To solve this problem, we need to determine two things: the centripetal acceleration of the car and the net force acting on it as it moves around the circle. The centripetal force is the net force acting on the car that keeps it moving in a circular path.

Step 1: Calculate the Centripetal Acceleration

The formula for centripetal acceleration $a_c$ is given by:

$a_c = \frac{v^2}{r}$

where:

• $v$ is the velocity of the car (12 m/s),
• $r$ is the radius of the circle (23 m).

Plugging in the values:

$a_c = \frac{12^2}{23}$

$a_c = \frac{144}{23} \approx 6.26 \, \text{m/s}^2$

So, the centripetal acceleration is approximately 6.26 m/s².

Step 2: Calculate the Net Force (Centripetal Force)

The net force acting on the car can be calculated using Newton's second law, specifically for circular motion, where the net force is the centripetal force $F_c$:

$F_c = m \cdot a_c$

where:

• $m$ is the mass of the car (700 kg),
• $a_c$ is the centripetal acceleration (6.26 m/s²).

Plugging in the values:

$F_c = 700 \times 6.26$

$F_c = 4382 \, \text{N}$

So, the net force acting upon the car is 4382 N.

Summary

• Centripetal Acceleration: 6.26 m/s²
• Net Force (Centripetal Force): 4382 N

Would you like more details or have any questions about these calculations?

Further Questions:

1. What is the difference between centripetal and centrifugal forces?
2. How would the force change if the car’s speed were doubled?
3. What happens to the centripetal force if the radius of the circle is halved?
4. How is centripetal acceleration different from linear acceleration?
5. In what situations in real life do we experience centripetal forces?

Tip: Remember that centripetal force always points towards the center of the circle, keeping the object moving in a circular path.