To determine who wins in a race between Cesar and Jake, we need to consider not just their masses (600 N for Cesar and 900 N for Jake), but also factors like acceleration and speed. Their masses can be associated with their weight, which reflects the gravitational pull on their mass.
Let's denote:
- \( F \) as the force exerted by each boy (which can be influenced by their strength, running technique, etc.)
- \( m_C \) for Cesar's mass (600 N gives \( m_C/\text{g} \) = mass, where g = 9.81 m/s²)
- \( m_J \) for Jake's mass (900 N likewise gives \( m_J/\text{g} \))
The equations for their acceleration (\( a \)) using Newton's second law \( F = ma \) can be expressed as:
-
Cesar’s acceleration: \[ a_C = \frac{F_C}{m_C} \]
-
Jake’s acceleration: \[ a_J = \frac{F_J}{m_J} \]
Scenarios:
-
Cesar Wins:
- If Cesar exerts greater force relative to his mass: \[ \frac{F_C}{600} > \frac{F_J}{900} \] This means if \( F_C \) is sufficiently higher than \( \frac{600}{900}F_J \), Cesar wins.
-
Jake Wins:
- Conversely, if Jake exerts more force relative to his mass: \[ \frac{F_J}{900} > \frac{F_C}{600} \] This means if \( F_J \) is sufficiently higher than \( \frac{900}{600}F_C \), Jake wins.
In summary, the force each boy can exert related to their mass determines the winner, with Cesar needing to generate a higher force-to-mass ratio to win, while Jake can rely on either greater strength or acceleration due to his mass at lower exerted forces.
1 answer