Points to remember in Physics Part 10

Points to remember in Physics Part 10

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

....This statement is true..... 

When a projectile is launched into the air, it follows a parabolic path. At the highest point of this path, the projectile momentarily stops moving in the vertical direction and starts to fall back down due to the force of gravity. At this point, the velocity of the projectile in the vertical direction is zero, which means that the speed of the projectile is also at its minimum. 

However, it's important to note that the horizontal speed of the projectile remains constant throughout its motion, assuming there are no external forces acting on it.

92. "The normal acceleration of the projectile at its highest position is equal to g"

.....The statement is true........ 

At the highest point of a projectile's motion, the only force acting on it is the force of gravity, which acts vertically downwards. This force can be resolved into two components: one in the vertical direction and one in the horizontal direction. The vertical component of the force is equal to the weight of the projectile, which is given by mg, where m is the mass of the projectile and g is the acceleration due to gravity.

The normal acceleration of the projectile is the acceleration perpendicular to its path of motion. At the highest point of its motion, the projectile changes direction and starts to move downwards. Therefore, the normal acceleration of the projectile is equal to the acceleration due to gravity, which is g.

Therefore, the statement "The normal acceleration of the projectile at its highest position is equal to g" is true.

93. The time of flight does not depend on the angles of projection. 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 first statement is false, while the second statement is true. 

For the first statement, the time of flight of a projectile depends on the angle of projection, as well as the initial speed of the projectile. The time of flight is maximum when the angle of projection is 45 degrees. At this angle, the projectile achieves the maximum range, which is the greatest distance travelled by the projectile before it hits the ground.

For the second statement, the maximum height and maximum distance of a projectile depends on its initial velocity and angle of projection. However, for a given initial velocity, the maximum height that a projectile can reach is achieved when it is projected vertically upwards. In this case, the initial velocity in the horizontal direction is zero, so all the initial velocity is converted into vertical velocity, which allows the projectile to reach the maximum height.

Similarly, the maximum range that a projectile can achieve is also dependent on its initial velocity and angle of projection. However, it can be shown that the maximum range is achieved when the angle of projection is 45 degrees. Therefore, the greatest distance up to which a man can throw the stone is H/2, where H is the greatest height to which he can throw the stone.

94. The weight of a body in projectile motion is zero.

.............

The weight of a body in projectile motion is not zero, it is constant throughout the motion. 

Weight is the force exerted by gravity on an object, and it is proportional to the mass of the object. In projectile motion, the force of gravity acts on the object and causes it to follow a parabolic path. 

At any point during the motion, the weight of the object can be calculated using the formula W=mg, where W is the weight, m is the mass of the object, and g is the acceleration due to gravity. The weight of the object is constant throughout the motion, and it acts vertically downwards.

It's important to note that the weight of an object is not the same as its mass. Mass is a measure of the amount of matter in an object, while weight is a measure of the force exerted on the object due to gravity.

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

..............

Instantaneous velocity is the velocity of an object at a specific instant in time, and it is a vector quantity that has both magnitude and direction. 

The trajectory of a particle is the path that it follows through space, and it is usually a curved path. At any point on the trajectory, the instantaneous velocity of the particle is tangential to the trajectory. This means that the direction of the velocity vector is parallel to the tangent line of the trajectory at that point.

The tangential direction is the direction in which the object is moving at that instant. The magnitude of the velocity vector represents the speed of the object at that instant. Therefore, the instantaneous velocity of a particle is always tangential to the trajectory of the particle.

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

.............

The slope of the tangent line to the trajectory of a particle at any point on the trajectory gives the rate of change of the position of the particle with respect to time, at that point. This rate of change of position is the derivative of the position of the particle with respect to time, which is equal to the instantaneous velocity of the particle.

Therefore, if we draw a tangent line to the trajectory of the particle at a particular point, the slope of this tangent line gives the instantaneous rate of change of position of the particle at that point, which is the instantaneous velocity of the particle. In other words, the magnitude of the instantaneous velocity of the particle is equal to the slope of the tangent line drawn at the trajectory of the particle at that instant.

This relationship is a consequence of the definition of velocity as the rate of change of position of an object with respect to time, and the geometrical definition of the tangent line as the limit of the secant lines that pass through a point on a curve.

97. Misconception: The direction of acceleration of a moving particle may be directly obtained from the trajectory of the particle.

..............

False. The direction of acceleration of a moving particle cannot be directly obtained from the trajectory of the particle alone. While the trajectory of a particle can provide information about the position and velocity of the particle over time, the acceleration of the particle depends on how its velocity changes over time. 

In other words, acceleration is the rate of change of velocity, and it is determined by considering the time rate of change of the particle's velocity vector.

To determine the direction of acceleration of a particle, one would need to analyze the changes in the particle's velocity vector over time, which requires additional information beyond the trajectory. For example, one would need to know the particle's velocity at different points in time and how it changes as the particle moves. This information can be obtained by measuring the particle's motion using appropriate experimental techniques or by using mathematical models to simulate the particle's behavior.

98. Misconception: The acceleration of a particle moving in a circular path with constant speed is zero.

.............

The acceleration of a particle moving in a circular path with constant speed is not zero. 

Although the particle's speed remains constant, its direction of motion is changing continuously, which means that its velocity vector is changing. 

Therefore, there must be an acceleration acting on the particle to produce this change in velocity vector.

The acceleration of a particle moving in a circular path with constant speed is called centripetal acceleration, and it is always directed towards the center of the circle. 

The magnitude of the centripetal acceleration is given by a = v²/r, where v is the speed of the particle and r is the radius of the circle. 

This equation shows that the magnitude of the centripetal acceleration is proportional to the square of the particle's speed and inversely proportional to the radius of the circle.

Therefore, even if the speed of the particle is constant, the magnitude of the centripetal acceleration is not zero as long as the particle is moving in a circular path. 

The direction of the centripetal acceleration is always towards the center of the circle, and it is responsible for keeping the particle moving in its circular path.

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

..................

This statement is true.

Tangential acceleration is the component of acceleration that is parallel to the direction of motion of a particle. It causes a change in the magnitude of the particle's velocity vector, or in other words, it changes the speed of the particle. 

This type of acceleration can be either positive or negative, depending on whether the speed of the particle is increasing or decreasing.

On the other hand, normal acceleration is the component of acceleration that is perpendicular to the direction of motion of a particle. It causes a change in the direction of the particle's velocity vector, but not in its magnitude. This type of acceleration is responsible for the curvature of the particle's path and is often associated with circular motion. The direction of the normal acceleration is always perpendicular to the tangent of the particle's path, and it is directed towards the center of curvature.

Therefore, tangential acceleration changes the speed of the particle, while normal acceleration changes its direction. In many cases, both types of acceleration are present, and they work together to produce the overall acceleration of the particle.

100. The path length or distance traveled by particles can never decrease with time

The path length or distance traveled by a particle is a scalar quantity that can only increase or remain constant with time. It cannot decrease because the particle cannot "untravel" a distance that it has already covered.

For example, if a particle moves along a straight line for 10 meters and then turns back and moves in the opposite direction for 5 meters, the total distance traveled by the particle will be 15 meters. Even if the particle turns back again and moves in the original direction, it cannot reduce the total distance traveled to less than 15 meters. Therefore, the path length or distance traveled by a particle can never decrease with time.