Question

1. a 2.6 kg toy electric train moving at constant speed on a circular track that has a radius of 1.2 meters goes around the track every 9.0 seconds.

a. what is the speed of the train given: 2.6kg, 1.2 unknown: $a_c = \frac{v^2}{r}$ $f_c = \frac{2.6}{1.2} = 2.167v^2$
b. what is the centripetal acceleration of the train?
c. calculate the magnitude of the centripetal force

Explanation:

Step1: Calculate speed

Circumference $C = 2\pi r = 2\pi(1.2) \approx 7.54$ m. Speed $v = \frac{C}{T} = \frac{7.54}{9.0} \approx 0.838$ m/s.

Step2: Find centripetal acceleration

$a_c = \frac{v^2}{r} = \frac{(0.838)^2}{1.2} \approx \frac{0.702}{1.2} \approx 0.585$ m/s².

Step3: Compute centripetal force

$F_c = m \cdot a_c = 2.6 \times 0.585 \approx 1.52$ N.

Answer:

a. ~0.84 m/s
b. ~0.59 m/s²
c. ~1.52 N