Points to remember in Physics Part 8

Points to remember in Physics - PART 8

71. Misconception: The net force in an inertial frame is zero.

In an inertial frame of reference, the net force on an object is not necessarily zero. 

According to Newton's second law of motion, the acceleration of an object is proportional to the net force acting on it, and inversely proportional to its mass. 

Therefore, if the net force on an object is zero, its acceleration will also be zero, which means that it will remain at rest or move with a constant velocity.

However, in an inertial frame of reference, the net force on an object is related to its motion according to the principle of inertia, which states that an object will remain in a state of rest or uniform motion in a straight line unless acted upon by an external force. 

Therefore, if an object is not subject to any external forces, it will move with a constant velocity in an inertial frame of reference.

72. The resistance of the human body is about 120 k-ohm.

It is true that under dry conditions, the resistance of the human body can be relatively high, around 100,000 ohms or more. 

This is because dry skin has a high resistance to electrical current. 

However, when the skin is moist, such as when a person sweats, the resistance of the skin decreases significantly, and the resistance of the body as a whole can be much lower, typically around 1,000 ohms or less.

It is important to note that electrical resistance is not a fixed value for the human body, and it can vary depending on a number of factors.

73. Misconceptions:

The following are the common misconceptions:

❌Distance is the magnitude of displacement.

✔️The magnitude of displacement is equal to the distance only if a particle moves along a straight line and does not reverse its motion. 

Otherwise, in general, 

Displacement ▪️is less than or equal to▪️ Distance

❌Average speed is equal to the magnitude of average velocity.

✔️The magnitude of average velocity ▪️is always less than or equal to▪️ the average speed. 

➖Illustrations

A particle moves along a semi-circular path of radius R from A to B  in a time T.

(i) Find the distance travelled by the particle.? 

(ii) Find the displacement of the particle.? 

(iii) Determine the average speed of the particle ? 

(iv) Determine the average velocity of the particle? 

➖Solution

The distance travelled is R

The displacement of the particle is 2R

The average speed of the particle is πR/T

(iv) The average velocity of the particle is

2R/T

74. What is meant by d ❘ v ❘ /dt  and  ❘ dv/dt ❘ ? 

▪️Can these be equal? 

▪️Can

1. d ❘ v ❘ /dt = 0 while ❘dv/dt ❘≉ 0

2. ❘ dv/dt ❘  ≉  0   while d ❘ v ❘ /dt = 0

🍁

Answer:

d ❘ v ❘ /dt means the time rate of change of speed, and

❘dv/dt❘ means the magnitude of acceleration.

These two can be equal in two situations:

1. when a particle moves with uniform velocity 2. when a particle moves with constant acceleration along a straight line.

Case 1:

d ❘ v ❘ /dt  = 0  ⇒ speed = constant 

❘ dv / dt ❘  ≉ 0 ⇒  ❘  acceleration ❘ ≉ 0

It happens only when a particle moves with constant speed along a circular path of constant radius.

Case 2:

❘ dv/dt  ❘  = 0 ⇒ ❘ acceleration ❘ = 0

d ❘ v ❘ / dt ≉ 0 ⇒ speed ≉ 0

For zero acceleration speed cannot change. Therefore, this case is not possible.

75. Misconception: Speed is constant when acceleration is not equal to zero

This statement is incorrect. Speed can remain constant even when acceleration is equal to zero. 

In fact, an object moving at a constant velocity has zero acceleration. 

Acceleration is the rate of change of velocity, so if the velocity is not changing, then the acceleration is zero. 

However, if the acceleration is not zero, the speed of the object can either increase or decrease.

76. Misconception: Acceleration is constant when speed is not zero 

This statement is also incorrect. 

▪️Acceleration can be constant even when the speed is zero. 

For example, consider an object that is at rest on a frictionless surface. If a constant force is applied to the object, it will experience a constant acceleration, but its speed will remain zero. 

▪️Conversely, an object can have a non-constant acceleration even when its speed is not zero. 

For example, when a car is driving on a road, it may experience changes in acceleration due to bumps, turns, or changes in the incline of the road, even if its speed remains constant.

77. Misconception: Magnitude of acceleration is constant when speed is not equal to zero 

This statement is not necessarily true. 

▪️The magnitude of acceleration can be constant or varying when the speed is not equal to zero, depending on the situation. 

For example, in uniform circular motion, the magnitude of acceleration is constant, but the speed of the object is not constant. Similarly, if an object is moving with a constant force acting on it, the magnitude of acceleration will be constant, but the speed of the object may increase or decrease depending on the direction of the force and the mass of the object. 

▪️On the other hand, if an object is moving on a surface with friction, the magnitude of acceleration may vary even when the speed is not zero, as the frictional force acting on the object will change with the speed of the object.

78. Slope of the x- t graph gives v - t graph.

If we have an x-t graph that represents the position of an object as a function of time, the slope of the graph at any point gives the velocity of the object at that point. This is because velocity is defined as the rate of change of position with respect to time.

To see why this is true, consider a small time interval Δt during which the position of the object changes by Δx. The average velocity of the object during this time interval is given by:

Average velocity = Δx / Δt

If we make Δt smaller and smaller, we get closer and closer to the instantaneous velocity of the object at that point in time. This is represented by the slope of the x-t graph at that point:

Instantaneous velocity = dx/dt

So the slope of the x-t graph at any point gives the instantaneous velocity of the object at that point. If we plot the velocity as a function of time (v-t graph), we can see how the velocity changes over time.

79. q=3·4x10^-30 C is possible exist in an atom? 

Not possible.

The charge of an atom is determined by the number of protons and electrons it contains. If an atom has an equal number of protons and electrons, it is electrically neutral. However, if an atom gains or loses electrons, it becomes ionized and has a net positive or negative charge.

In the case of q=3·4x10^-30 C, this is a very small charge and is unlikely to occur on an atom naturally. 

It is possible that this charge could be artificially induced on an atom through various experimental methods, such as ion implantation or electron beam irradiation.

And this is not a typical or natural state for an atom.

80. Resistance of conductor depends upon length.

The resistance of a conductor is directly proportional to its length. 

This means that as the length of a conductor increases, its resistance also increases. 

This is because the longer the conductor, the more difficult it is for electrons to flow through it, due to the increased collisions between electrons and the atoms of the conductor. 

The resistance of a conductor is also affected by its cross-sectional area, temperature, and the material it is made of.