To determine which motor and body combination Devon should use to build the car with the greatest acceleration, we need to apply Newton's second law of motion, which states:
[tex]\[ F = m \cdot a \][/tex]
This can be rearranged to solve for acceleration [tex]\(a\)[/tex]:
[tex]\[ a = \frac{F}{m} \][/tex]
where:
- [tex]\( F \)[/tex] is the force applied by the motor.
- [tex]\( m \)[/tex] is the mass of the body.
- [tex]\( a \)[/tex] is the acceleration.
We will calculate the acceleration for each combination of motor and body.
### Motor 1 with Body 1
- Force of Motor 1 ([tex]\( F_1 \)[/tex]) = 10 N
- Mass of Body 1 ([tex]\( m_1 \)[/tex]) = 0.2 kg
[tex]\[ a_1 = \frac{F_1}{m_1} = \frac{10 \text{ N}}{0.2 \text{ kg}} = 50 \text{ m/s}^2 \][/tex]
### Motor 1 with Body 2
- Force of Motor 1 ([tex]\( F_1 \)[/tex]) = 10 N
- Mass of Body 2 ([tex]\( m_2 \)[/tex]) = 0.6 kg
[tex]\[ a_2 = \frac{F_1}{m_2} = \frac{10 \text{ N}}{0.6 \text{ kg}} = 16.67 \text{ m/s}^2 \][/tex]
### Motor 2 with Body 1
- Force of Motor 2 ([tex]\( F_2 \)[/tex]) = 15 N
- Mass of Body 1 ([tex]\( m_1 \)[/tex]) = 0.2 kg
[tex]\[ a_3 = \frac{F_2}{m_1} = \frac{15 \text{ N}}{0.2 \text{ kg}} = 75 \text{ m/s}^2 \][/tex]
### Motor 2 with Body 2
- Force of Motor 2 ([tex]\( F_2 \)[/tex]) = 15 N
- Mass of Body 2 ([tex]\( m_2 \)[/tex]) = 0.6 kg
[tex]\[ a_4 = \frac{F_2}{m_2} = \frac{15 \text{ N}}{0.6 \text{ kg}} = 25 \text{ m/s}^2 \][/tex]
Now, comparing all the accelerations:
- Motor 1 with Body 1: 50 m/s²
- Motor 1 with Body 2: 16.67 m/s²
- Motor 2 with Body 1: 75 m/s²
- Motor 2 with Body 2: 25 m/s²
The greatest acceleration is 75 m/s² for the combination of Motor 2 with Body 1.
Therefore, Devon should use Motor 2 with Body 1 to build the car with the greatest acceleration.
