Conservation Laws in Physics – Definitions, Applications, Examples
Conservation laws are fundamental principles of physics that state that certain physical quantities remain constant in a system, even as the system evolves or undergoes transformations. In other words, these laws describe how some properties of a system cannot be created or destroyed, only transferred from one form to another.
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There are several conservation laws in physics, including:
Conservation of Energy:
The law of conservation of energy states that the total energy in a closed system remains constant. Energy can neither be created nor destroyed; it can only be converted from one form to another. This law is essential in the study of mechanics, thermodynamics, and electromagnetism.
Example: Consider a roller coaster at the top of a hill. At this point, the roller coaster has potential energy due to its height. As the roller coaster descends down the hill, the potential energy is converted into kinetic energy. The total energy in the system (potential energy + kinetic energy) remains constant throughout the ride, obeying the law of conservation of energy.
Conservation of Momentum:
The law of conservation of momentum states that the total momentum of a closed system remains constant. Momentum is the product of an object’s mass and velocity, and it is a measure of its motion. This law is critical in the study of mechanics, especially in the areas of collisions and explosions.
Example: Suppose two objects of equal mass are moving towards each other at the same speed. When they collide, they will exert equal and opposite forces on each other, causing their momenta to change. However, the total momentum of the system (the sum of the momenta of the two objects) will remain constant.
Conservation of Angular Momentum:
The law of conservation of angular momentum states that the total angular momentum of a closed system remains constant. Angular momentum is a measure of an object’s rotational motion, and it is the product of its moment of inertia and angular velocity. This law is important in the study of rotational mechanics.
Example: Consider an ice skater spinning on the ice with arms outstretched. As the skater brings their arms inwards, their moment of inertia decreases, causing an increase in their angular velocity. However, the total angular momentum of the system (the product of the moment of inertia and angular velocity) remains constant.
Conservation of Charge:
The law of conservation of charge states that the total electric charge in a closed system remains constant. This law is fundamental in the study of electromagnetism and is closely related to the principle of charge conservation.
Example: Consider a simple circuit with a battery, a switch, and a light bulb. When the switch is closed, a current flows through the circuit, causing the light bulb to glow. The flow of current is due to the movement of electric charges, and the total charge in the system remains constant.
Conservation of Mass:
The law of conservation of mass states that the total mass in a closed system remains constant. This law is fundamental in the study of mechanics and thermodynamics and is closely related to the principle of mass conservation.
Example: Suppose a chemical reaction occurs between two substances, A and B, to form a new substance, C. The mass of substance C will be equal to the sum of the masses of substances A and B, and no mass will be created or destroyed during the reaction, in accordance with the law of conservation of mass.
These conservation laws play a crucial role in understanding the behavior of physical systems and predicting their future evolution. They provide a framework for describing the fundamental properties of matter and energy and are widely used in the development of theories and models in various branches of physics.
Problems Based on Conservation Laws in Physics
Q.1. A 500-kg roller coaster car is at the top of a hill that is 40 meters high. What is the car’s kinetic energy at the bottom of the hill? Assume no energy is lost due to friction.
Solution:
The potential energy of the roller coaster car at the top of the hill is given by: PE = mgh PE = 500 kg × 9.8 m/s² × 40 m PE = 196,000 J
Since no energy is lost due to friction, all of the potential energy is converted into kinetic energy at the bottom of the hill. Therefore, the kinetic energy of the car is also 196,000 J.
Q.2. Two cars, A and B, collide head-on. Car A has a mass of 1,000 kg and a velocity of 20 m/s, while car B has a mass of 1,500 kg and a velocity of -10 m/s. What is the final velocity of the two cars if they stick together after the collision?
Solution:
Using the law of conservation of momentum, we know that the total momentum of the system before and after the collision must be the same.
Therefore: Momentum before collision = Momentum after collision
The total momentum of the system before the collision is:
Pbefore = mA × vA + mB × vB
Pbefore = 1,000 kg × 20 m/s + 1,500 kg × (-10 m/s)
Pbefore = 5,000 kg·m/s
After the collision, the two cars stick together, so their masses are combined:
mAB = mA + mB mAB = 1,000 kg + 1,500 kg
mAB = 2,500 kg
The final velocity of the two cars is given by:
vfinal = Pbefore / mAB vfinal = 5,000 kg·m/s / 2,500 kg vfinal = 2 m/s
Therefore, the final velocity of the two cars after the collision is 2 m/s.
Q.3. An ice skater with a moment of inertia of 2 kg·m² is spinning at 3 rad/s with arms outstretched. What will be their new angular velocity if they bring their arms in to a position where their moment of inertia is 1 kg·m²?
Solution:
The initial angular momentum of the skater is given by:
Linitial = Iinitial × ωinitial Linitial = 2 kg·m² × 3 rad/s
Linitial = 6 kg·m²/s
When the skater brings their arms in, their moment of inertia decreases to 1 kg·m².
Therefore, their new angular velocity is given by:
Lfinal = Ifinal × ωfinal Lfinal = 6 kg·m²/s (since angular momentum is conserved)
Ifinal × ωfinal = 6 kg·m²/s 1 kg·m² × ωfinal = 6 kg·m²/s
ωfinal = 6 rad/s
Therefore, the new angular velocity of the skater is 6 rad/s.
