A 43.3 kg boy and a 60.0 kg girl are on the surface of a frozen lake, 10.5 m apart. Using a rope, the boy exerts a horizontal 5.90 N force on the girl, pulling her toward him. Calculate the magnitude of the boy's acceleration.
a = F/m = 5.9 / 60 = 0.098m/s^2.
To calculate the magnitude of the boy's acceleration, we need to 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.
First, let's identify the given information:
Mass of the boy (m₁) = 43.3 kg
Mass of the girl (m₂) = 60.0 kg
Distance between them (d) = 10.5 m
Force exerted by the boy on the girl (F) = 5.90 N
Now, we can calculate the gravitational force between them using the formula:
Fg = G * (m₁ * m₂) / d²
where G is the gravitational constant (approximately 6.67430 × 10⁻¹¹ Nm²/kg²).
Substituting the given values:
Fg = (6.67430 × 10⁻¹¹ Nm²/kg²) * ((43.3 kg) * (60.0 kg)) / (10.5 m)²
Simplifying this expression will give us the magnitude of the gravitational force acting between them.
Next, we need to calculate the net force acting on the girl. Since the boy is pulling the girl towards him, the tension in the rope (T) will contribute to the net force.
Net Force (F_net) = F - T
Now, we can use Newton's second law to calculate the acceleration (a) of the girl, since the boy's acceleration will be the same magnitude:
F_net = m₂ * a
Rearranging the formula, we get:
a = F_net / m₂
Finally, we substitute the calculated net force and mass of the girl to find the magnitude of the acceleration of the boy.