gets to the bottom? 2. If one estimates the Cd with Cd=24/Re formula, the settling velocity would be unrealistically large. Why?A uniform aluminum beam 9.00 m long, weighing 300 N,rests symmetrically on two supports 5.00 m apart (Fig. ). A boyweighing 600 N starts at point A and walks toward the right. (a) In thesame diagram construct two graphs showing the upward forces FA andFB exerted on the beam at points A and B, as functions of the coordinatex of the boy. Let 1 cm = 100 N vertically and 1 cm = 1.00 m horizontally.(b) From your diagram, how far beyond point B can the boy walkbefore the beam tips? (c) How far from the right end of the beam shouldsupport B be placed so that the boy can walk just to the end of the beamwithout causing it to tip?A spaceship has crashed into an ocean on an unknown planet with radius 6.42 * 10 ^ 6 * m and mass 5.82 * 10 ^ 24 The atmospheric pressure at sea level is 202.0 kPa and the ocean has density of 0.817 * 10^ 3 kg/m3 . If the spacecraft can withstand external pressure of 3 atm how deep will the craft sink before being crushed?