A constant force applied to object A causes it to accelerate at 5 m/s2
m
/
s
2
. The same force applied to object B causes an acceleration of  3 m/s2
m
/
s
2
. Applied to object C, it causes an acceleration of 8 m/s2
m
/
s
2
. What is the ratio of Mass A to mass B?

To solve this problem, we can use Newton's Second Law of Motion, which states:

\[
F = m \cdot a
\]

Where:
- \( F \) is the applied force,
- \( m \) is the mass of the object,
- \( a \) is the acceleration of the object.

Since the force applied to each object is constant, we can compare the masses of objects A and B using the formula:

\[
m_A \cdot a_A = m_B \cdot a_B
\]

Rearranging this to find the ratio of the masses:

\[
\frac{m_A}{m_B} = \frac{a_B}{a_A}
\]

Given:
- \( a_A = 5 \, \text{m/s}^2 \),
- \( a_B = 3 \, \text{m/s}^2 \).

Substitute the values:

\[
\frac{m_A}{m_B} = \frac{3}{5}
\]

Thus, the ratio of the mass of object A to the mass of object B is \( \frac{3}{5} \), or 0.6.

### Would you like further details or clarification on this?

Here are 5 related questions you might find interesting:
1. What would the ratio of mass B to mass C be using similar reasoning?
2. How would the problem change if the force applied varied between the objects?
3. What is the relationship between mass and acceleration when force is constant?
4. Can we find the individual masses if we know the force value?
5. How would the acceleration change if object A and B were connected and pulled together by the same force?

### Tip: When the force is constant, the mass and acceleration are inversely proportional—greater mass results in less acceleration.

A constant force applied to object A causes it to accelerate at 5 m/s². The same force applied to object B causes an acceleration of 3 m/s². What is the ratio of Mass A to Mass B?

This problem involves calculating the ratio of Mass A to Mass B when a constant force is applied to both objects, resulting in different accelerations. Learn how to use Newton's Second Law of Motion to solve this physics problem with detailed explanations and formulas. Ideal for students in Grades 9-12.

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