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The problem states:

> A bowling ball rolled with a force of 20 N accelerates at a rate of \(5 \, \text{m/s}^2\); a second ball rolled with the same force accelerates at \(6 \, \text{m/s}^2\). What are the masses of the two balls?

To solve for the mass, we can use Newton's Second Law:
\[
F = m \cdot a
\]
where:
- \( F \) is the force,
- \( m \) is the mass,
- \( a \) is the acceleration.

### Step 1: Solve for the first ball's mass
Given:
- Force, \( F = 20 \, \text{N} \)
- Acceleration, \( a = 5 \, \text{m/s}^2 \)

Rearrange the formula to find \( m \):
\[
m = \frac{F}{a}
\]
Substitute the values:
\[
m = \frac{20 \, \text{N}}{5 \, \text{m/s}^2} = 4 \, \text{kg}
\]
So, the mass of the first ball is \( 4 \, \text{kg} \).

### Step 2: Solve for the second ball's mass
Given:
- Force, \( F = 20 \, \text{N} \)
- Acceleration, \( a = 6 \, \text{m/s}^2 \)

Using the same formula:
\[
m = \frac{F}{a} = \frac{20 \, \text{N}}{6 \, \text{m/s}^2} \approx 3.33 \, \text{kg}
\]
So, the mass of the second ball is approximately \( 3.33 \, \text{kg} \).

### Answers
1. The mass of the first ball is \( 4 \, \text{kg} \).
2. The mass of the second ball is \( 3.33 \, \text{kg} \).

Would you like more details on these calculations, or have any questions?

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### Related Questions
1. What would the acceleration be if a 10 N force was applied to a 2 kg mass?
2. If the second ball had an acceleration of 7 m/s² instead of 6 m/s², what would its mass be?
3. How does doubling the force on the first ball affect its acceleration?
4. What force is needed to accelerate a 5 kg mass at 4 m/s²?
5. How would the answer change if the force on both balls was 30 N instead?

### Tip
Remember that force, mass, and acceleration are directly related through Newton's Second Law. If you know any two of these, you can always find the third.

A bowling ball rolled with a force of 20 N accelerates at a rate of 5 m/s^2; a second ball rolled with the same force accelerates at 6 m/s^2. What are the masses of the two balls?

Learn how to calculate the masses of two bowling balls using Newton's Second Law. The problem involves a force of 20 N applied to two balls with different accelerations (5 m/s^2 and 6 m/s^2). Suitable for students in Grades 9-10.

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