7.If a washing machine's drum has a radius of 28 cm and spins at 4.1 rev/s, what is the strength of the artificial gravity to which the clothes are subjected? Express your answer as a multiple of g.
To determine the strength of the artificial gravity to which the clothes are subjected, we can use the equation:
Centripetal acceleration (a) = (angular velocity)^2 x radius
First, convert the angular velocity from revolutions per second to radians per second by multiplying it by 2π:
Angular velocity (ω) = 4.1 rev/s * 2π rad/rev = 8.2π rad/s
Next, substitute the given radius and angular velocity into the equation to calculate the centripetal acceleration:
a = (8.2π rad/s)^2 * 28 cm
Now, we need to convert the centimeter unit to meters:
a = (8.2π rad/s)^2 * 0.28 m
Finally, express the acceleration in terms of g by dividing the centripetal acceleration by the acceleration due to gravity (g ≈ 9.8 m/s^2):
a/g = (8.2π rad/s)^2 * 0.28 m / 9.8 m/s^2
a/g ≈ 1.165
Therefore, the strength of the artificial gravity to which the clothes are subjected is approximately 1.165 times the acceleration due to gravity (g).