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Block in Fig 5.62 weighs 1.40N and block B weighs 4.20N. The coefficient of kinetic friction between all surfaces is .30. Find the magnitude of the horizontal force F necessary to drag block B to the left at constant speed if A and B are connected by a light flexible cord passed around a fixed, frictionless pulley. 

To find the magnitude of the horizontal force \( F \) needed to drag block \( B \) to the left at a constant speed, let's analyze the forces on both blocks \( A \) and \( B \). Here's the step-by-step solution:

### Step 1: List Given Data
- Weight of block \( A \): \( W_A = 1.40 \, \text{N} \)
- Weight of block \( B \): \( W_B = 4.20 \, \text{N} \)
- Coefficient of kinetic friction \( \mu_k = 0.30 \)
- The system moves at a constant speed, meaning acceleration \( a = 0 \).

### Step 2: Determine Normal Forces
Since the weights of the blocks act vertically, the normal forces for each block are given by their weights:

- Normal force on \( A \): \( N_A = W_A = 1.40 \, \text{N} \)
- Normal force on \( B \): \( N_B = W_B = 4.20 \, \text{N} \)

### Step 3: Calculate Frictional Forces
The kinetic frictional force \( f_k \) for each block is given by:
\[
f_k = \mu_k \cdot N
\]
- Friction force on \( A \): \( f_{kA} = \mu_k \cdot N_A = 0.30 \cdot 1.40 = 0.42 \, \text{N} \)
- Friction force on \( B \): \( f_{kB} = \mu_k \cdot N_B = 0.30 \cdot 4.20 = 1.26 \, \text{N} \)

### Step 4: Analyze Forces on Block \( A \)
Block \( A \) is connected to block \( B \) via a light flexible cord that goes over a frictionless pulley. Since block \( B \) is moving at a constant speed, block \( A \) will also move at a constant speed to the left. Therefore, the forces on block \( A \) in the horizontal direction must balance out.

Let \( T \) be the tension in the cord connecting \( A \) and \( B \). The forces on block \( A \) in the horizontal direction are:
1. Tension \( T \) pulling \( A \) to the left.
2. Frictional force \( f_{kA} = 0.42 \, \text{N} \) opposing the motion to the right.

Since block \( A \) moves at constant speed:
\[
T = f_{kA} = 0.42 \, \text{N}
\]

### Step 5: Analyze Forces on Block \( B \)
For block \( B \), the forces in the horizontal direction are:
1. The applied force \( F \) pulling \( B \) to the left.
2. The frictional force \( f_{kB} = 1.26 \, \text{N} \) opposing the motion to the right.
3. The tension \( T = 0.42 \, \text{N} \) pulling block \( B \) to the right (because it’s attached to \( A \)).

Since block \( B \) is also moving at a constant speed:
\[
F = f_{kB} + T
\]
Substitute the values:
\[
F = 1.26 + 0.42 = 1.68 \, \text{N}
\]

### Final Answer
The magnitude of the horizontal force \( F \) necessary to drag block \( B \) to the left at a constant speed is:
\[
\boxed{1.68 \, \text{N}}
\]

Would you like further details or have any questions?

### Additional Questions
1. How would the force \( F \) change if the coefficient of kinetic friction increased?
2. What would happen to the tension \( T \) if block \( A \) was heavier?
3. How would the result differ if the pulley had friction?
4. What is the effect of changing the direction of \( F \) on the motion of blocks \( A \) and \( B \)?
5. If \( F \) were applied to block \( A \) instead, how would the system's behavior change?

### Tip
In problems involving friction, identifying all surfaces in contact and calculating individual frictional forces separately helps in balancing the equations efficiently.

Block in Fig 5.62 weighs 1.40N and block B weighs 4.20N. The coefficient of kinetic friction between all surfaces is .30. Find the magnitude of the horizontal force F necessary to drag block B to the left at constant speed if A and B are connected by a light flexible cord passed around a fixed, frictionless pulley.

Learn how to calculate the horizontal force needed to drag block B to the left at a constant speed in a pulley system with friction. This physics problem involves concepts of forces, kinetic friction, and Newton's laws. Given block weights (1.40N and 4.20N) and a friction coefficient of 0.30, find the solution step-by-step.

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