Understanding Newton's Laws in Block Contact Problems: Why the Force Isn't Always 100 N

In this article, we will explore a common physics problem involving two blocks placed in contact on a smooth horizontal surface. The key point to discuss is why the magnitude of the force that the 2 kg block exerts on the 3 kg block is not 100 N, even though a 100 N force is applied to the 2 kg block. We will use Newton's laws of motion to analyze this situation step-by-step.

Given Conditions

Mass of block 1 ((m_1)): 2 kg Mass of block 2 ((m_2)): 3 kg Applied force ((F)): 100 N

Analysis of the Situation

Total Mass and Acceleration:

When the 100 N force is applied to the 2 kg block, both blocks will accelerate together as a single system. The total mass ((M)) of the system is:

[M m_1 m_2 2 text{kg} 3 text{kg} 5 text{kg}]

The acceleration ((a)) of the system can be calculated using Newton's second law:

[F Ma Rightarrow a frac{F}{M} frac{100 text{N}}{5 text{kg}} 20 text{m/s}^2]

Thus, the acceleration of the system (both blocks) is 20 m/s2.

Force Exerted by Block 1 on Block 2

Now, consider the forces acting on the 3 kg block (block 2). The only horizontal force acting on block 2 is the contact force exerted by the 2 kg block. To find the force that the 2 kg block exerts on the 3 kg block, we apply Newton's second law to the 3 kg block:

[F_{text{contact}} m_2 cdot a 3 text{kg} cdot 20 text{m/s}^2 60 text{N}]

Therefore, the force that the 2 kg block exerts on the 3 kg block is 60 N. This is the amount of force needed to accelerate the 3 kg block at the same acceleration of 20 m/s2. The remaining force (100 N - 60 N 40 N) is the net force that accelerates the 2 kg block itself.

Conclusion

In summary, the force that the 2 kg block exerts on the 3 kg block is not 100 N, but 60 N. This is because both blocks accelerate together as a single system, and the force needed to accelerate the 3 kg block is 60 N, which is provided by the contact force from the 2 kg block. The 40 N of the applied force is used to accelerate the 2 kg block.

Key Takeaways:

The total mass accelerated is 5 kg. The acceleration of both blocks is 20 m/s2. The net force on the 3 kg block is 60 N, which is the force of the 2 kg block on the 3 kg block by Newton's third law. Check: The net force on the 2 kg block is 40 N, leading to the same acceleration as the 3 kg block (20 m/s2).

This problem illustrates how the application of forces and Newton's laws can help us understand complex motion scenarios involving multiple objects in contact. The key insight is that the force exerted between two objects in contact is not always equal to the applied force, but rather determined by the mass distribution and the overall acceleration of the system.