Certainly! Let's solve this problem step by step.
1. Identify the given data:
- Force, [tex]\( F = 10 \, \text{N} \)[/tex]
- Acceleration of body [tex]\( m_1 \)[/tex], [tex]\( a_1 = 2 \, \text{m/s}^2 \)[/tex]
- Acceleration of body [tex]\( m_2 \)[/tex], [tex]\( a_2 = 5 \, \text{m/s}^2 \)[/tex]
2. Determine the masses [tex]\( m_1 \)[/tex] and [tex]\( m_2 \)[/tex]:
Using the formula [tex]\( F = m \cdot a \)[/tex]
- For body [tex]\( m_1 \)[/tex]:
[tex]\[
F = m_1 \cdot a_1
\][/tex]
[tex]\[
m_1 = \frac{F}{a_1} = \frac{10 \, \text{N}}{2 \, \text{m/s}^2} = 5 \, \text{kg}
\][/tex]
- For body [tex]\( m_2 \)[/tex]:
[tex]\[
F = m_2 \cdot a_2
\][/tex]
[tex]\[
m_2 = \frac{F}{a_2} = \frac{10 \, \text{N}}{5 \, \text{m/s}^2} = 2 \, \text{kg}
\][/tex]
3. Calculate the total mass when both bodies are tied together:
[tex]\[
\text{Total mass} = m_1 + m_2 = 5 \, \text{kg} + 2 \, \text{kg} = 7 \, \text{kg}
\][/tex]
4. Determine the acceleration for the combined mass using the same force:
Using the formula [tex]\( F = m \cdot a \)[/tex] again, for the total mass:
[tex]\[
F = \text{Total mass} \cdot \text{Total acceleration}
\][/tex]
[tex]\[
10 \, \text{N} = 7 \, \text{kg} \cdot a
\][/tex]
[tex]\[
a = \frac{10 \, \text{N}}{7 \, \text{kg}} \approx 1.4286 \, \text{m/s}^2
\][/tex]
Therefore, the acceleration produced by the same force when both bodies are tied together is approximately [tex]\( 1.43 \, \text{m/s}^2 \)[/tex].
