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 49 kg. The woman pushes on the man with a force of 58 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 apply Newton's second law of motion, which states that the acceleration of an object is directly proportional to the net force applied to it and inversely proportional to its mass.
Let's first calculate the acceleration of the man:
a) Acceleration of the man:
To find the acceleration of the man, we need to divide the net force applied to him by his mass.
Net force on the man = Force applied by the woman = 58 N (due east)
Mass of the man = 84 kg
Using Newton's second law: F = ma
58 N = (84 kg) * a
Now we can solve for acceleration (a):
a = 58 N / 84 kg
a ≈ 0.69 m/s² (eastward)
Therefore, the magnitude of the man's acceleration is approximately 0.69 m/s², and its direction is eastward.
b) Acceleration of the woman:
Since no external force is mentioned acting on the woman, we can assume there is no net force acting on her. As a result, the acceleration of the woman would be zero (0 m/s²).