If a washing machine's drum has a radius of 24 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 experienced by the clothes in the washing machine, we need to calculate the centripetal acceleration.
The centripetal acceleration can be calculated using the formula:
a = r * ω^2
where:
a is the centripetal acceleration,
r is the radius of the drum, and
ω (omega) is the angular velocity.
In this case, the radius of the drum is given as 24 cm, which is equivalent to 0.24 meters. The angular velocity is given as 4.1 rev/s.
First, let's convert the angular velocity from revolutions per second to radians per second. Since one revolution is equal to 2π radians, we can multiply the given angular velocity by 2π to convert it:
ω = 4.1 rev/s * 2π rad/rev
Next, we can substitute the values into the centripetal acceleration formula:
a = 0.24 m * (4.1 * 2π rad/rev)^2
We can now calculate the centripetal acceleration.
First, calculate the value inside the parentheses:
ω = 4.1 * 2π ≈ 25.759 rad/s
Next, square the value of ω:
(ω^2) = (25.759 rad/s)^2 ≈ 664.245 m^2/s^2
Finally, substitute the value of (ω^2) back into the centripetal acceleration formula:
a = 0.24 m * 664.245 m^2/s^2 ≈ 159.898 m/s^2
The strength of the artificial gravity experienced by the clothes in the washing machine is approximately 159.898 m/s^2.
Since we are comparing this artificial gravity to normal gravity (g), we can express the answer as a multiple of g. To do this, we divide the result by the acceleration due to gravity on Earth, which is approximately 9.8 m/s^2:
a/g = (159.898 m/s^2) / (9.8 m/s^2) ≈ 16.3
Therefore, the strength of the artificial gravity to which the clothes are subjected is approximately 16.3 times the strength of Earth's gravity (g).