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We know that a force is something that can be felt but cannot be seen. We just know by Newton’s second law of motion that on applying force to the car, it starts accelerating.

However, a new term comes into our knowledge and that is ‘pseudo force’, so do you know what is Pseudo Force?

Well! A frictional or inertial or an apparent force that acts on the object with mass ‘m’ in motion without regarding an inertial frame of reference. For thus we can consider a rotating frame reference.

The word ‘pseudo’ means something imaginary, fictitious, or does not exist, only we consider something. A force is something we apply in pushing, pulling, or rolling an object over the surface.

When it comes to pseudo force, we are actually talking about an imaginary force. That doesn’t exist but we still consider it as the part to study the nature of forces in Physics.

Let’s say there are two bodies viz: P and Q and they are sitting in an accelerated metro and R observe both of them from the platform. Here, if R draws a free body diagram of Q, it will have a net force that gives acceleration; however, when P draws a free body diagram or FBD for Q then for a body ‘P’, Q is at rest so to counter the force shown by P, Q needs a fictitious force in his frame and this fictitious force is nothing but the pseudo force.

In the above statement, we said that a pseudo force is also called a fictitious force. A fictitious force arises when a frame of reference is accelerating when compared to a non-accelerating frame. Let’s suppose that a person is standing at a bus stop and he watches an accelerating car, he infers that when a force is exerted on the car and it is accelerating.

Now what happens next is, if the same person A sits in the car and watches another person B standing in his place at the bus stop, he observes that though no force acts on the standing person, still the person A observes that arbitrarily person B is moving along with his car but in the opposite direction. So, here

Let’s consider another scenario where a man pushes a swing for his child, and the swing makes an oscillatory motion, so the force is acting on it that tries to reduce its speed, and eventually swing comes to rest. So, here, a force is acting but we are not sure from which direction or what magnitude of force acts on the swing. So, for a child swinging, he feels that air is moving along with him, so it is a fictitious force again.

Let’s consider a basic pseudo force example to understand in a better way:

Let’s consider a scenario of a ball hung from the roof of a train by means of an inextensible string. No, if the train is at rest or is moving with a uniform speed in a straight line the string will remain in a vertical position and passengers infer that the total force acting on the ball is zero.

Let’s suppose that the train begins to accelerate, the string starts making an angle with respect to the vertical while making the to-and-fro motion.

In this situation, for a passenger, there are two forces, and they are not collinear; however; the ball appears to remain in a state of equilibrium (as long as the acceleration of the train remains constant). In this type of condition, the concept of pseudo force is required.

Below is the diagram to elaborate the pseudo force definition:

[Image will be Uploaded Soon]

Since pseudo force is an imaginary force like a frictional force so it always acts in the direction opposite to that of the direction of motion of an object. So, we indicate the formula for the pseudo force by a negative sign. So, here the formula goes:

FP = - ma…(1)

Here,

FP = pseudo force,(we sued a subscript ‘p’ to distinguish it from the force we consider). It is also measured in N.

m = mass of the moving object. It is measured in Kg.

a = acceleration caused by an object’s frame of reference when it is subjected to an external force. It is measured in ms⁻².

The negative sign we used in equation (1) shows that the pseudo force always acts in the direction opposite to that of the acceleration of the object’s frame of reference.

The work done by a pseudo force is zero as it acts to appear on the body.

We can consider an example of thinking of picking a pile of bricks in our dreams, though we are applying the force here we are not doing it in actuality. So, here the actual work is done is zero, as Physics talks about facts and practical implications.

FAQ (Frequently Asked Questions)

Question 1: Can the Work Done by the Pseudo Force be Conservative? Elaborate it with an Example.

Answer: Pretty yes.

We can say that pseudo forces do work and if we describe these forces as conservative, then yes the corresponding mechanical energy would be conserved. The best example we can consider here is the gravitational pull we feel at the surface of the Earth. It is in fact the sum of the "true" gravitational force concerning Newton's law of gravitation and the latitude-dependent centrifugal force that we experience while the Earth is rotating.

It gives rise to an effective pseudo-gravitational force whose magnitude depends on the latitude which, for most of our practical purposes in Physics, is considered conservative.

Question 2: Can We Say that a Pseudo Force is Conservative?

Answer: No, we cannot be sure whether a pseudo force is conservative; however, the condition for any force to be conservative is that the curl of the force vanishes, this is equivalent to the work done in a closed path being zero or we can say, whatever amount heat is absorbed by the Carnot engine comes back to the source again without any wastage, while it is an imaginary engine. So focusing on the actual scenario, not in every case, the pseudo force can be conservative.

Question 3: Is Work Done Positive?

Answer: Yes. It’s because force and displacement act in the same direction, so their product comes out to be positive, so work done is also positive.