Points to remember in physics - Part 13

Points to remember in physics - Part 13

1. Carbon 12 scale ❓

The Carbon-12 scale, also known as the unified atomic mass unit (u), is a standard unit of mass that is used in chemistry and physics to express the mass of atoms and molecules. It is defined as one-twelfth of the mass of a neutral atom of carbon-12, which has six protons and six neutrons in its nucleus.

By definition, one u is equal to 1/12th of the mass of a carbon-12 atom, which is approximately 1.66054 x 10^-27 kilograms. The Carbon-12 scale allows scientists to compare the masses of different atoms and molecules on a relative scale, where the mass of a single hydrogen atom is approximately 1.0078 u.

The Carbon-12 scale is widely used in nuclear physics, particle physics, and chemistry, and it is useful in calculating the masses of complex molecules and isotopes.

2. Pyroelectricity❓

Pyroelectricity is the ability of certain materials to generate an electric charge in response to a change in temperature. 

When a pyroelectric material is heated or cooled, its crystal structure changes, producing a net electric polarization in the material. This polarization creates an electric field, which can be measured and used for various applications.

Pyroelectricity is different from the better-known phenomenon of piezoelectricity, which is the ability of certain materials to generate an electric charge in response to mechanical stress or pressure.

Pyroelectric materials can be used in various applications, such as temperature sensors, motion detectors, and infrared detectors. In pyroelectric sensors, a pyroelectric material is used to detect changes in temperature, which can be used to detect the presence of a person or animal, for example. 

Pyroelectric materials can also be used in energy harvesting, where the temperature difference between two materials is used to generate electricity.

3. The speed of the projectile is minimum at its highest position✔️

When a projectile is launched into the air, it follows a curved path known as a trajectory. This trajectory can be described as an upward motion followed by a downward motion due to the force of gravity acting on the projectile.

At the highest point of the trajectory, often referred to as the apex or highest position, the speed of the projectile is at its minimum. This occurs because the projectile is momentarily at rest before changing direction and starting its descent.

As the projectile rises, its initial upward velocity gradually decreases due to the opposing force of gravity. Eventually, the upward velocity becomes zero at the highest point, resulting in a momentary pause in the projectile's motion. At this moment, the speed is at its minimum value.

After reaching the highest position, the projectile starts descending due to the continued influence of gravity. As it descends, the speed gradually increases, reaching its maximum value when the projectile reaches its lowest point in the trajectory. This is because the force of gravity accelerates the projectile downwards, increasing its speed as it falls.

It's important to note that the minimum speed at the highest position applies to projectiles under the influence of only gravity, assuming no other external forces such as air resistance are significant.

4. The normal acceleration of the projectile at its highest position is equal to g.✔️

At the highest position of a projectile's trajectory, the normal acceleration, which is the acceleration perpendicular to the path of motion, is equal to the acceleration due to gravity (represented as 'g'). This relationship holds true when considering the projectile in the absence of other external forces such as air resistance.

The normal acceleration at any point on the trajectory of a projectile can be determined by analyzing the forces acting on it. In the case of a projectile at its highest position, only the force of gravity acts upon it. The force of gravity always acts vertically downwards, perpendicular to the trajectory.

According to Newton's second law of motion, the net force acting on an object is equal to the product of its mass and acceleration. In this case, the mass of the projectile remains constant, so the net force is solely determined by the force of gravity. The force of gravity is given by the equation F = mg, where 'm' represents the mass of the projectile and 'g' represents the acceleration due to gravity.

Since the force of gravity is the only force acting on the projectile at its highest position, it is also the net force. Thus, the net force is equal to F = mg. Since the normal force, which is perpendicular to the trajectory, balances the force of gravity at the highest position, it must be equal in magnitude but opposite in direction.

Therefore, the normal force is also given by F = mg. By applying Newton's second law once again, dividing the net force by the mass of the projectile, we find that the acceleration due to gravity is equal to the normal acceleration at the highest position, which is g.

5. The greatest height to which a man can throw a stone is H. The greatest distance up to which he can throw the stone is H/2.✔️

The greatest distance a projectile can travel is achieved when it is launched at an angle of 45 degrees with respect to the horizontal. At this angle, the range (the horizontal distance covered) is maximized for a given initial velocity.

