To solve this problem, we need to understand the relationship between force, mass, and acceleration. According to Newton's second law of motion, the force [tex]\( F \)[/tex] acting on an object is given by:
[tex]\[ F = m \cdot a \][/tex]
where [tex]\( m \)[/tex] is the mass of the object and [tex]\( a \)[/tex] is the acceleration.
1. Determine the force (F) using the first object:
Given:
- Mass of the first object, [tex]\( m_1 = 4 \)[/tex] kg
- Acceleration of the first object, [tex]\( a_1 = 13 \)[/tex] m/s²
We can calculate the force as follows:
[tex]\[ F = m_1 \cdot a_1 \][/tex]
Substituting the values:
[tex]\[ F = 4 \, \text{kg} \cdot 13 \, \text{m/s}^2 \][/tex]
[tex]\[ F = 52 \, \text{N} \][/tex]
2. Use the same force (F) for the second object:
Given:
- Acceleration of the second object, [tex]\( a_2 = 2 \)[/tex] m/s²
We need to find the mass of the second object, [tex]\( m_2 \)[/tex].
3. Relate the force to the second object's mass and acceleration:
Since the force is constant, we can use:
[tex]\[ F = m_2 \cdot a_2 \][/tex]
Rearranging the equation to solve for [tex]\( m_2 \)[/tex]:
[tex]\[ m_2 = \frac{F}{a_2} \][/tex]
Substituting the known values:
[tex]\[ m_2 = \frac{52 \, \text{N}}{2 \, \text{m/s}^2} \][/tex]
[tex]\[ m_2 = 26 \, \text{kg} \][/tex]
Therefore, the mass of the second object is 26 kg.
