A force of magnitude 7.50 N pushes three boxes with masses m1=1.30 kg, m2=3.20 kg, and m3=4.90 k

step 1 So problem 22 says a force of magnitude 7 .5 newtons pushes on three boxes with masses, 1 .3 kil

A force of magnitude 7.50 N pushes three boxes with masses...

A force of magnitude 7.50 $\mathrm{N}$ pushes three boxes with masses $m_{1}=1.30 \mathrm{kg}, m_{2}=3.20 \mathrm{kg},$ and $m_{3}=4.90 \mathrm{kg},$ as shown in FIGURE 5-29. Find the magnitude of the contact force (a) between boxes 1 and $2,$ and $($ b) between boxes 2 and $3 .$

Key Concepts

Free-Body Diagrams

Free-body diagrams are visual tools that depict all the forces acting on an individual object. They are crucial for understanding the dynamics of each object within a system, as they help in systematically identifying and resolving the forces, including those at the contact points between objects.

Contact Forces

In scenarios where objects are in contact, contact forces develop at the interfaces between them as a result of the external force applied to the system. These forces ensure that the objects accelerate together and can be determined by analyzing the interactions between specific pairs of masses using Newton's Second Law.

System Acceleration

When multiple objects are in contact and move together due to an applied force, they share a common acceleration. By considering the entire collection as a single system, one can calculate the acceleration from the net external force and then use it to analyze the forces transmitted between individual objects.

Newton's Second Law

Newton's Second Law states that the net force acting on an object is equal to the product of its mass and its acceleration. This principle is fundamental for analyzing forces in dynamics problems, as it allows us to set up equations for each object once a system's acceleration is known.

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