Question

name:
ucm-circu
base your answers to questions 19 and 20 on the information below.
a go - cart travels around a flat, horizontal, circular track with a radius of 25 meters. the mass of the go - cart with the rider is 200 kilograms. the magnitude of the maximum centripetal force exerted by the track on the go - cart is 1200 newtons.

1. what is the maximum speed the 200 - kilogram go - cart can travel without sliding off the track?
2. 8.0 m/s
3. 12 m/s
4. 150 m/s
5. 170 m/s

Explanation:

Step1: Recall centripetal force formula

Centripetal force $F_c = \frac{mv^2}{r}$

Step2: Rearrange for speed $v$

$v = \sqrt{\frac{F_c r}{m}}$

Step3: Substitute values

$F_c=1200N$, $r=25m$, $m=200kg$
$v = \sqrt{\frac{1200 \times 25}{200}} = \sqrt{\frac{30000}{200}} = \sqrt{150} \approx 12m/s$

Answer:

1. 12 m/s