What is the acceleration (magnitude and direction) of the man and the woman standing on ice when the woman pushes the man with a force due east?
To determine the acceleration of the man and the woman, we'll use Newton's second law of motion, which states that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass.
Given:
Mass of the man (m_man) = 82 kg
Mass of the woman (m_woman) = 48 kg
Force exerted by the woman on the man (F_woman) = 45 N (in the east direction)
(a) Acceleration of the man:
Using Newton's second law, we have:
F_man = m_man * a_man
Since the man is acted upon by an external force (the force exerted by the woman), the net force on the man is given by:
F_man = F_woman
Substituting the values, we have:
F_woman = m_man * a_man
45 N = 82 kg * a_man
Solving for a_man:
a_man = 45 N / 82 kg
a_man ≈ 0.549 m/s²
Therefore, the acceleration of the man is approximately 0.549 m/s², in the direction of the force applied by the woman (east direction).
(b) Acceleration of the woman:
Since the woman exerts a force on the man and there are no other external forces acting on her, the net force on the woman is zero. Therefore, she will not experience any acceleration in this scenario.
In summary:
(a) The man's acceleration is approximately 0.549 m/s² in the east direction.
(b) The woman does not experience any acceleration.