A uniform bar of mass 12 kg and length 1.4 m is held by a hinge on a vertical wall. A string is attached to the end so that the bar is in mechanical equilibrium. The angle between the bar and the string is 25o. Find the tension in the string.

Summing moments about the hinge

12*g*1.4/2-Tension*1.4*sin25=0

Tension=12*9.8*.7 /(1.4*sin25)

To find the tension in the string, we can use the concept of torque equilibrium. In mechanical equilibrium, the net torque acting on an object is zero.

In this case, the bar is in mechanical equilibrium, so the net torque acting on the bar must be zero. The torque produced by the tension in the string is equal in magnitude and opposite in direction to the torque produced by the weight of the bar.

To calculate the torque produced by the weight of the bar, we need to find the center of gravity of the bar. The center of gravity is located at the midpoint of the bar, which is 1.4 m / 2 = 0.7 m from the hinge.

Now, let's calculate the torque produced by the weight of the bar. The weight of an object can be calculated using the equation:

Weight = Mass * Gravity

where the mass of the bar is given as 12 kg and the acceleration due to gravity is approximately 9.8 m/s^2.

Weight = 12 kg * 9.8 m/s^2 = 117.6 N

The torque produced by the weight of the bar can be calculated using the equation:

Torque = Distance * Force * sin(θ)

where the distance is the perpendicular distance from the hinge to the line of action of the force (which is the distance from the hinge to the center of gravity), the force is the weight of the bar, and θ is the angle between the line of action of the force and the lever arm (which is the angle between the bar and the string).

Torque = 0.7 m * 117.6 N * sin(25°)

Finally, since the tension in the string produces an equal but opposite torque, we can set up the equation:

Torque produced by tension = Torque produced by weight of the bar

Tension * length of the bar * sin(θ) = 0.7 m * 117.6 N * sin(25°)

Now, we can solve this equation to find the tension in the string.