To solve this problem, we need to calculate the centripetal acceleration and the net force acting on the object. The formulas for these calculations are as follows:

Given:

• Mass $m = 12.85 \, \text{kg}$
• Velocity $v = 12.9 \, \text{m/s}$
• Radius $r = 1.8 \, \text{m}$

a. Centripetal Acceleration

The formula for centripetal acceleration $a_c$ is:

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

Substituting the given values:

$a_c = \frac{(12.9 \, \text{m/s})^2}{1.8 \, \text{m}}$

$a_c = \frac{166.41 \, \text{m}^2/\text{s}^2}{1.8 \, \text{m}} \approx 92.45 \, \text{m/s}^2$

b. Net Force Acting on the Object

The net force $F$ acting on the object moving in a circle is the centripetal force, which is given by:

$F = m \times a_c$

Substituting the mass and the calculated centripetal acceleration:

$F = 12.85 \, \text{kg} \times 92.45 \, \text{m/s}^2 \approx 1187.08 \, \text{N}$

Summary:

a. Centripetal acceleration: $92.45 \, \text{m/s}^2$
b. Net force acting on the object: $1187.08 \, \text{N}$

Do you want more details or have any questions?

---

Here are 5 related questions for further exploration:

1. How would the centripetal acceleration change if the radius of the circular track was doubled?
2. What would be the net force if the mass of the object was increased to 20 kg while keeping the same velocity and radius?
3. How does the velocity affect the centripetal force if all other factors remain constant?
4. Can you calculate the period of the object’s motion around the track?
5. What would be the velocity required to produce a centripetal acceleration of 50 m/s² on the same track?

Tip: Centripetal force always points towards the center of the circular path, and it is essential for keeping the object in circular motion.