Hannah is pushing with a 16.5 N force on a 1.5kg mass. The 1.5kg mass, and the 4 kg mass that is pushed up against it, move together. Assuming this is a frictionless surface, what is the force of the 4 kg box ON the 1.5 kg box?
The force of the 4 kg box on the 1.5 kg box is equal in magnitude and opposite in direction to the force of the 1.5 kg box on the 4 kg box, according to Newton's third law of motion. Since the two boxes move together, we can consider them as a single system. In this case, the force applied to the 1.5 kg box is also acting on this combined 5.5 kg system.
The force of the 1.5 kg box on the 4 kg box can be found using Newton's second law, which states that the force is equal to the mass of the object multiplied by its acceleration (F = m*a).
First, we need to find the acceleration of the system. Using Newton's second law, we can find the acceleration by dividing the force by the total mass of the system:
a = F_total / (m_1 + m_2)
Where F_total is the total force applied, m_1 is the mass of the 1.5 kg box, and m_2 is the mass of the 4 kg box.
a = 16.5 N / (1.5 kg + 4 kg) = 16.5 N / 5.5 kg ≈ 3 m/s^2
Now that we have the acceleration, we can find the force of the 1.5 kg box on the 4 kg box using Newton's second law:
F = m * a
In this case, since the force acting on the 1.5 kg box is also acting on the 4 kg box, we can directly use the 3 m/s^2 acceleration for both boxes. Therefore, the force of the 1.5 kg box on the 4 kg box is:
F = 4 kg * 3 m/s^2 = 12 N
Since the force of the 4 kg box on the 1.5 kg box is equal in magnitude but opposite in direction, their interaction force is 12 N.