To solve this problem, we need to analyze the motion of the two masses before and after the string is cut. Let's break it down step by step, starting with the forces acting on the system and how they affect the motion of both masses.
Understanding the System
We have two bodies: one with a mass of 4 kg (let's call it Mass A) and the other with a mass of 6 kg (Mass B). They are connected by a light string on a smooth horizontal surface, meaning there is no friction acting on them. When a horizontal force is applied to Mass A, both masses will accelerate together until the string is cut.
Acceleration of the System
When the force is applied to Mass A, both masses will experience the same acceleration because they are connected. The total mass of the system is:
- Total mass = Mass A + Mass B = 4 kg + 6 kg = 10 kg
Let’s denote the applied force as F. According to Newton's second law, the acceleration (a) of the system can be expressed as:
a = F / total mass
Velocity Before the String is Cut
Since the force is applied for 2 seconds, we can find the velocity of the system just before the string is cut. The velocity (v) after a time (t) under constant acceleration is given by:
v = a * t
Substituting the expression for acceleration:
v = (F / 10 kg) * 2 s
After the String is Cut
After 2 seconds, when the string is cut, Mass B (the heavier mass) will continue to move with the velocity it had just before the string was cut. We know that after an additional 2 seconds, the velocity of Mass B is 2 m/s. This means that the velocity of Mass B remains constant after the string is cut, as no external force is acting on it.
Finding the Initial Velocity
Since Mass B has a final velocity of 2 m/s after the string is cut, we can use this information to find the initial velocity just before the string was cut. The velocity of Mass B just before the cut must also be 2 m/s, as it continues at that speed:
v = (F / 10 kg) * 2 s = 2 m/s
Now, we can rearrange this equation to solve for the force F:
F = 2 m/s * 10 kg / 2 s
F = 10 N
Final Result
The force initially applied to the lighter body (Mass A) is 10 Newtons. This force caused both masses to accelerate together until the string was cut, after which Mass B continued to move at the velocity it had just before the cut.
