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One end of a heavy beam of mass M = 50.0 kg is hinged to a vertical wall, and the other en...

One end of a heavy beam of mass M = 50.0 kg is hinged to a vertical wall, and the other end is tied to a steel cable of length 3.0 m, as shown in the figure. The other end of the cable is also attached to the wall at a distance of 4.0 m above the hinge. A mass m = 20.0 kg is hung from one end of the beam by a rope.

a) Determine the tensions in the cable and the rope,

b) Find the force the hinge exerts on the beam.

Step-by-Step Solution

Solution 1
Step #1 of 10

THINK:

(a) Determine the tension in the cable and rope.

(b) Find the forces the hinge exerts on the beam.

Step #2 of 10

SKETCH:

The represented free body diagram as below:

Step #3 of 10

RESEARCH:

When beam is at equilibrium,

The net torque on it is zero, therefore …… (1)

The total force along direction and direction is zero due no motion.

Therefore

Step #4 of 10

SIMPLIFY:

From the sketch, and length of the beam is

Use hinge as a pivot point. From the equation (1), we have

Step #5 of 10

Therefore the tension in the cable is

…… (2)

Here the tension in the rope is …… (3)

Step #6 of 10

(b)

Since the horizontal and vertical force are,

From the figure,

The force the hinge exerts on the beam is

…… (4)

Step #7 of 10

Given data:

Mass of the beam is

Length of the steel cable is

The other end of the cable is attached to the wall at a distance above the hinge is

Mass of the hinging object is

Step #8 of 10

CALCULATE:

(a)

The tension in the rope is

From the figure , the angle:

Step #9 of 10

By substituting all known values in the equation (2), we get the tension in the cable.

Step #10 of 10

(b)

By substituting all known values in the equation (4), we get the force the hinge exerts on the beam.

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