meter stick is located at 50.5 cm and the stick is supported at 60 cm. where must a 190 gram load be hung in order to have equilibrium?
To find the position where a 190 gram load must be hung in order to achieve equilibrium, we need to consider the torques acting on the meter stick.
Torque is the product of the force and the distance from the pivot point. In this case, our pivot point is the point where the stick is supported at 60 cm. Let's call this point A. The distance from the support point A to the 190 gram load can be denoted as "x."
Now, let's analyze the torques acting on the meter stick in a balanced system:
1. Torque due to the weight of the meter stick:
The weight of the meter stick acts downward at its center, which is located at 50.5 cm. To calculate the torque, we need to multiply the weight of the meter stick (assume it to be concentrated at its center) by the distance from the pivot point A to the center of the meter stick (50.5 cm - 60 cm):
Torque(A) = (Weight of the meter stick) * (Distance from A to center of stick)
2. Torque due to the 190 gram load:
The load acts downward at distance x from the pivot point A. To calculate the torque, we need to multiply the weight of the load by the distance from the pivot point A to the load:
Torque(A) = (Weight of the load) * (x)
For equilibrium to be achieved, the total torques acting on the meter stick must sum up to zero. Mathematically, this can be represented as:
Torque(A) + Torque(A) = 0
Now, let's substitute the values:
(Weight of the meter stick) * (Distance from A to center of stick) + (Weight of the load) * (x) = 0
Given that the load weighs 190 grams, the weight can be calculated by multiplying the mass by the acceleration due to gravity (9.8 m/s²). Let's convert the load weight into Newtons:
Weight of the load = (190 grams) * (9.8 m/s²) = 1.862 Newtons
Now, let's substitute the values into the equation and solve for x:
(Weight of the meter stick) * (Distance from A to center of stick) + (Weight of the load) * (x) = 0
((Mass of the meter stick) * (g)) * (Distance from A to center of stick) + (1.862 N) * (x) = 0
Once you have the mass of the meter stick, g (acceleration due to gravity), the distance from A to the center of the stick, as well as the weight of the load (1.862 N), you can solve the equation to find the value of x.