Final answer:
To determine how far from the axis of rotation a man can stand on a rotating merry-go-round without sliding, we need to consider the maximum static friction force. This force can be found using the coefficient of static friction and the normal force. By using the equation for the maximum static friction force and the angular velocity of the merry-go-round, we can calculate the distance from the axis of rotation.
Step-by-step explanation:
To determine how far from the axis of rotation the man can stand without sliding, we need to find the maximum value of the static friction force.
The maximum static friction force can be found using the equation:
fs_max = μs * N,
where fs_max is the maximum static friction force, μs is the coefficient of static friction, and N is the normal force.
Since the man is standing horizontally on the merry-go-round, the normal force is equal to his weight, which can be calculated using:
N = mg,
where m is the mass of the man and g is the acceleration due to gravity. Assuming the radius of the merry-go-round is R, the maximum static friction force can be written as:
fs_max = μs * mg,
Finally, the distance from the axis of rotation that the man can stand without sliding can be calculated using the equation:
R = fs_max / ω^2,
where ω is the angular velocity of the merry-go-round.