Centripital Acceleration Question

[pinky2468]

I can get the first part, but I am getting tripped up on the second part.

A 220 kg boat is negotiating a circular turn (radius=32m) around a buoy. During the turn, the engine causes a net tangetntial force of magnitude 550N to be applied to the boat. The initial tangential speed of the boat going around the turn is 5.0 m/s a)find the tangential acceleration b)after the boat is 2.0 s into the turn find the centripetal acceleration.

So for part a)
F=mr(alpha) (alpha=angular acceleration, I can't make the symbol) alpha= .078 rad/s^2

Tang. acceleration= r(alpha)= 2.5 m/s^2

I am stuck on part b, I think the fact that I am given the initial tangential speed. So do I find the final and take the average?

 

[doriang101]

part b

Since you are given the force of the engine, and the intial speed, you know the acceleration of the boat. From that you can deduce the final speed of the boat after 2 seconds from v2 = v1 + at(t = 2,a=550/massofboat,v1=5m/s). Then the acceleration you seek is simply
a = v^2/R m/s^2

 

[wais]

For part b), you do not need to find the final tangential speed. You can use the formula for centripetal acceleration: a = v^2/r, where v is the tangential speed and r is the radius of the circular turn. Since the tangential speed remains constant at 5.0 m/s, you can plug that in for v and the given radius of 32m to find the centripetal acceleration.

a = (5.0 m/s)^2 / 32m = 0.781 m/s^2

So the centripetal acceleration of the boat after 2.0 seconds into the turn is 0.781 m/s^2.