A washing machine needs 16 s to speed up from rest to top speed of 5 rotation for every 3.03 s. If the damp cloths inside are 9.54 cm from the center, what is it's radial acceleration at top speed?
To calculate the radial acceleration of the washing machine at top speed, we need to use the formula for radial acceleration:
a = ω^2 * r
where:
a = radial acceleration
ω = angular velocity
r = radius
First, let's calculate the angular velocity of the washing machine at top speed. We know that the washing machine takes 16 seconds to speed up from rest to the top speed of 5 rotations for every 3.03 seconds.
To find the angular velocity, we can divide the number of rotations by the time taken:
ω = number of rotations / time
ω = 5 rotations / 3.03 s
Now, let's calculate the angular velocity:
ω = 1.6501650165 rad/s
Next, we need to convert the given distance from the center (9.54 cm) to meters (since the formula requires SI units):
r = 9.54 cm = 0.0954 m
Now, we can calculate the radial acceleration:
a = ω^2 * r
Substituting the values we obtained:
a = (1.6501650165 rad/s)^2 * 0.0954 m
Finally, we can calculate the value of the radial acceleration:
a ≈ 0.256 m/s^2
Therefore, the radial acceleration of the washing machine at top speed is approximately 0.256 m/s^2.