Centripetal acceleration problem?

Question

a bobsled track contains two turns with the radii of 33 m and 24m. Find the centripetal acceleration at each turn for a speed of 34 m/s. Express the answers as multiples of g.( how many times does gravity go into the answer.)

Answer 1

a=V^2/R

a/g=V^2/Rg

a1=(34)^2/(33 x 9.81)=3.6g
a2=(34)^2/(24 x 9.81)=4.9g

Answer 2

Radial(centripetal - "seeking the center") acceleration is defined as the square of the velocity term over the radial distance. In mathematical language it can be written as follows:

a:=v^2/r

In this case our velocity is 34 m/s > square this and stick it over the two radii.

a1=(34 m/s)^2 / (33 m) = 35 m/s^2 = 3.6 g

a2=(34 m/s)^2 / (24 m) = 48.2 m/s^2 = 4.9 g

That is quite a bit of g!!

Answer 3

a = v^2/r

now you need to do this 2x, once per radius...

a=34^2 /33 = 35 m/s^2 / 9.8 = 3.6 g

a=34^2 /24 = 48.2 m/s^2/ 9.8 = 4.9 g

The acceleration of the 1st turn is 3.6g
and the acceleration of the 2nd turn is 4.9g...