A 2000 kg car travels at a constant speed of 12 m/s around a circular curve of radius 30 m. What is the magnitude of the centripetal acceleration of the car as it goes around the curve?

Answer 1

We are given

m = 2000 kg

r = 30 m

v = 12 m/s

Centripetal acceleration, a = v²/r

= (12m/s)² /30m

= 4.8 m/s²

Centripetal force:

Recall force = mass * acceleration

F = m v²/ r

= (2000 ) (12²) )/30

= 9600 N

Answer 2

Hi Kaitlyn,

Let's first collect the known values:

m = 2000kg

v = 12m/s

r = 30m

Now, we know we need to convert this speed value to a rotational motion value for speed. To do this, we use the function:

ω*r = v

where ω is angular velocity, r is radius and v is linear velocity. Let's plug in the knowns.

ω = (12m/s) / (30m) = 0.4 rad/s

Centripetal acceleration is also a function of angular velocity and radius.

α = ω²r = (0.4rad/s)² (30m) = 4.8m/s² towards the center

Now, if you're asking for centripetal force, then we can use the mass in the equation:

F_c = (mv²)/r

F_c = (2000*12²)/30 = 9600N