If a man throws a stone at an angle other than 45 degrees, the maximum distance he can achieve will be less than half of the maximum height. The height and distance achieved by a projectile depend on various factors, including the initial velocity, launch angle, and the acceleration due to gravity. However, it's important to note that the relationship between the maximum height and maximum distance is not simply H and H/2.

To determine the specific relationship between the maximum height and maximum distance achieved by a projectile, additional information about the launch conditions, such as the initial velocity and launch angle, would be required

6. The weight of a body in projectile motion is zero.❌

The weight of a body in projectile motion is not zero. Weight is the force exerted on an object due to gravity and is equal to the product of the mass of the object and the acceleration due to gravity (W = mg).

In projectile motion, an object is subject to two main forces: the force of gravity and any initial velocity imparted to it. These forces act independently of each other. The force of gravity acts vertically downward, pulling the object towards the Earth, while the initial velocity determines the object's horizontal and vertical motion.

The weight of the object remains constant throughout the projectile motion. It is always present and directed vertically downward, regardless of the object's position or velocity during its trajectory. The vertical component of the object's velocity may change due to the effect of gravity, but the weight itself remains the same.

It's important to note that while the weight remains constant, the apparent weight or the normal force experienced by the object may vary in different parts of the trajectory. For example, at the highest point of the trajectory, the object's vertical velocity is momentarily zero, and the normal force equals the weight. In other parts of the trajectory, the normal force may be different from the weight due to the object's acceleration or other external forces at play.

7. The instantaneous velocity of a particle is always tangential to the trajectory of the particle.✔️

In the context of particle motion, the instantaneous velocity of a particle is always tangential to the trajectory of the particle.

Velocity is a vector quantity that describes both the speed and direction of motion. When a particle moves along a curved path, its velocity vector is constantly changing in magnitude and direction. At any given point along the trajectory, the instantaneous velocity vector represents the velocity of the particle at that precise moment.

The tangent to the trajectory at a specific point represents the direction of motion at that point. The instantaneous velocity vector is always directed along this tangent line, perpendicular to the radius of curvature at that point. This means that the instantaneous velocity vector is tangential to the trajectory, indicating the direction in which the particle is moving at that moment.

The magnitude of the instantaneous velocity vector represents the speed of the particle at that point. It indicates how fast the particle is moving along the trajectory.

8. The instantaneous magnitude of velocity is equal to the slope of the tangent drawn at the trajectory of the particle at that instant.✔️

The instantaneous magnitude of velocity is equal to the slope of the tangent drawn at the trajectory of the particle at that instant.

When a particle moves along a curved path, its velocity is constantly changing. The magnitude of the velocity vector represents the speed of the particle, while the direction of the velocity vector indicates the direction of motion.

The tangent line to the trajectory of the particle at a specific point represents the instantaneous direction of motion at that instant. The slope of this tangent line represents the rate of change of the position of the particle with respect to time at that point.

The instantaneous magnitude of velocity is determined by taking the derivative of the position vector with respect to time. Mathematically, this is represented as v = dS/dt, where v is the velocity vector, S is the position vector, and dt represents an infinitesimally small change in time.

Taking the derivative of the position vector with respect to time yields the velocity vector. The magnitude of this velocity vector is equal to the instantaneous speed of the particle. Moreover, the slope of the tangent line drawn at the trajectory of the particle at that instant is equal to this magnitude of velocity.

Therefore, the instantaneous magnitude of velocity is indeed equal to the slope of the tangent drawn at the trajectory of the particle at that instant. It represents the rate of change of the position of the particle with respect to time at that point.

9. The direction of acceleration of a moving particle may be directly obtained from the trajectory of the particle.❌

No, the direction of acceleration of a moving particle cannot be directly obtained from the trajectory of the particle alone. The trajectory of a particle provides information about its position and path of motion but does not directly reveal the direction of its acceleration.

Acceleration is the rate of change of velocity and is a vector quantity. It includes both the magnitude and direction of the change in velocity. The direction of acceleration is determined by the net force acting on the particle and is not solely dependent on the trajectory.

The acceleration of a particle can be influenced by various factors, including applied forces, friction, gravity, and other external influences. These factors can affect the direction of the acceleration independently of the particle's trajectory.

To determine the direction of acceleration, additional information is needed, such as the forces acting on the particle or the specific conditions of the motion. Newton's second law of motion, F = ma, relates the net force acting on an object to its acceleration, where F represents the net force, m is the mass of the particle, and a is the acceleration

10. The time of flight of a projectile does depend on the angles of projection ✔️

I apologize for my previous response. The time of flight of a projectile does actually depend on the angle of projection. 

