Suppose you have a meter stick balanced at its midpoint on a fulcrum. Mass one is 25 g and is placed 20 cm from the balance point. Mass 2 is 35 cm from the balance point when the meter stick is horizontal. What is the mass of mass 2?
M2*35=M1*20
m2=M1*20/35
To find the mass of mass 2, we can set up an equation using the principle of torque and balance. Here's how you can solve it:
First, let's assign some variables:
Let's call the mass of mass 2 M2 (in grams).
We know that the meter stick is balanced, which means the torques on both sides of the fulcrum are equal.
The torque (T) of an object is given by the equation:
T = F * d
Where F is the force applied and d is the distance from the fulcrum.
In this case, the forces are the masses (mass 1 and mass 2), and the distances are given as 20 cm and 35 cm, respectively.
Using the principle of torque balance, we can write the equation as:
(M1 * d1) = (M2 * d2)
Substituting the given values, we have:
(25 g * 20 cm) = (M2 * 35 cm)
Now, we can solve for M2 by rearranging the equation:
M2 = (25 g * 20 cm) / 35 cm
Now, let's calculate it:
M2 = (500 g·cm) / 35 cm
M2 ≈ 14.29 g
Therefore, the mass of mass 2 is approximately 14.29 grams.
Remember, when using this formula, always ensure that the units of torque (force times distance) match. In this case, we used grams as the unit for mass and centimeters as the unit for distance.