To determine which object has the greatest acceleration, we will use Newton's second law of motion, which states that [tex]\( a = \frac{F}{m} \)[/tex], where [tex]\( a \)[/tex] is acceleration, [tex]\( F \)[/tex] is force, and [tex]\( m \)[/tex] is mass.
Let's calculate the acceleration for each object step by step:
1. Object 1:
- Mass ( [tex]\(m_1\)[/tex] ): [tex]\(10 \, \text{kg}\)[/tex]
- Force ( [tex]\(F_1\)[/tex] ): [tex]\(4 \, \text{N}\)[/tex]
- Acceleration ( [tex]\(a_1\)[/tex] ): [tex]\[
a_1 = \frac{F_1}{m_1} = \frac{4 \, \text{N}}{10 \, \text{kg}} = 0.4 \, \text{m/s}^2
\][/tex]
2. Object 2:
- Mass ( [tex]\(m_2\)[/tex] ): [tex]\(100 \, \text{g} = 0.1 \, \text{kg}\)[/tex] (converted to kg)
- Force ( [tex]\(F_2\)[/tex] ): [tex]\(20 \, \text{N}\)[/tex]
- Acceleration ( [tex]\(a_2\)[/tex] ): [tex]\[
a_2 = \frac{F_2}{m_2} = \frac{20 \, \text{N}}{0.1 \, \text{kg}} = 200 \, \text{m/s}^2
\][/tex]
3. Object 3:
- Mass ( [tex]\(m_3\)[/tex] ): [tex]\(10 \, \text{g} = 0.01 \, \text{kg}\)[/tex] (converted to kg)
- Force ( [tex]\(F_3\)[/tex] ): [tex]\(4 \, \text{N}\)[/tex]
- Acceleration ( [tex]\(a_3\)[/tex] ): [tex]\[
a_3 = \frac{F_3}{m_3} = \frac{4 \, \text{N}}{0.01 \, \text{kg}} = 400 \, \text{m/s}^2
\][/tex]
4. Object 4:
- Mass ( [tex]\(m_4\)[/tex] ): [tex]\(1 \, \text{kg}\)[/tex]
- Force ( [tex]\(F_4\)[/tex] ): [tex]\(20 \, \text{N}\)[/tex]
- Acceleration ( [tex]\(a_4\)[/tex] ): [tex]\[
a_4 = \frac{F_4}{m_4} = \frac{20 \, \text{N}}{1 \, \text{kg}} = 20 \, \text{m/s}^2
\][/tex]
Now, we compare the accelerations we've calculated:
- Object 1: [tex]\( 0.4 \, \text{m/s}^2 \)[/tex]
- Object 2: [tex]\( 200 \, \text{m/s}^2 \)[/tex]
- Object 3: [tex]\( 400 \, \text{m/s}^2 \)[/tex]
- Object 4: [tex]\( 20 \, \text{m/s}^2 \)[/tex]
From these calculations, Object 3 has the greatest acceleration, which is [tex]\( 400 \, \text{m/s}^2 \)[/tex].
Therefore, based on the data, Object 3 has the greatest acceleration.
