Two skaters, a man and a woman, are standing on ice. Neglect any friction between the skate blades and the ice. The mass of the man is 81 kg, and the mass of the woman is 60 kg. The woman pushes on the man with a force of 50 N due east. Determine the acceleration (magnitude and direction) of (a) the man and (b) the woman.
(a) The man has an acceleration of about 0.62 meters per second squared east.
(b) The woman has an acceleration of 0 meters per second squared nowhere since the woman is in mechanical equilibrium. The woman stops once she hits the man with a force of 50 N.
To determine the acceleration of the man and woman, we can apply 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.
(a) Acceleration of the man:
The net force acting on the man is the force applied by the woman, which is 50 N due east. Since there are no other forces acting on the man, the net force is equal to the force applied.
Using Newton's second law (F = ma), we can rearrange the formula to solve for acceleration (a = F/m).
Plugging in the values, we have:
a_man = 50 N / 81 kg = 0.62 m/s^2 due east.
Therefore, the acceleration of the man is 0.62 m/s^2 due east.
(b) Acceleration of the woman:
Since the woman is pushing the man, the force she applies on him also acts on her in the opposite direction. According to Newton's third law of motion, the force she applies on the man of 50 N constitutes an equal and opposite force acting on the woman. Therefore, the force acting on the woman is -50 N (opposite direction of the force applied by the man).
Using the same formula (F = ma), we can calculate the acceleration of the woman:
a_woman = -50 N / 60 kg = -0.83 m/s^2 due west.
Therefore, the acceleration of the woman is 0.83 m/s^2 due west. Note that the negative sign indicates that the acceleration is in the opposite direction of the force applied.
In summary:
(a) The man has an acceleration of 0.62 m/s^2 due east.
(b) The woman has an acceleration of 0.83 m/s^2 due west.