Question

Samantha drives her car of mass 800kg clockwise around a circular track of radius 60m. She completes 12 laps around the track in 4 minutes. Find Samantha's centripetal acceleration in m/s2

Answer 1

5.92
`\frac{\textbf{m}}{\textbf{s}^{\textbf{2}}}`

Step-by-step explanation:

The motion of the car can be described as uniform motion in a circle. Hence, speed of the car is assumed constant.

She completes 12 laps in 4 minutes. So each lap takes 20 seconds.

`|Velocity|=\frac{\text{Distance}}{\text{Time taken}}=\frac{\text{Circumference}}{\text{Lap time}}=(2\pi r)/(T)`

Radius of lap =
`r=60\text{ }m`.

`v=\frac{2*\pi* 60 \text{ }m}{20\text{ }sec}=6\pi (m)/(sec)`

Mass of car =
`m=800\text{ }kg`

Centripetal acceleration =
`(v^(2))/(r)=\frac{(6\pi\text{ }(m)/(sec))^(2)}{60\text{ }m}=5.92(m)/(s^(2))`

∴ Centripetal Acceleration = 5.92
`(m)/(s^(2))`