A block of wood floats in a bucket of water placed in a lift. Will the block sink more or less if the lift starts accelerating up?

Explanation

To determine whether a block of wood will sink more or less when a lift starts accelerating upwards, we can analyze the forces acting on the block in both stationary and accelerating conditions.

### Step-by-Step Solution:

1. **Understand the Initial Conditions**:
- The block of wood is floating in water inside a stationary lift.
- The buoyant force (upward force) acting on the block is equal to the weight of the water displaced by the submerged part of the block.

2. **Identify Forces Acting on the Block**:
- The forces acting on the block are:
- Weight of the block (downward): \( W = mg \)
- Buoyant force (upward): \( F_B = \rho_L \cdot V_s \cdot g \)
- Where \( \rho_L \) is the density of the liquid (water), \( V_s \) is the volume of the block submerged in water, and \( g \) is the acceleration due to gravity.

3. **Condition When Lift is Stationary**:
- In a stationary lift, the buoyant force equals the weight of the block:
\[ F_B = W \implies \rho_L \cdot V_s \cdot g = mg \]
- The volume submerged can be expressed as:
\[ V_s = \frac{m}{\rho_L} \]

4. **Condition When Lift Accelerates Upwards**:
- When the lift accelerates upwards with acceleration \( a \), the effective gravitational force on the block changes to \( g' = g + a \).
- The new buoyant force is:
\[ F_B' = \rho_L \cdot V_s' \cdot (g + a) \]
- The weight of the block remains the same:
\[ W = mg \]

5. **Apply Newton's Second Law**:
- The net force acting on the block when the lift accelerates upwards is given by:
\[ F_B' - mg = ma \]
- Rearranging gives:
\[ F_B' = mg + ma = m(g + a) \]

6. **Equating Buoyant Forces**:
- Setting the buoyant force equal to the new effective weight:
\[ \rho_L \cdot V_s' \cdot (g + a) = m(g + a) \]
- This implies:
\[ V_s' = \frac{m}{\rho_L} \]

7. **Conclusion**:
- Since \( V_s' = V_s \), the volume of the block submerged does not change when the lift accelerates upwards. Thus, the block will neither sink more nor less; it will maintain its position.

### Final Answer:
The block of wood will neither sink more nor less when the lift starts accelerating upwards; it will maintain its position.