Question

which way will the meter stick rotate if the objects are hung on the stick as shown below? each object is labeled with its mass in kilograms.
fulcrum
counter - clockwise no rotation clockwise

Explanation:

Step1: Recall Torque Formula

Torque \(\tau = r \times F\), where \(r\) is the distance from the fulcrum and \(F = mg\) (force due to gravity, \(g\) is constant so we can compare torques using \(r \times m\)).

Step2: Calculate Torque on Left (Counter - Clockwise)

Wait, actually, the left side objects: Wait, no, the fulcrum is at 50 cm. Wait, the left side: Wait, the objects on the left? Wait, no, the diagram: the fulcrum is at 50. The right side has a 1 kg at 60 cm. The left side: Wait, maybe I misread. Wait, the left side has objects? Wait, no, the meter stick: 0 - 100 cm, fulcrum at 50. The right side: 1 kg at 60 cm (distance from fulcrum \(r_{right}=60 - 50 = 10\) cm). The left side: Wait, maybe the left side has multiple objects? Wait, the left side of the fulcrum (before 50 cm) – but in the diagram, the left side (0 - 50) has no objects? Wait, no, maybe the left side objects are hung at 0 cm? Wait, the left side has four objects: 1, 2, 4, 8 kg? Wait, maybe they are hung at 0 cm? Let's assume:

Left side: mass \(m_{left}=1 + 2+4 + 8=15\) kg, distance from fulcrum \(r_{left}=50 - 0 = 50\) cm.

Right side: mass \(m_{right}=1\) kg, distance from fulcrum \(r_{right}=60 - 50 = 10\) cm.

Torque left: \(\tau_{left}=r_{left}\times m_{left}=50\times15 = 750\) (kg - cm)

Torque right: \(\tau_{right}=r_{right}\times m_{right}=10\times1 = 10\) (kg - cm)

Wait, no, that can't be. Wait, maybe the left side objects are hung at 0 cm? Wait, maybe I made a mistake. Wait, the fulcrum is at 50. So for the left side (distance from fulcrum is 50 cm, if hung at 0), and right side is 10 cm (hung at 60). But the left side has 1 + 2+4 + 8 = 15 kg, right side 1 kg.

Torque is \(r\times m\) (since \(g\) is same). So left torque: \(50\times15 = 750\), right torque: \(10\times1 = 10\). Since left torque (counter - clockwise) is greater than right torque (clockwise), the meter stick will rotate counter - clockwise.

Answer:

Counter - clockwise