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 84 kg, and the mass of the woman is 68 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
To determine the acceleration of the man and the woman, we can 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.
(a) To find the acceleration of the man, we need to calculate the net force acting on him. The net force is the vector sum of all the forces acting on the man.
In this case, the only force acting on the man is the force exerted by the woman pushing him. The force exerted by the woman is 50 N due east. Since there is no friction, there are no other forces acting on the man.
Net force on man = force exerted by woman = 50 N due east
Using Newton's second law, we can calculate the acceleration of the man:
Acceleration of man = Net force on man / Mass of man
Acceleration of man = 50 N / 84 kg
To determine the magnitude of the acceleration, divide the magnitude of the net force by the mass of the man:
Magnitude of acceleration of man = 50 N / 84 kg = 0.595 m/s^2
The direction of the acceleration of the man is the same as the direction of the net force, which is due east.
(b) To find the acceleration of the woman, we again use Newton's second law. Since the woman is pushing the man, the net force acting on the woman is equal in magnitude but opposite in direction to the force exerted by the woman on the man.
Net force on woman = - force exerted by woman = -50 N due east
Using Newton's second law, we can calculate the acceleration of the woman:
Acceleration of woman = Net force on woman / Mass of woman
Acceleration of woman = -50 N / 68 kg
To determine the magnitude of the acceleration, divide the magnitude of the net force by the mass of the woman:
Magnitude of acceleration of woman = 50 N / 68 kg = 0.735 m/s^2
The direction of the acceleration of the woman is opposite to the direction of the net force, which is due west.