Classical Mechanics : Newton's Laws of Motion

Michael Kurniawan 1910403011 University of Cincinnati Newton's laws of motion 1. What is Newton's First Law of Motion? Newton's First Law of Motion is often referred to as the law of inertia. It states that an object will remain at rest or in uniform motion in a straight line unless acted upon by an external force. Essentially, objects resist changes in their state of motion. This law helps to explain why objects tend to maintain their current state, whether it's motionless or moving at a constant velocity. 2. How is Newton's First Law of Motion mathematically expressed? ∑ F=0 Here, ∑ F represents the vector sum of all the forces acting on an object, and the equation states that this sum is equal to zero when the object is in equilibrium. In simpler terms, if the net force acting on an object is zero, the object will remain at rest or continue moving at a constant velocity. 3. Provide examples from everyday life that illustrate the application of Newton's First Law of Motion. a. When a soccer ball is kicked across a field, it eventually comes to a stop due to friction and air resistance. Without these external forces, the ball would continue moving at a constant velocity indefinitely. b. If you slide a book along a table and then stop pushing it, the book eventually comes to a stop because of the force of friction between the book and the table. Without this frictional force, the book would continue sliding indefinitely. c. When riding in a car and the driver suddenly applies the brakes, passengers lurch forward. This reaction occurs because the passengers were moving with the car, and when the car decelerates, their bodies tend to continue moving forward due to inertia until acted upon by the seatbelt or another external force. 4. What is Newton's Second Law of Motion? Newton's Second Law of Motion states that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. Mathematically, it can be expressed as: 𝐹=𝑚⋅𝑎 Where: • F is the net force acting on the object, • m is the mass of the object, • a is the acceleration of the object. 5. How is Newton's Second Law of Motion mathematically expressed? F = dp / dt Where: • F is the net force acting on the object, • p is the momentum of the object, • t is time. 6. Explain the relationship between force, mass, and acceleration according to Newton's Second Law of Motion. According to Newton's Second Law of Motion, the relationship between force, mass, and acceleration can be summarized as follows: a. If the mass of an object remains constant, an increase in the net force acting on it will result in a proportional increase in acceleration. b. If the net force acting on an object remains constant, acceleration is inversely proportional to the mass of the object. In other words, objects with greater mass experience less acceleration for the same force applied. This law explains how the motion of an object changes when subjected to external forces and provides a quantitative relationship between force, mass, and acceleration, allowing for precise predictions of motion under various conditions. 7. What is the acceleration of an object pulled by a force of 10 N and has a mass of 2 kg? To find the acceleration (a), we can use Newton's Second Law of Motion, which states 𝐹 = 𝑚𝑎 where F is the force applied, 𝑚 is the mass, and 𝑎 is the acceleration. Given that the force (F) is 10 N and the mass (m) is 2 kg, we can plug these values into the equation: 𝑎 = 𝐹/ 𝑚 𝑎 = 10 N / 2 kg 𝑎 = 5 m/s2 So, the acceleration of the object is 5 m/s2 8. Name the factors that affect the acceleration of an object according to Newton's Second Law of Motion. According to Newton's Second Law of Motion, the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. Therefore, the factors that affect the acceleration of an object are: a. The magnitude of the net force applied to the object: Increasing the force increases the acceleration, while decreasing the force decreases the acceleration. b. The mass of the object: Increasing the mass decreases the acceleration for a given force, while decreasing the mass increases the acceleration for a given force. 9. What is Newton's Third Law of Motion? Newton's Third Law of Motion states that for every action, there is an equal and opposite reaction. In other words, when one object exerts a force on a second object, the second object exerts a force of equal magnitude but in the opposite direction on the first object. This law highlights the reciprocal nature of forces and explains phenomena such as motion, interaction between objects, and the conservation of momentum. 10. Provide an example of the application of Newton's Third Law of Motion in everyday life. Newton's Third Law of Motion is observable in various aspects of daily life. One classic example is the propulsion of a boat. As the boat's engine exerts a backward force on the water (action), the water simultaneously exerts an equal and opposite forward force on the boat (reaction). This reaction force propels the boat forward through the water. Similarly, when you swim, your arms push backward against the water (action), and the water pushes forward on your arms (reaction), propelling you forward. 11. How does Newton's Third Law of Motion explain the reaction to action force? Newton's Third Law of Motion provides a fundamental principle that governs the interaction between objects. It asserts that forces always occur in pairs, with one force acting as the action and the other as the reaction. When an object applies a force on a second object, the second object simultaneously exerts an equal and opposite force on the first object. This principle ensures that momentum is conserved in interactions, as every action force results in an equal and opposite reaction force. In essence, it explains how forces arise from interactions between objects and how these forces are balanced. 12. What is a normal force and how does it relate to Newton's Third Law of Motion? A normal force is a contact force exerted by a surface to support an object resting on it. It acts perpendicular to the surface and prevents the object from passing through the surface. The normal force arises as a reaction force according to Newton's Third Law of Motion. For example, when you stand on the ground, the ground exerts an upward normal force on your feet to support your weight. This normal force is equal in magnitude and opposite in direction to the force exerted by your body on the ground due to gravity. Thus, the normal force is a manifestation of Newton's Third Law, ensuring that objects remain in equilibrium when resting on surfaces by providing the necessary support to counteract external forces. 13. A rocket propels gas backward. How does Newton's Third Law of Motion explain the motion of the rocket? Newton's Third Law of Motion states that for every action, there is an equal and opposite reaction. In the case of a rocket, the action is the expulsion of gas (exhaust) backward from the rocket engine. According to Newton's Third Law, there is an equal and opposite reaction, so the rocket experiences a forward force due to the expulsion of gas. This reaction force propels the rocket forward, following the principle of conservation of momentum. As the rocket expels gas backward, the gas exerts a force on the rocket, accelerating it forward in the opposite direction. 14. Explain why a car accelerates forward when its rear wheels push gas backward. When a car accelerates forward, its rear wheels push gas backward due to the combustion of fuel in the engine. According to Newton's Third Law of Motion, for every action, there is an equal and opposite reaction. So, as the rear wheels push gas backward (action), the gas exerts an equal and opposite force on the car in the forward direction (reaction). This reaction force propels the car forward, driving its acceleration. It's important to note that this process occurs because the car's engine converts the chemical energy of the fuel into kinetic energy, resulting in the expulsion of gas backward and the generation of forward propulsion force. 15. How are Newton's Laws of Motion used in calculating the dynamics of objects in the universe, such as planets and stars? Newton's Laws of Motion, particularly the Second Law (F = ma) and the Law of Universal Gravitation, are fundamental principles used to understand and calculate the dynamics of celestial objects in the universe. These laws describe the interactions between masses and the resulting motion. For example: a. Newton's Second Law allows us to calculate the gravitational force acting on a planet or star and determine its acceleration due to gravity. b. The Law of Universal Gravitation, combined with Newton's Second Law, enables us to predict the orbits of planets around the sun and moons around planets, as well as the motion of stars within galaxies. c. Newton's Third Law explains how celestial bodies exert gravitational forces on each other, resulting in the complex dynamics observed in the universe, such as planetary orbits, gravitational interactions between galaxies, and the formation of structures like star clusters and galaxies.