Question

A horizontal uniform beam of mass M = 3.00 kg and length L =2.00 m is supported on the left by a hinge attached to a wall and on the right by a cable. The cable makes an angle θ = 60.0o with the horizontal. What tension T must the cable provide to hold the beam stationary?

Answer 1

Answer:

Tension T = 17 N

Explanation:

Given:

Mass of the beam M = 3.00 kg

Length of the beam L = 2.00 m

Angle θ = 60.0°

Solution :

The beam is fixed on the wall by the hinge. Since the beam is uniform, the center of mass will be at its geometric center

Since it is at equilibrium, the net torque mus be zero. The weight of the beam is pulling it down and the vertical component of the tension is lifting it up.

$T_{y}L-Mg\frac{L}{2} =0\\ \\T sin\theta L=Mg\frac{L}{2}\\\\ T =\frac{Mg}{2sin\theta} \\\\ T=\frac{3.00\times9.8}{2\times sin60^{o}} \\ \\T= 16.97 N\\\\T=17 N$