A 63 kg boy and a 44 kg girl use an elastic rope
while engaged in a tug-of-war on a frictionless
icy surface.
If the acceleration of the girl toward the
boy is 1.7 m/s
2
, determine the magnitude of
the acceleration of the boy toward the girl
To determine the magnitude of the acceleration of the boy toward the girl, we can use Newton's second law of motion, which states that the net force acting on an object is equal to the mass of the object multiplied by its acceleration.
First, let's consider the forces acting on the boy and the girl in the horizontal direction. The only force acting on the boy is the tension in the rope pulling him toward the girl, and the only force acting on the girl is the tension in the rope pulling her toward the boy.
According to Newton's second law, the net force on the boy is equal to the mass of the boy multiplied by his acceleration, and similarly for the girl:
Net force on the boy = mass of the boy × acceleration of the boy
Net force on the girl = mass of the girl × acceleration of the girl
Since the rope is elastic, the tension in the rope is the same for both the boy and the girl.
Therefore, we can set up the following equation:
mass of the boy × acceleration of the boy = mass of the girl × acceleration of the girl
Substituting the given values:
63 kg × acceleration of the boy = 44 kg × 1.7 m/s^2
To find the acceleration of the boy, we can rearrange the equation:
acceleration of the boy = (44 kg × 1.7 m/s^2) / 63 kg
Solving this equation, the acceleration of the boy toward the girl is approximately 1.18 m/s^2.