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?
A - To balance the plank, we need to ensure that the total torque (rotational force) on both sides of the fulcrum is equal. The torque is calculated by multiplying the weight (mass times gravitational acceleration) by the distance from the fulcrum.
In this case, the bag of sand on one side has a mass of 20 kg and is placed at one end of the 5-meter plank. Assuming the fulcrum is at the center of the plank, the distance from the fulcrum to the bag of sand is 2.5 meters (half of the length of the plank).
To balance the plank, we need to find the distance from the fulcrum to the other side where we will place another bag of 10 kg. Let's call this distance x.
Since torque is equal on both sides, we can write the equation:
(20 kg * 9.8 m/s^2 * 2.5 m) = (10 kg * 9.8 m/s^2 * x)
Simplifying the equation:
20 * 2.5 = 10 * x
50 = 10 * x
x = 50 / 10
x = 5
Therefore, the other bag of sand, with a mass of 10 kg, should be placed at a distance of 5 meters from the fulcrum.
B - When the plank is balanced, the center of gravity of the system is located exactly at the fulcrum. In this case, the fulcrum acts as the pivot point, and the center of gravity is the point where the total weight of the system can be considered to be concentrated.