a) What is the magnitude of tension in the cable? (b) What are the magnitude and

Question

a) What is the magnitude of tension in the cable? (b) What are the magnitude and direction (left or right) of the horizontal component of the force on the beam from the hinge? (c) What are the magnitude and direction (up or down) of the vertical component of the force on the beam from the hinge? 1. A uniform beam of weight 800 N and length 10.0 m is supported horizontally by a hinge and a cable; on the left it is hinged to a wall and at a distance 7.0 m from the wall it is held up by a cable with an angle 30.0°. And a block which weighs 200 N is placed at a distance 9.0 m from the wall. cable Hinge 7.0 m Wall 9.0 m (from the wall to the center of mass of the block) 10 pts (a) What is the magnitude of tension in the cable?

Explanation / Answer

here,

length of rod , l = 10 m

weight , W = 800 N

a)

let the tension in the string be T

using moment of force about the left end

W * l/2 + w * 9 - T * 7 * sin(theta) = 0

800 * 10/2 + 200 * 9 = T * 7 * sin(30)

T = 1657.1 N

b)

let the horizontal component of normal force at hinge be Fx

Fx = T * cos(theta)

Fx = 1657.1 * cos(30) N

Fx = 1433 N

and the direction is towards right

c)

let the magnitude of the vertical component of the force on the beam from the hinge be Fy

Fy + T * sin(theta) - W - w = 0

Fy + 1657.1 * sin(30) - 800 - 200 = 0

Fy = 171.5 N

the direction of the vertical componenet of the force on the beam is upwards

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