Problem 8: (10 points) A 1500-N uniform beam at 68.5 to the horizontal is suppor

Question

Problem 8: (10 points) A 1500-N uniform beam at 68.5 to the horizontal is supported by a cable at an angle 0-21.5° to the horizontal as shown in the figure. An object of weight w 1850 N hangs from its top end. (a) Find the tension in the support cable. (b) Find the components of the reaction force exerted by the pivot on the beam. 209 Pivot Problem 7:(10 points) A box is suspended by a uniform beam, of length 2.20 m and weight 80.0 N. A cable is attached perpendicular to the beam at its midpoint, and can support a maximum of 200 N. What is the maximum weight of the box that can be suspended by this system before the cable breaks? 400 box 50.0°

Explanation / Answer

Given,

W = 1500 N ; phi = 68.5 deg and theta = 21.5 deg ; w = 1850 N

a)considering the sum of torques about the pivot point

-1850 L sin21.5 - 1500 x L/2 sin21.5 + T x 3/4 L sin(68.5 + 21.5) = 0

-678 - 275 + 3/4T = 0 => T = 4 x (678 + 275)/3 = 1270.6 N

Hence, T = 1270.6 N

b)Horizontal F is

Fx = T cos21.5 = 1270 x cos21.5 = 1182.3 N

in Y direction

Fy + T sin21.5 - 1500 - 1850 = 0

Fy = 2884 N

Hence, Fx = 1182.3 N and Fy = 2884 N

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