A meter stick balances horizontally on a knife-edge at the 50.0 cm mark. With two 5.00 g coins stacked over the 12.0 cm mark, the stick is found to balance at the 43.0 cm mark. What is the mass of the meter stick?
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To solve this problem, we can use the principle of torque. Torque is the measure of the turning force on an object.
First, let's calculate the torque produced by the coins on one side of the meter stick. The torque is given by the formula:
Torque = Force × Distance
In this case, the force is the weight of the coins, and the distance is the distance from the 50.0 cm mark to the center of mass of the coins. Since the coins are stacked on top of each other, their combined mass is 2 × 5.00 g = 10.00 g = 0.01000 kg.
The torque produced by the coins is:
Torque_coins = (0.01000 kg) × (9.8 m/s²) × (50.0 cm - 12.0 cm)
Note that we convert grams into kilograms by dividing by 1000 and we convert cm into meters by dividing by 100.
Torque_coins = 0.01000 kg × 9.8 m/s² × 0.38 m
Next, let's calculate the torque produced by the meter stick itself. The weight of the meter stick is acting at its center of mass, which is at the 50.0 cm mark. The torque produced by the meter stick is:
Torque_stick = Mass_stick × 9.8 m/s² × (43.0 cm - 50.0 cm)
We need to find the mass of the meter stick, so let's call it Mass_stick. We can rearrange the equation to solve for Mass_stick:
Mass_stick = (Torque_coins + Torque_stick) / (9.8 m/s² × (43.0 cm - 50.0 cm))
Now, we can substitute the known values:
Mass_stick = (Torque_coins + Torque_stick) / (9.8 m/s² × (-0.07 m))
After substituting the values and performing the calculations, you should be able to find the mass of the meter stick.