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Block A
 in (Figure 1) weighs 1.30 N
, and block B
 weighs 3.60 N
. The coefficient of kinetic friction between all surfaces is 0.310.

Find the magnitude of the horizontal force  F⃗ 
  necessary to drag block  B
  to the left at constant speed if  A
  is held at rest (figure (b)).

Let's break this problem down and solve it step by step:

### Given dataLet's break this problem down and solve it step by step:

### Given 
- Block \( A \) weighs \( 1.30 \, \text{N} \).
- Block \( B \) weighs \( 3.60 \, \text{N} \).
- Coefficient of kinetic friction between all surfaces: \( \mu_k = 0.310 \).
- Block \( A \) is held at rest, and we need to find the horizontal force \( \vec{F} \) necessary to drag block \( B \) to the left at a constant speed.

### Step 1: Calculate normal forces
The normal force exerted on each block is equal to the weight of the block because the forces are vertical.

- For block \( A \), the normal force is \( N_A = 1.30 \, \text{N} \).
- For block \( B \), the normal force is the sum of its own weight and the weight of block \( A \), since block \( A \) is sitting on top of block \( B \).
  \[
  N_B = 3.60 \, \text{N} + 1.30 \, \text{N} = 4.90 \, \text{N}
  \]

### Step 2: Calculate friction forces
The kinetic friction force is given by:
\[
f_k = \mu_k \cdot N
\]

- Friction force between block \( A \) and block \( B \):
  \[
  f_{A/B} = \mu_k \cdot N_A = 0.310 \cdot 1.30 \, \text{N} = 0.403 \, \text{N}
  \]

- Friction force between block \( B \) and the surface:
  \[
  f_{B/\text{surface}} = \mu_k \cdot N_B = 0.310 \cdot 4.90 \, \text{N} = 1.519 \, \text{N}
  \]

### Step 3: Analyze forces acting on block \( B \)
Since block \( A \) is held at rest, the force required to drag block \( B \) at a constant speed is the sum of the friction forces opposing the motion:

\[
F_{\text{net}} = f_{A/B} + f_{B/\text{surface}} = 0.403 \, \text{N} + 1.519 \, \text{N} = 1.922 \, \text{N}
\]

### Final Answer:
The magnitude of the horizontal force \( \vec{F} \) necessary to drag block \( B \) to the left at constant speed is \( 1.922 \, \text{N} \).

---

Would you like a deeper explanation or further details? Here are some related questions:

1. How would the force change if block \( A \) were allowed to slide freely?
2. What role does the coefficient of friction play in determining the force?
3. How would increasing the weight of block \( B \) affect the required force?
4. How do we calculate normal forces in more complex systems like inclined planes?
5. What happens to the frictional force if the surface between \( B \) and the ground changes?

**Tip**: When objects are in contact, the normal force and friction play crucial roles in determining how much force is needed to move them at a constant velocity. Always account for all points of contact.

Block A weighs 1.30 N, and block B weighs 3.60 N. The coefficient of kinetic friction between all surfaces is 0.310. Find the magnitude of the horizontal force F necessary to drag block B to the left at constant speed if A is held at rest (figure b).

Learn how to calculate the horizontal force required to drag block B weighing 3.60 N when block A, weighing 1.30 N, is held at rest. Includes details on friction force calculations and the coefficient of kinetic friction (0.310).

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