A 38.3 kg girl and a 55.4 kg boy are on the surface of a frozen lake, 10.0 m apart. Using a rope, the girl exerts a horizontal 5.50 N force on the boy, pulling him toward her. Calculate the magnitude of the girl's acceleration.
To calculate the magnitude of the girl's acceleration, we can use Newton's second law of motion, which states that the acceleration of an object is equal to the net force acting on it divided by its mass.
In this case, the girl exerts a horizontal force of 5.50 N on the boy. Since the girl is pulling the boy towards her, the direction of the force is horizontal. Therefore, we can use the horizontal component of the force to calculate the acceleration.
To determine the horizontal component of the force, we need to find the angle between the force vector and the horizontal axis. However, it is not stated in the question, so we assume that the angle is 0 degrees. This means that the force is purely horizontal.
Now we can calculate the acceleration of the boy using Newton's second law:
Acceleration = Net force / Mass
The net force is equal to the force exerted by the girl.
Acceleration = 5.50 N / 55.4 kg
Acceleration ≈ 0.0992 m/s^2
Therefore, the magnitude of the girl's acceleration is approximately 0.0992 m/s^2.
To calculate the magnitude of the girl's acceleration, we need to use Newton's second law of motion, which states that the force acting on an object is equal to its mass multiplied by its acceleration.
Given:
Mass of the girl (m₁) = 38.3 kg
Force applied by the girl (F) = 5.50 N
Let's assume the girl's acceleration is a.
Using the formula F = m₁ * a, we can rearrange it to find the acceleration:
a = F / m₁
Substituting the given values:
a = 5.50 N / 38.3 kg
a ≈ 0.143 m/s²
Therefore, the magnitude of the girl's acceleration is approximately 0.143 m/s².