Question

(15 points) A 40.0 kg beam is attached to a wall with a hi.nge and its far end is supported by a cable. The angle between the beam and the cable is 90o. If the beam is inclined at an angle of θ = 31.0° with respect to horizontal.
1. What is the horizontal component of the force exerted by the hi.nge on the beam? (Use the `to the right' as + for the horizontal direction.)
2. What is the magnitude of the force that the beam exerts on the hi.nge?

Answer 1

The horizontal component of the force  is 336 N

The magnitude of the force that the beam exerts on the hi_nge is 537.9 Newtons

What is the horizontal component of the force exerted by the hi_nge on the beam?

The system of the beam, hi_nge and cable are in equilibrium.

The horizontal component of the force exerted by the beam is given below as:

Horizontal component of the force = mg × cos 31°

Horizontal component of the force = 40 × 9.8 × cos 31°

Horizontal component of the force  = 336 Newtons

The magnitude of the force that the beam exerts on the hi_nge is given as:

F = mg × cos 31° + mg × sin 31°

F = 40 × 9.8 × cos 31° + 40 × 9.8 × sin 31°

F = 537.9 Newtons

Hence, the magnitude of the force that the beam exerts on the hi_nge is 537.9 Newtons.

In conclusion, the system of forces acting on the hi_nge and the beam are in equilibrium.

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