A buoy is held inside water contained in a vessel by tying it with a thread to the base of the vessel. Name the three forces that keep the buoy in equilibrium and state the direction in which each force acts.

Answer

To solve the problem, we need to identify the three forces acting on the buoy when it is held in equilibrium inside the water. Let's break this down step by step:

### Step 1: Identify the Weight of the Buoy
The first force acting on the buoy is its weight (W). The weight is calculated using the formula:
\[ W = m \cdot g \]
where \( m \) is the mass of the buoy and \( g \) is the acceleration due to gravity. The direction of this force is **downward**.

### Step 2: Identify the Buoyant Force
The second force is the buoyant force (F_b), which is the upward force exerted by the fluid (water) on the buoy. According to Archimedes' principle, the buoyant force is equal to the weight of the fluid displaced by the buoy. This can be expressed as:
\[ F_b = \rho_w \cdot g \cdot V_d \]
where \( \rho_w \) is the density of water, \( g \) is the acceleration due to gravity, and \( V_d \) is the volume of water displaced by the buoy. The direction of this force is **upward**.

### Step 3: Identify the Tension Force
The third force acting on the buoy is the tension (T) in the thread that holds the buoy down. Since the buoy is in equilibrium, the tension force must balance the forces acting on the buoy. The tension acts in the **downward** direction.

### Step 4: Summarize the Forces
In summary, the three forces acting on the buoy are:
1. **Weight (W)**: Acts downward.
2. **Buoyant Force (F_b)**: Acts upward.
3. **Tension (T)**: Acts downward.

### Conclusion
The buoy is in equilibrium when the upward buoyant force is balanced by the downward forces (weight and tension). Therefore, the buoy remains stationary in the water.

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