A plank of uniform construction 5 metres in length and of mass 25kg. is balanced on a sawhorse stand which acts as a fulcrum. a bag of sand having a mass of 20kg. is suspended from one end of the plank. on the other end of the plank, a concrete block of mass 15 kg is hing at the end.
A- where would you place another bag of sand, of mass 10 kg, to balance this plank? 1.25meters!
B- when the plank is balanced, where is the center of gravity of the system located?
To answer both questions, we need to understand the concept of torque and the principle of moments.
A) To balance the plank, the torques on both sides of the fulcrum need to be equal. Torque, denoted as τ, is a measure of how effectively a force can cause rotation around a pivot or fulcrum.
The formula for torque is τ = r * F * sin(θ), where r is the distance from the fulcrum to the point of force application, F is the force applied, and θ is the angle between the force and the lever arm.
In this case, the torques on each side of the fulcrum should be equal. At one end, we have a mass of 20 kg suspended at a distance of 2.5 meters from the fulcrum, which creates a clockwise torque. On the other end, we have a mass of 15 kg hanging at the end of the plank, creating a counterclockwise torque.
Assuming the mass of the plank itself is negligible compared to the other masses, we can equate the torques:
20 kg * 9.8 m/s^2 * 2.5 m = 15 kg * 9.8 m/s^2 * x
Now, we solve for x, the distance from the fulcrum to the point where the 10 kg bag of sand should be placed:
x = (20 kg * 9.8 m/s^2 * 2.5 m) / (15 kg * 9.8 m/s^2)
x = 1.25 meters
Therefore, to balance the plank with the 10 kg bag of sand, it should be placed 1.25 meters from the fulcrum, on the side opposite to the 20 kg bag of sand.
B) When the plank is balanced, the center of gravity of the system is located at the fulcrum itself. The center of gravity is the point where the entire weight of the system can be considered to act. In this case, since the plank is balanced on the sawhorse stand acting as the fulcrum, the center of gravity lies at the fulcrum.