**Answer:**

a) , b) approximately 25g's, c) 28.46 rpm

**Explanation:**

In order to solve this problem, we must first do a drawing of the situation to better visualize it (look at attached picture).

a)

Now, the very first thing we must do is convert the frequency to angular speed, we can do this like this:

so we get that:

once we have the angular speed, we can use it to find the centripetal acceleration by using the following formula:

which yields:

b)

we can use it to figure out how many g's this represents, we know that:

so, we can do the conversion

so we have approximately 25 g's on the machine.

c)

In order to produce a maximum acceleration of 8g's we can do the following.

First, turn the 8g's to

next, we use the same formula, but this time we solve for the angular speed:

which solves to:

and substitute the provided data:

which yields:

we can use this to find our frequency, like this:

so the frequency the machine should have to reach an acceleration of 8g's is:

f=28.46rpm