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The problem involves a 200 kN block resting on a wedge of negligible weight, and the objective is to find the value of force \( P \) that will move the wedge. The static friction coefficient is the same on both surfaces of the wedge, and the friction between the block and the vertical wall must be neglected. The angle of the wedge appears to be \( 30^\circ \), and the friction coefficient \( \mu \) is given as 0.30.

### Step-by-Step Solution Outline:

1. **Free-Body Diagram (FBD):**
   - The block experiences a downward gravitational force of 200 kN.
   - There is normal force \( N_1 \) acting between the block and the wedge.
   - There is also a friction force \( F_1 = \mu N_1 \) opposing the motion of the block down the wedge.
   - The wedge experiences a normal force \( N_2 \) at its base due to the ground, and there is friction \( F_2 = \mu N_2 \) resisting its movement.
   - The force \( P \) is applied horizontally to move the wedge.

2. **Equilibrium Equations:**
   - Use Newton's second law for both the block and wedge in the vertical and horizontal directions.
   - Break forces into their components along the direction of the wedge and perpendicular to it.

3. **Key Equations:**
   - For the block: \[ \text{Vertical equilibrium: } N_1 \cos(30^\circ) + F_1 \sin(30^\circ) = 200 \text{ kN} \]
   - For the wedge: Apply equilibrium conditions considering the applied force \( P \) and friction forces.

4. **Solve for \( P \):**
   - With the known angle \( 30^\circ \) and friction coefficient \( \mu = 0.30 \), solve the system of equations to find the force \( P \).

Would you like me to continue with the detailed calculations, or do you have any specific questions at this stage?

Here are 5 relative questions that expand on this:
1. How does the friction force affect the motion of the wedge?
2. What is the role of the angle of the wedge in the force calculation?
3. How does the coefficient of friction impact the force \( P \)?
4. What assumptions are made in this problem regarding friction and the vertical wall?
5. How would the solution change if the friction between the block and the wall were considered?

**Tip**: In problems involving wedges and friction, always ensure to break forces into components parallel and perpendicular to the inclined surface for accurate equilibrium equations.

A 200 kN block rests on a wedge of negligible weight. The coefficient of friction is the same at both surfaces of the wedge, and friction between the block and the vertical wall may be neglected. What is the force P needed to move the wedge? The angle of the wedge is 30°, and the coefficient of friction μ = 0.30.

This problem involves calculating the horizontal force P required to move a 200 kN block resting on a 30° wedge, with a static friction coefficient of 0.30. Key concepts include friction, equilibrium, and force components. This solution is suitable for undergraduate engineering students learning statics.

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