Second Law: Motion under Same Force

Draw a free-body diagram for each mass separately, then apply Newton's second law to find the system's acceleration. Calculate the net force on each mass using only horizontal components. The contact force between the masses equals the net force on the individual mass, and by Newton's third law, these forces are equal and opposite on each mass.

A free-body diagram isolates each object and shows all forces acting on it. For accelerating bodies, identify force directions and magnitudes, then resolve them into x and y components. This visual representation allows you to apply Newton's second law systematically to find acceleration and unknown forces like contact forces between objects.

When an elevator accelerates upward, the scale must push up with a force greater than the person's weight to accelerate them upward. The scale reading reflects this increased normal force, which equals the person's weight plus the additional force needed for upward acceleration. Greater elevator acceleration produces a greater scale reading.

During downward acceleration, gravity and the acceleration force both act downward, reducing the normal force the scale must exert. The scale reading becomes less than the person's weight. At constant downward velocity, acceleration is zero, so the scale reading returns to the person's weight.

Newton's first law applies to bodies in equilibrium where net force is zero. Newton's second law applies to accelerating bodies where net force is not zero. For accelerating bodies, determine force directions and magnitudes, construct a free-body diagram, and apply the second law considering force components in x and y directions.

During free fall, the elevator accelerates downward at g, the acceleration due to gravity. The scale reading becomes zero because no normal force is needed—gravity alone provides all the acceleration. The person experiences weightlessness since there is no contact force between them and the scale.

Contact forces between two masses follow Newton's third law: for every action, there is an equal and opposite reaction. When mass mA pushes on mass mB through contact, mass mB exerts an equal force back on mass mA in the opposite direction. These paired forces maintain the same magnitude regardless of the masses' individual accelerations.