Centripetal Acceleration and Force

[FaraDazed]

Homework Statement

A small truck of mass 1600kg rides in a circle of which has a radius of 40m at a constant speed of 70m/s

Calculate:
(a) its centripetal acceleration
(b)the centripetal force acting.

Homework Equations

[itex]
a_{centripetal} = {v^2 \over r} \\
F_{centripetal} = {mv^2 \over r}

[/itex]

The Attempt at a Solution

I think I got the correct answers its just the figures seem absurdly high, so can someone check my understanding please?

So for part a
[itex]
a_{centripetal} = {70^2 \over 40} \\
a_{centripetal} = 122.5 m/s^2
[/itex]

And part b
[itex]
F_{centripetal} = \frac{1600 \times 70^2}{40} \\
F_{centripetal} = \frac{7840000}{40} \\
F_{centripetal} = 196kN
[/itex]

The figures just seem to high to me, we only had one lesson on this so I may have taken down something wrong or might have misunderstood the question.

 

[Doc Al]

Looks fine to me.

 

[FaraDazed]

Looks fine to me.

OK, thanks :)

 

[tiny-tim]

Hi FaraDazed!

The figures just seem to high to me …

looks ok to me, too

imagine you had to pull on a rope to keep it in a circle …

wouldn't you expect to pull really hard? ​

 

[Nickie]

Any help would be appreciated.

Your calculations for both parts are correct. The figures may seem high because of the high speed and mass of the truck. Centripetal acceleration and force are directly proportional to the square of the velocity, so as the speed increases, so does the acceleration and force. Additionally, the radius of the circle is relatively small, which also contributes to the high values.