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 95 kg, and the mass of the woman is 55 kg. The woman pushes on the man with a force of 57 N due east. Determine the acceleration (magnitude and direction) of (a) the man and (b) the woman.
They retain a total momentum of zero as they accelerate in opposite directions
Forces on each are equal and opposite.
M1*a1 = -M2*a2 = 57 N
a1 (man) * 95 = 57
a1 = 0.60 m/s^2 (East)
a2 = -(M1/M2)*a1 = -1.036 m/s^2
(The minus sign means the woman accelerates to the west)
To determine the acceleration of both 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 can use the formula:
Acceleration = Net Force / Mass
The mass of the man is given as 95 kg, and the net force acting on him is the force exerted by the woman, which is 57 N. As the woman pushes the man due east, the acceleration of the man will also be in the same direction (east).
Substituting the values, we get:
Acceleration of the man = 57 N / 95 kg ≈ 0.6 m/s^2 (east)
(b) To find the acceleration of the woman, we can use the same formula:
Acceleration = Net Force / Mass
The mass of the woman is given as 55 kg, and the net force acting on her is also 57 N. However, since the woman is not exerting any other force on another object, her acceleration can be determined by using the formula:
Acceleration of the woman = Net Force / Mass
Substituting the values, we get:
Acceleration of the woman = 57 N / 55 kg ≈ 1.04 m/s^2 (east)
Therefore, the magnitude of the acceleration for the man is approximately 0.6 m/s^2, and the magnitude of the acceleration for the woman is approximately 1.04 m/s^2. Both accelerations are directed towards the east.
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. The equation can be written as:
a = F / m
where a is the acceleration, F is the net force, and m is the mass.
(a) To find the acceleration of the man, we'll use his mass, which is 95 kg, and the net force acting on him, which is the force exerted by the woman, equal to 57 N. Since the woman is pushing towards the east, the force will also act towards the east direction. Therefore, we can plug the values into the equation:
a_man = 57 N / 95 kg
Calculating the value will give us the acceleration of the man.
(b) To determine the acceleration of the woman, we'll use the same equation. However, the net force acting on the woman is the reaction force from the man, which will have the same magnitude but act in the opposite direction. So the force acting on the woman will also be 57 N, but it will be directed towards the west. Plugging the values into the equation:
a_woman = 57 N / 55 kg
Calculating the value will provide the acceleration of the woman.
Note: The acceleration is a scalar value representing its magnitude, but since the forces and resulting accelerations are in opposite directions for the man and the woman, the directions will be opposite as well.