A meter stick has a mass of 200g and its center of gravity is at the 50.0 cm mark. If 150g is attached to the stick at the 10 cm mark, where would an upward force on the stick need to be placed to balance the stick and the added mass?
To balance the meter stick and the added mass, we need to find the position where the upward force needs to be placed.
First, let's calculate the total mass of the meter stick and the added mass:
Meter stick mass = 200g
Added mass = 150g
Total mass = Meter stick mass + Added mass
Total mass = 200g + 150g
Total mass = 350g
Next, we need to find the center of mass of the system:
Center of mass position = (Meter stick mass * Meter stick center of gravity + Added mass * Added mass position) / Total mass
Center of mass position = (200g * 50.0 cm + 150g * 10 cm) / 350g
Center of mass position = (10,000 g·cm + 1,500 g·cm) / 350g
Center of mass position = 11,500 g·cm / 350g
Center of mass position ≈ 32.9 cm
The center of mass of the system is approximately at the 32.9 cm mark. Therefore, to balance the stick and the added mass, the upward force should be placed at this position.