The time of flight is the total time that a projectile is in the air. This time is influenced by the initial velocity of the projectile and the angle at which it was launched. When a projectile is launched at an angle, its initial velocity can be broken down into horizontal and vertical components. The vertical component determines the time it takes for the projectile to reach its maximum height, while the horizontal component determines the distance the projectile travels before hitting the ground. 

Therefore, the time of flight will be different for different angles of projection, since the vertical and horizontal components of the initial velocity will change.

11. The acceleration of a particle moving in a circular path with constant speed is zero.✔️

A particle moving in a circular path with constant speed has an acceleration with magnitude ac = v²/r. The direction of the acceleration vector is toward the center of the circle. This is a radial acceleration and is called the centripetal acceleration. 

The tangential acceleration is zero because the speed is constant.

12. Tangential acceleration and centripetal acceleration 

The rate of change speed of the particle in the circular path is known as tangential acceleration. It is equal to the product of angular acceleration (α) and the radius (r) of the circular path. i.e (a_t=rα).

Formula of centripetal acceleration and tangential acceleration:

(i) We can find tangential acceleration with the help of the tangential acceleration formula, which is given as:

a_t=dv/dt

 or a_t=rα

(ii) And, we can find centripetal acceleration with the help of the centripetal acceleration formula, which is given as:

a_c=v²/r

Direction of the tangential acceleration

Ans: A tangential acceleration works in the direction of a tangent at the point of circular motion. Its direction is always in the perpendicular direction to the centripetal acceleration of a rotating object.

Causes: tangential acceleration

Ans: The tangential force component will create tangential acceleration, which will cause the object to accelerate along the tangent. Then, the object will undergo non-uniform circular motion as both the direction and magnitude of the velocity of the object changes.

Centripetal acceleration

Centripetal acceleration can be defined as the component of acceleration in the radial direction (towards the centre).

Difference between centripetal and tangential acceleration

Tangential acceleration is in the direction of the tangent to the circle, whereas centripetal acceleration is in the radial direction of the circle pointing inwards to the centre.

Example of both centripetal and tangential acceleration: 

Suppose you are holding a thread to the end of which is tied to a stone. Now when you start whirling it around, you will notice that two forces have to be applied simultaneously. 

One which pulls the thread inwards and the other which throws it sideways or tangentially. Both these forces will generate their respective accelerations. The one-pointed inwards will generate centripetal or radial acceleration, and the one pointing sideways will generate tangential acceleration.

13. Tangential acceleration changes the speed of the particle whereas the normal acceleration changes its direction.✔️

The tangential acceleration is the component of acceleration tangent to the circle and perpendicular to the radial acceleration. It changes the speed of the particle. 

The normal acceleration is the component of acceleration perpendicular to the circle and tangent to the radial acceleration. It changes the direction of the particle.

14. We cannot have an isolated force.✔️

It's true that a truly isolated force is not possible in the physical world. Any force that acts on an object will also be affected by that object in some way, according to Newton's Third Law of Motion. 

For example, if you push on a wall, the wall pushes back on you with an equal and opposite force. This means that any force that exists must have some kind of interaction with its surroundings.

15. Reaction follows the action.❌

According to Newton's third Law, the statement "Reaction follows the action" aligns with Newton's third law of motion. Newton's third law states that "For every action, there is an equal and opposite reaction."

In the context of physics, this law implies that whenever an object exerts a force on another object, the second object exerts an equal and opposite force back on the first object. These forces are referred to as action and reaction forces. 

The action force and the reaction force act on different objects, and they are equal in magnitude and opposite in direction. 

Newton's third law demonstrates the fundamental principle of action and reaction in physical interactions. *It emphasizes that forces don't exist in isolation but rather always occur in pairs*, with one force corresponding to the action and the other to the reaction.

Reaction doesn't follow the action. It appears together on two different objects. 

16. Mass of a body is a measure of its inertia.✔️

Inertia refers to the tendency of an object to resist changes in its state of motion. The greater the mass of an object, the greater its inertia and resistance to changes in motion.

Mass can be thought of as a measure of the amount of matter contained in an object. The more matter an object possesses, the more inertia it has. This means that objects with larger masses require more force to accelerate or decelerate compared to objects with smaller masses.