In a lab, a block weighing 80 N is attached to a spring scale, and both are pulled to the right on a horizontal surface, as shown above. Friction between the block and the surface is negligible. What is the acceleration of the block when the scale reads 32 N?

To determine the acceleration of the block, we can apply Newton's second law, which states that the net force acting on an object is equal to its mass times its acceleration:

\[
F = m \cdot a
\]

Here’s how to approach the solution:

1. **Identify the Given Values:**
   - Force exerted by the spring scale, \( F = 32 \, \text{N} \).
   - Weight of the block, \( W = 80 \, \text{N} \).
   
2. **Calculate the Mass of the Block:**
   - Weight (\( W \)) is related to mass (\( m \)) by the equation:
     \[
     W = m \cdot g
     \]
     where \( g \) is the acceleration due to gravity (approximately \( 9.8 \, \text{m/s}^2 \)).
   - Rearranging for \( m \), we get:
     \[
     m = \frac{W}{g} = \frac{80}{9.8} \approx 8.16 \, \text{kg}
     \]

3. **Apply Newton's Second Law to Find the Acceleration:**
   - Since there is negligible friction, the only horizontal force on the block is the force exerted by the spring scale.
   - According to \( F = m \cdot a \), we can solve for \( a \) as follows:
     \[
     a = \frac{F}{m} = \frac{32}{8.16} \approx 3.92 \, \text{m/s}^2
     \]

Thus, the acceleration of the block is approximately:

\[
a \approx 3.92 \, \text{m/s}^2
\]

Would you like further details on the steps or have any questions?

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Here are some related questions for further practice:

1. How would the acceleration change if the weight of the block was doubled?
2. If friction were not negligible, how would that affect the force needed to achieve the same acceleration?
3. What would the spring scale read if the block accelerated at \( 5 \, \text{m/s}^2 \) instead?
4. How would the acceleration change if the block were on an incline instead of a horizontal surface?
5. How is Newton’s second law applied in cases where multiple forces act on an object?

**Tip:** Remember, weight and mass are different; weight depends on gravity, while mass is constant regardless of location.

Discover how to calculate the acceleration of an 80 N block using Newton's Second Law when a spring scale reads 32 N. This example includes step-by-step calculations for determining mass, applying force, and deriving acceleration, ideal for Grades 9-12.

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