Of course! Let's go through the solution step by step.
### Step 1: Calculate the Applied Force
We are given:
- Mass, [tex]\( m_1 = 16 \)[/tex] kg
- Acceleration, [tex]\( a_1 = 3 \)[/tex] m/s²
We need to calculate the applied force using Newton's second law of motion, which is given by:
[tex]\[ F = m \times a \][/tex]
Substituting the known values:
[tex]\[ F = 16 \, \text{kg} \times 3 \, \text{m/s}^2 \][/tex]
[tex]\[ F = 48 \, \text{N} \][/tex]
So, the applied force is [tex]\( 48 \)[/tex] Newtons (N).
### Step 2: Calculate the Acceleration for the Second Object
We are now given:
- The applied force, [tex]\( F = 48 \)[/tex] N (which we just calculated)
- The mass of the second object, [tex]\( m_2 = 24 \)[/tex] kg
We need to calculate the acceleration using the same applied force on the new mass. Again, using Newton's second law:
[tex]\[ F = m \times a \][/tex]
Rearranging for acceleration [tex]\( a \)[/tex]:
[tex]\[ a = \frac{F}{m} \][/tex]
Substituting the known values:
[tex]\[ a_2 = \frac{48 \, \text{N}}{24 \, \text{kg}} \][/tex]
[tex]\[ a_2 = 2 \, \text{m/s}^2 \][/tex]
So, the acceleration of the second object with mass [tex]\( 24 \)[/tex] kg under the same applied force is [tex]\( 2 \)[/tex] m/s².
### Summary
- The applied force on the initial object is [tex]\( 48 \)[/tex] N.
- When the same force is applied to a second object of mass [tex]\( 24 \)[/tex] kg, the resulting acceleration is [tex]\( 2 \)[/tex] m/s².
