A washing machine needs 17.9 s to speed up from rest to top speed of 5 rotation for every 2.78 s. If the damp cloths inside are 7.13 cm from the center, what is it's radial acceleration at top speed?

acceleration=wf^2/r=(2PI*5/2.78)^2/.0713

omega top = 5 * 2 pi radians/2.78 s

= 11.3 radians/s

omega = alpha t
11.3 = alpha (17.9)
alpha = .631 radians/s^2

but is you want linear radial acceleration only that is
Ac = v^2/r =omega^2 r
= 11.3^2 * .0713 = 9.10 m/s^2
(close to 1 g :)

To find the radial acceleration at top speed, we need to first calculate the angular acceleration and then use it to find the radial acceleration.

The angular acceleration can be calculated using the formula:

angular acceleration (α) = change in angular velocity (ω) / change in time (t)

Given that the washing machine speeds up from rest to 5 rotations for every 2.78 seconds, we can find the change in angular velocity:

change in angular velocity (ω) = 5 rotations / 2.78 s

Next, we need to convert rotations to radians by multiplying it with 2π (since 1 rotation = 2π radians):

change in angular velocity (ω) = 5 rotations / 2.78 s * 2π radians/rotation

Now, we can calculate the angular acceleration:

angular acceleration (α) = change in angular velocity (ω) / change in time (t)

angular acceleration (α) = (5 rotations / 2.78 s * 2π radians/rotation) / 17.9 s

Once we have the angular acceleration, we can find the radial acceleration using the formula:

radial acceleration (aᵣ) = angular acceleration (α) * radius (r)

Given that the damp cloths inside are 7.13 cm from the center, we need to convert it to meters:

radius (r) = 7.13 cm * 1 m/100 cm

Finally, we can calculate the radial acceleration:

radial acceleration (aᵣ) = angular acceleration (α) * radius (r)

Now, we can substitute the values into the formula to get the answer.