a mother (50kg) and her child (25) kg are facing each other in the middle of a friction less pond of ice. The mother pushes horizontally with a force of 100N.
a) what is the magnitude of child's acceleration
b) what is the magnitude of mother's acceleration
F = ma
a) The magnitude of the child's acceleration can be found using Newton's second law, which states that the force acting on an object is equal to the mass of the object multiplied by its acceleration.
F = ma
In this case, the force applied by the mother is 100N. We can assume that the force applied by the child on the mother is negligible since it is not specified. Therefore, the force causing the child to accelerate is the force applied by the mother.
100N = (25kg)a
a = 100N / 25kg
a = 4 m/s^2
b) Since the mother is pushing the child, her force is the cause of the child's acceleration. Therefore, the magnitude of the mother's acceleration would be the same as that of the child.
The magnitude of the mother's acceleration is also 4 m/s^2.
To find the magnitudes of both the mother and child's accelerations, we can use Newton's second law of motion, which states that the force applied to an object is equal to the product of its mass and acceleration (F = ma).
a) Magnitude of child's acceleration:
The total force acting on the system is the force applied by the mother. Since the system is isolated, there are no external forces. Therefore, the force exerted by the mother on the child is equal in magnitude but opposite in direction.
F_child = -F_mother = -100N (opposite direction)
Using Newton's second law, we can calculate the acceleration of the child:
F_child = m_child * a_child
a_child = F_child / m_child
= -100N / 25kg
= -4 m/s²
However, since we are interested in the magnitude of the acceleration, we take the absolute value:
|a_child| = |-4 m/s²| = 4 m/s²
Therefore, the magnitude of the child's acceleration is 4 m/s².
b) Magnitude of mother's acceleration:
To find the magnitude of the mother's acceleration, we can assume that the only horizontal force acting on the system is the force applied by the mother. The total mass of the system (mother and child combined) is 50 kg + 25 kg = 75 kg.
Using Newton's second law, we can calculate the acceleration of the system:
F_mother = (m_mother + m_child) * a_mother
Rearranging the equation, we can solve for a_mother:
a_mother = F_mother / (m_mother + m_child)
= 100N / 75 kg
= 4/3 m/s²
Therefore, the magnitude of the mother's acceleration is 4/3 m/s².
To find the magnitudes of the child's and mother's acceleration, 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 magnitude of the child's acceleration (a_child), we can apply Newton's second law to the child's mass and the horizontal force exerted by the mother. The net force on the child is the force applied by the mother (100N) since there is no other external force acting on the system. Therefore, we have:
Net force = Mass of the child × Acceleration of the child
100N = 25kg × a_child
Solving for a_child, we get:
a_child = 100N / 25kg = 4 m/s^2
So, the magnitude of the child's acceleration is 4 m/s^2.
b) Similarly, to find the magnitude of the mother's acceleration (a_mother), we can apply Newton's second law to the mother's mass and the horizontal force she applies. The net force on the mother is also 100N since it is the same force she is exerting. Therefore, we have:
Net force = Mass of the mother × Acceleration of the mother
100N = 50kg × a_mother
Solving for a_mother, we get:
a_mother = 100N / 50kg = 2 m/s^2
So, the magnitude of the mother's acceleration is 2 m/s^2.