Newton's Law of Motion - First, Second & Third - Physics

Newton's First Law states that an object at rest will remain at rest unless an unbalanced force acts upon it. This is demonstrated with a box on a surface: the weight force (mass times gravity) pulling it down is balanced by the normal force pushing it up, resulting in a net force of zero, so the box stays still. An unbalanced force is required to initiate movement.

The second part of Newton's First Law, also known as the law of inertia, states that an object in motion will continue in motion with constant velocity unless acted upon by a net force. Examples include a ball rolling on a carpet (stops due to friction) versus a puck on ice (moves longer due to less friction), and the Earth orbiting the Sun in space (virtually no friction, so it continues to move).

Key takeaways for problem-solving: if an object is at rest or moving with constant velocity, the net force acting on it is zero. This also means the acceleration is zero, as acceleration is the change in velocity over time. If the net force is not zero, there is acceleration.

Newton's Second Law is articulated as net force being equal to the product of mass and acceleration (F = ma). This relationship shows that force is directly proportional to mass and acceleration. If mass is constant and acceleration increases, force increases. If force is constant, increasing mass decreases acceleration, and vice versa. Numerical examples illustrate these proportionalities.

The Second Law can also be expressed in terms of momentum (p = mv), where momentum is mass in motion. The net force is equal to the rate of change of momentum over time (F = Δp/Δt). The impulse-momentum theorem states that the force multiplied by the change in time (impulse) equals the change in momentum (FΔt = Δp).

Newton's Third Law states that for every action, there is an equal and opposite reaction (F_A = -F_B). This means forces come in pairs of equal magnitude and opposite direction. Examples include a person throwing a basketball (the person recoils in the opposite direction) and a person on a boat throwing a ball (the boat moves in the opposite direction).

An astronaut in space can use Newton's Third Law to maneuver. By throwing an object in one direction, the astronaut will be propelled in the opposite direction. This is a practical application for returning to Earth or moving towards other celestial bodies, as there is minimal friction in space to slow down the acquired velocity.

A car traveling with constant velocity has a horizontal net force of zero and an acceleration of zero. If the frictional force is 1500 Newtons, the applied force from the engine must also be 1500 Newtons to maintain a net force of zero and constant velocity.

A 200 Newton force on a 10 kg box on a frictionless surface results in an acceleration of 20 m/s². Starting from rest, after 8 seconds, the final speed will be 160 m/s. It will take 25 seconds to reach a speed of 500 m/s.

For a 20 kg box with a 300 Newton applied force and 200 Newton frictional force, the net horizontal force is 100 Newtons. This results in an acceleration of 5 m/s². Starting from rest, the box will travel 360 meters in 12 seconds.

An 8 kg object speeding up from 20 m/s to 50 m/s in 6 seconds has an acceleration of 5 m/s². The net horizontal force acting on the object is 40 Newtons. If the frictional force is 35 Newtons, the applied force must be 75 Newtons to achieve this net force.

An 80 kg astronaut throws a 2 kg package with an acceleration of 4 m/s². The force exerted on the package is 8 Newtons. By Newton's Third Law, the package exerts an equal and opposite force of -8 Newtons on the astronaut, causing the astronaut to accelerate at -0.1 m/s².

A 120 kg skater pushes an 80 kg skater, giving the lighter skater an acceleration of 1.5 m/s². Using Newton's Third Law (F = ma) for both skaters, the acceleration of the 120 kg skater is -1 m/s². The force exerted on each skater is 120 Newtons, equal in magnitude but opposite in direction.

A quick review of Newton's laws: First Law (Inertia): objects at rest stay at rest, objects in motion stay in motion unless acted upon by a net force. Constant velocity means zero net force and zero acceleration. Second Law (F=ma): net force equals mass times acceleration; heavier objects have smaller accelerations for a given force. Third Law (Action-Reaction): for every action, there is an equal and opposite reaction force (M1A1 = -M2A2).