A 500 + 1 g aluminum block sits in the middle of
a balance. Strings with small mass hangers are
attached as shown in the diagram. The hanger on
the right has a total mass of 100 g (50 g from the
hanger itself, plus an additional 50 g weight). The
hanger on the left has a mass of 50 g. Under these
conditions, the balance is expected to read 400.1
+/- 0.1g. What is the magnitude of the Normal force on the Block from the Balance in this case? 

To find the magnitude of the normal force on the block from the balance, we can analyze the forces involved in this scenario.

### Given:
- The mass of the aluminum block is \( 500 \, \text{g} + 1 \, \text{g} = 501 \, \text{g} \).
- The total mass on the right hanger is \( 100 \, \text{g} \) (including the hanger and additional weight).
- The total mass on the left hanger is \( 50 \, \text{g} \).
- The balance reads \( 400.1 \, \text{g} \pm 0.1 \, \text{g} \).

### Approach:

1. **Force Acting on the Block:**
   - The total weight of the block is the gravitational force acting on it:
   \[
   W_{\text{block}} = m_{\text{block}} \cdot g = 501 \, \text{g} \cdot 9.8 \, \text{m/s}^2 = 4.908 \, \text{N}.
   \]
   
2. **Net Force on the System:**
   - The reading of the balance is \( 400.1 \, \text{g} \), which implies that the net force acting on the block (and transmitted through the balance) corresponds to this mass reading.
   \[
   F_{\text{net}} = 400.1 \, \text{g} \cdot 9.8 \, \text{m/s}^2 = 3.92098 \, \text{N}.
   \]

3. **Determine the Normal Force:**
   - The normal force \( N \) from the balance acts upward on the block to balance the forces. The net force on the block is the difference between its weight and the normal force.
   
   - So, the equation balancing forces in the vertical direction is:
   \[
   N = W_{\text{block}} - F_{\text{net}}.
   \]
   Substituting the values:
   \[
   N = 4.908 \, \text{N} - 3.921 \, \text{N} = 0.987 \, \text{N}.
   \]

### Conclusion:
The magnitude of the normal force on the aluminum block from the balance is approximately **0.987 N**.

---

Would you like further details or clarifications on any step?

Here are 5 related questions for practice:
1. What would happen to the normal force if the block mass increased by 100g?
2. How would the system change if the mass on the right hanger increased by 20g?
3. Can you calculate the normal force if the balance read 450.1g?
4. How is the balance reading affected by the mass difference between the two hangers?
5. What would the balance read if the system were perfectly balanced with no net force?

**Tip:** When working with forces, always ensure units are consistent, especially between mass (g or kg) and force (N).

A 500 + 1 g aluminum block sits in the middle of a balance. Strings with small mass hangers are attached as shown in the diagram. The hanger on the right has a total mass of 100 g (50 g from the hanger itself, plus an additional 50 g weight). The hanger on the left has a mass of 50 g. Under these conditions, the balance is expected to read 400.1 +/- 0.1g. What is the magnitude of the Normal force on the Block from the Balance in this case?

Find the normal force on a 500g aluminum block on a balance with unequal masses on the hangers. Using Newton's second law and understanding forces in equilibrium, this problem covers key concepts such as gravitational force and net force. Suitable for Grades 9-12.

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