Alex Newton Chapter 8 Summary Recitation 04

Alex Newton Chapter 8 Summary Recitation 04

Alex Newton Chapter 8 Summary Recitation # 4 Linear Motion is a product of specific systems mass and its velocity. Linear momentum is a vector quantity. Linear motion acts in the same direction as the velocity direction of a body. Several principles have been made to explain the theory behind linear motion. This chapter looks at these set principles which govern bodies in momentum.

From Newton's second law of momentum, “The net exterior force is the same as the change in momentum of a system over the time over which it changes.” The relationship between force and momentum exists if and only if mass remains constant. Impulse is an integral of force over an interval of time for which it acts. Since force is a vector quantity, then impulse is a vector quantity acting in the direction of the force. Impulse has a standard unit of measurement, usually newton second.

Any resultant force causes acceleration, leading to a change in the velocity of a body. The extent of this change depends on the duration of force application and the magnitude of the force exerted. A larger force results in a greater change in linear motion. Momentum can be conserved, based on Newton’s law, which states “action and reaction forces are equal and opposite.” This law demonstrates that, in every interaction, force exists as a pair of opposed forces.

For forces acting against each other to balance, the forces must be equal in magnitude. The law of momentum conservation states that for colliding bodies, the total momentum before collision equals the total after collision. This means that the momentum lost by one body is gained by the other. An elastic impact occurs when bodies collide and the total dynamic energy is conserved. Dynamic energy is the work needed to accelerate a body from rest to a certain velocity.

A body’s energy at rest is potential energy, which implies that the energy during a collision remains unchanged in that form. However, in practice, total kinetic energy is not always conserved because some energy converts into heat or noise during impact. During an elastic collision, some energy is transformed; yet, the total kinetic energy remains constant, and the bodies rebound without lasting deformation. In inelastic collisions, part of the internal kinetic energy is lost, causing the objects to stick together or deform, reducing the system's kinetic energy.

This energy loss occurs when colliding bodies deform or generate heat, which results in a less elastic interaction. Collisions can also happen in two dimensions; for example, a moving body collides with a stationary one, and after impact, the moving body slows down, losing kinetic energy in the process. The energy lost appears as heat, deformation, or sound. Rocket propulsion is based on Newton’s third law, which states that for every action, there is an equal and opposite reaction. The rocket engine expels hot gases downward at high velocity, creating an upward thrust that propels the rocket.

The acceleration of a rocket depends on the rate of change of its exhaust velocity and the mass flow rate. The engine’s hot gases are expelled at high speed, producing a reactive force that pushes the rocket upward. The principle shows that the faster the gases are expelled, and the lighter the rocket becomes, the greater the acceleration. When the rocket burns fuel rapidly, it accelerates quickly because of the increased thrust, and when its mass decreases, the same force produces a higher acceleration.

Thrust increases as the rocket sheds mass through exhaust gases, and the acceleration is further affected by gravitational pull. As the rocket’s mass reduces, less gravitational pull acts upon it, allowing for higher acceleration. The change in velocity of the rocket depends on the exhaust velocity and the mass ratio of the rocket before and after burning fuel, illustrating the importance of mass expulsion in propulsion. The physical principle behind rocket motion exemplifies Newton’s third law effectively: the expelled gases exert an equal and opposite force on the rocket, resulting in forward movement. This process demonstrates the conservation of momentum at a system level, where the momentum of expelled gases is equal and opposite to the momentum gained by the rocket itself.

Paper For Above instruction

In this comprehensive discussion of linear motion based on Newtonian principles, the core concepts revolve around how momentum, force, energy, and reactions govern the movement of bodies. The discussion begins with the fundamental notion that linear momentum, as a vector quantity, is directly related to a body's mass and velocity, and that this momentum acts in the same direction as the body's motion. Newton’s second law of momentum emphasizes that the net external force causes a change in momentum proportional to the force applied over a period, assuming mass remains constant. The concept of impulse, defined as force integrated over time, further clarifies how forces influence the body's motion in both magnitude and direction, given that force and impulse are vector quantities, with units measured in newton seconds. When a force acts on a body, it causes acceleration—depending on the magnitude of that force and the duration of its application—leading to a change in the velocity of the object, which underlines Newton’s law that larger forces induce greater accelerations. The principle of conservation of momentum states that, in isolated systems, the momentum before and after any collision remains unchanged, provided energy is conserved in elastic impacts, where total kinetic energy is maintained. These impacts involve bodies rebounding without permanent deformation, with energy transforming primarily into kinetic energy during separation. Conversely, in inelastic collisions, some kinetic energy is transformed into heat, sound, or deformation, reducing the internal kinetic energy after impact, and in some cases, objects may stick together, indicating complete inelasticity. Collisions occurring in two dimensions demonstrate similar principles, with loss of kinetic energy and changes in velocity depending on collision parameters. Rocket propulsion exemplifies Newton's third law, illustrating the principle of action and reaction: as gases are expelled downward at high velocities, the rocket receives an equal and opposite force propelling it upward. The acceleration of the rocket depends on the rate of fuel consumption and the velocity of expelled gases. The faster the gases are expelled, the greater the thrust, especially as the rocket's mass decreases, resulting in increased acceleration due to the shorter duration of gravitational influence and increased reactive force. Overall, these physical laws and principles—momentum conservation, energy transformation, and reaction forces—are integral to understanding the dynamics of motion in many systems, from simple collisions to complex rocket propulsion systems, illustrating the fundamental interconnectedness of force, energy, and motion in classical physics.

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