To find the number of revolutions per second the cylinder should make in order for the clothes to lose contact with the wall when the angle è is 73.0°, we can use the concept of centripetal force.
The force exerted by the wall on the clothes is the centripetal force required to keep the clothes moving in a circular path. When the clothes lose contact with the wall, the centripetal force becomes zero.
The centripetal force can be calculated using the formula:
F = m * (v^2 / r)
where F is the force, m is the mass of the clothes, v is the velocity, and r is the radius.
In this case, we are given the values for r and è, and we need to find the velocity v.
The vertical component of the velocity can be calculated using the formula:
v = √(g * r * (1 - cos(è)))
where g is the acceleration due to gravity (9.8 m/s^2) and cos(è) is the cosine of the angle.
Substituting the given values into the formula, we get:
v = √(9.8 * 0.36 * (1 - cos(73°)))
Solving this equation, we find that v ≈ 2.89 m/s.
To find the number of revolutions per second, we need to convert the velocity to angular velocity (ω) and then divide by 2π:
ω = v / r
ω = 2.89 / 0.36
Finally, the number of revolutions per second is given by:
n = ω / (2π)
n = (2.89 / 0.36) / (2 * π)
n ≈ 4.03 revolutions per second.
Therefore, the cylinder should make approximately 4.03 revolutions per second for the clothes to lose contact with the wall when the angle è is 73.0°.