A 600 kg racing car completes one qualifying lap in 4.52 seconds around a circular track with a radius of 51.2 meters. If the car moves with constant velocity, what is t he centripetal acceleration of the car.

Question

A 600 kg racing car completes one qualifying lap in 4.52 seconds around a circular track with a radius of 51.2 meters. If the car moves with  constant velocity, what is t he centripetal acceleration of the car.

anonymous · Answer

$$a_{s} = \frac{ m \times v^{2} }{ r } $$

s = 2pi r = 2 x 3.14 x 51.2 = 321.536 m

v = s/t = 321.536/4.52 = 71.136 m/s

$$a_{s} =\frac{ 600 \times 71.136^{2} }{ 51.2 }$$

as = 59074 m/s2

anonymous · Answer

Careful, Formula for acceleration is $$a = \frac{ v ^{2} }{ r }$$, with mass in it is the centripetal force!

anonymous · Answer

oh yeah, thank you @furnessj for correct me..,

s = 2pi r = 2 x 3.14 x 51.2 = 321.536 m 

v = s/t = 321.536/4.52 = 71.136 m/s

$$a_{s} = \frac{ v ^{2} }{ r } = \frac{ 71.136^{2} }{ 51.2 } = 98.834$$

anonymous · Answer

what is the magnitude and direction of the centripetal force of the car around the track?

anonymous · Answer

The centripetal force is ALWAYS aimed directly at the centre of the circle that the body is moving around. Or, put another way, tangential to the velocity at that time, towards the inside of the curve. (you don't always get a full circle!)
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