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The problem in the image involves a block sliding along a flat horizontal surface with an initial velocity of \( v_0 = 2.0 \, \text{m/s} \) and experiencing a constant resistive force of \( F = 4.0 \, \text{N} \), which brings the block to rest after covering a distance \( d = 2.0 \, \text{m} \).

We are asked to find the mass \( m \) of the block.

### Step-by-step solution:

1. **Using the work-energy principle**:  
   The work done by the resistive force brings the block to rest. According to the work-energy theorem:
   \[
   W = \Delta K
   \]
   where \( W \) is the work done by the force, and \( \Delta K \) is the change in kinetic energy.

   The initial kinetic energy \( K_i \) is:
   \[
   K_i = \frac{1}{2} m v_0^2
   \]
   Since the block comes to rest, the final kinetic energy \( K_f = 0 \). Therefore, the change in kinetic energy is:
   \[
   \Delta K = K_f - K_i = 0 - \frac{1}{2} m v_0^2 = -\frac{1}{2} m v_0^2
   \]
   
2. **Calculating the work done by the resistive force**:  
   The work done by a constant force is given by:
   \[
   W = F \cdot d
   \]
   where \( F = 4.0 \, \text{N} \) and \( d = 2.0 \, \text{m} \). Therefore:
   \[
   W = 4.0 \, \text{N} \times 2.0 \, \text{m} = 8.0 \, \text{J}
   \]

3. **Equating the work done to the change in kinetic energy**:  
   According to the work-energy theorem, the work done by the force is equal to the negative of the change in kinetic energy:
   \[
   -\frac{1}{2} m v_0^2 = W
   \]
   Substituting the values:
   \[
   -\frac{1}{2} m (2.0 \, \text{m/s})^2 = -8.0 \, \text{J}
   \]
   Simplifying:
   \[
   \frac{1}{2} m \times 4 = 8.0
   \]
   \[
   2m = 8.0
   \]
   \[
   m = 4.0 \, \text{kg}
   \]

### Final Answer:
The mass of the block is \( \boxed{4.0 \, \text{kg}} \).

Would you like more details or have any questions?

Here are 5 related questions to explore further:
1. What is the significance of the work-energy theorem in mechanics?
2. How does the resistive force impact the motion of objects?
3. Can you derive the formula for work done by a force using basic principles of energy?
4. What would happen to the stopping distance if the resistive force doubled?
5. How does this problem change if the surface is inclined?

**Tip**: Always ensure that all forces acting on a body are accounted for when solving problems involving work and energy.

A block sliding along a flat horizontal surface at an initial velocity of 2.0 m/s experiences a constant resistive force of 4.0 N that brings it to rest in a distance of 2.0 m. What is the mass of the block?

Solve a physics problem using the work-energy principle. A block slides on a horizontal surface with an initial velocity of 2.0 m/s and a resistive force of 4.0 N brings it to rest after 2.0 m. Learn how to calculate the block's mass.

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