The aim of this question is to understand and apply **Newton’s laws of motion** to moving objects.

According to **Newton’s motion laws**, a body can’t just **move by itself**. Instead, an agent called the **force acts** on a body to move it from rest or to stop it. This **force causes the change in speed,** thereby creating **acceleration** that is **proportional to the mass** of the body. In reaction to this force, the body exerts a **reaction force** on the object causing the first force. Both of these **action and reaction forces** have **equal magnitudes** with o**pposite directions** such that they try to cancel out each other in a broader sense.

Mathematically, **Newton’s second law** of motion dictates that the **relationship** between **force** $ F $ acting on a body of **mass** $ m $ and the **acceleration** $ a $ is given by the **following formula**:

\[ F \ = \Â m a \]

## Expert Answer

**Given:**

\[ \text{ Total Mass } \ = \ m \ = \ m_{ A } \ + \ m_{ B } \ = \ 20 \ + \ 5 \ = \ 25 \ kg \]

\[ \text{ Total Force } \ =\ F \ = \ 250 \ N \]

According to the** second law of motion:**

\[ F \ = \Â m a \]

\[ \Rightarrow a \ = \Â \dfrac{ F }{ m } \]

**Substituting values** in the above equation:

\[ \Rightarrow a \ = \Â \dfrac{ 250 }{ 25 } \]

\[ \Rightarrow a \ = \Â 10 \ m/s^{ 2 } \]

Since both **boxes A and B are in contact** with each other, both of them **must move with the same acceleration**. So for the case of box B:

\[ \text{ Mass of Box B} \ = \ m_{ B } \ = \ 5 \ kg \]

\[ \text{ Acceleration of Box B} \ = \ a_{ B } \ = \ a \ = \ 10 \ m/s^{ 2 } \]

According to the **second law of motion:**

\[ F_{ B } \ = \Â m_{ B }Â a_{ B } \]

**Substituting values:**

\[ F_{ B } \ = \Â ( 5 )Â ( 10 ) \]

\[ \Rightarrow F_{ B } \ = \Â 100 \ N \]

## Numerical Result

\[ F_{ B } \ = \Â 50 \ N \]

## Example

If the mass of **box A was 24 kg** and that of **box B was 1 kg**, how much **force** will be **exerted on B** in this case provided that the **force acting on box A remains the same**?

**Given:**

\[ \text{ Total Mass } \ = \ m \ = \ m_{ A } \ + \ m_{ B } \ = \ 24 \ + \ 1 \ = \ 25 \ kg \]

\[ \text{ Total Force } \ =\ F \ = \ 250 \ N \]

According to the **second law of motion:**

\[ F \ = \Â m a \]

\[ \Rightarrow a \ = \Â \dfrac{ F }{ m } \]

**Substituting values** in the above equation:

\[ \Rightarrow a \ = \Â \dfrac{ 250 }{ 25 } \]

\[ \Rightarrow a \ = \Â 10 \ m/s^{ 2 } \]

Since both boxes **A and B are in contact** with each other, both of them **must move with the same acceleration**. So for the case of box B:

\[ \text{ Mass of Box B} \ = \ m_{ B } \ = \ 1 \ kg \]

\[ \text{ Acceleration of Box B} \ = \ a_{ B } \ = \ a \ = \ 10 \ m/s^{ 2 } \]

According to the **second law of motion:**

\[ F_{ B } \ = \Â m_{ B }Â a_{ B } \]

**Substituting values:**

\[ F_{ B } \ = \Â ( 1 )Â ( 10 ) \]

\[ \Rightarrow F_{ B } \ = \Â 10 \ N \]