Content Writer | Updated On - May 9, 2024
Pseudo force (also known as an inertial force, fictitious force, or d'Alembert force) applies to all masses whose motion is specified by a non-inertial reference frame, such as a rotating reference frame. Pseudo force occurs when a frame of reference accelerates about a non-accelerating frame. Force accelerates the object by push and pulls motion that influences the object to change the velocity in response. Several forces in nature are categorized into two forces. They are:
- Contact Force: The contact force is generated when two objects come into contact with one another, for example, pulling a cart.
- Non-Contact Force: A non-contact force exerts its effects on a target without any physical contact, for example, gravity.
Read More: Relative Velocity
| Table of Contents |
Key Terms: Force, Acceleration, Pseudo Force, Inertia, Frame of Reference, Centripetal Force, Euler Force, Newton’s Law of Motion
What is Pseudo Force?
[Click Here for Sample Questions]
The force F is caused by the acceleration ‘a' of the non-inertial reference frame itself and not by any physical interaction between two objects. Pseudo forces, like frames, can accelerate in whatever direction they choose (but only in direct response to the acceleration of the frame). Instead of any physical interaction between two objects, the acceleration 'a' of the non-inertial reference frame generates the force F. As frames, pseudo forces are capable of accelerating in any direction. A pseudo force does no work as it appears to act on the body.
For frames accelerated in common ways, four pseudo forces are defined:
- One force is generated by a relative acceleration of the origin in a straight line - rectilinear acceleration
- Two forces are induced by rotation - Coriolis force and Centrifugal force
- The fourth force is caused by a changing rate of rotation - the Euler force
Read More: Rectilinear Motion
Laws of Motion Video Lecture
Formula for Pseudo-Force
[Click Here for Previous Year's Questions]
A pseudo force always acts in the opposite direction as an object's frame of reference acceleration. In other words, a pseudo force will always act in the opposite direction as an object's frame of reference accelerates. As you may be aware, Newton's second law governs motion.
The mass and acceleration of an object determine the net force acting on it. (For example, Fnet = ma). In a similar vein, the pseudo-force formula can be written as follows:
| Pseudo force formula: Fp = - ma |
Fp → Pseudo force acting on an object
m → Mass of an object
a → Acceleration of an object's frame of reference
The negative sign indicates that pseudo force is acting in the opposite direction to the acceleration of an object's frame of reference.
Read More:
Pseudo Force Examples
[Click Here for Sample Questions]
Here are a few examples that demonstrate pseudo force
Railroad Cart
Consider a situation in which one person is standing on a railroad cart and another is standing on the ground near the railway track. When the cart begins to move forward, the observer on the ground notices the vehicle moving but notices no movement in the rocks surrounding him. The guy standing on the railroad cart, on the other hand, perceives the rock on the ground as moving at the same rate as the railroad cart, which seems to be stationary to him.
The rocks move backward without applying any force, according to the person standing on the cart. The rocks appear to be shifting due to the cart's movement. A force seems to be acting on the rocks in the frame, pulling them backward. The pseudo force is the name given to this fake power.
Read More: Navier – Stokes Equation
Taking a Box that contains a Brick
For instance, a brick is housed in a box, and the box is moved around by a rope or a string. The box and the brick accelerate in an upward direction about the ground, i.e. the inertial frame. The brick appears at rest about the box, i.e., the non-inertial frame, whereas the box is speeding upward. The gravitational force acts in a downward direction on the brick, while the usual contact force acts in an upward direction.
A pseudo force must act in the opposite direction of the box's acceleration since the reference frame is accelerating. The pseudo force's magnitude is equal to the product of the brick's mass and the frame's acceleration. Because the brick is at rest, the net force acting on it must be zero, or the upward and downward forces must be equal. As a result, the magnitude of the net force equals the sum of the pseudo force and gravitational force magnitudes.
Read More: Time Constant Formula
Car
When an automobile accelerates forward, all other things in the frame of reference tend to move in the opposite direction from the observer in the car. Outside the car, for example, the moon, the sun, the tree, other things, and people, tend to travel in the opposite direction of the car's acceleration. This proves the presence of a pseudo-force.
Lift
A powerful force is felt as we descend in a lift, pulling our bodies upward. The objects outside the moving lift appear to be traveling with the same amount of acceleration as the lift but in the opposite direction due to this illusory force. This fictional force known as the pseudo force is the force that causes this to happen.
Read More: Equations of Motions
Straight Line Acceleration
[Click Here for Previous Year's Questions]
When a car speeds quickly, it's natural to feel "pushed back into the seat." There is no physical force pushing the driver backward in an inertial frame of reference related to the road. However, there is a rearward fake force in the driver's non-inertial reference frame associated with the accelerating car.
Read More: Measurement of Speed
The car is speeding from the perspective of an inertial reference frame with a constant velocity that matches the car's initial motion. A force must be applied to the passenger for them to remain within the car. This force is exerted by the seat, which has begun to move forward with the car and is compressed against the passenger until the total force is transmitted to maintain the person moving with the car. As a result of the imbalanced force of the seat, the passenger accelerates in this frame.
There is a fictional force pulling the passenger backward from the point of view of the interior of the automobile, an accelerating reference frame, with a magnitude equal to the passenger's mass times the car's acceleration. This force pushes the passenger back into the seat until the seat compresses and counteracts the force. Because the imaginary and actual forces of the seat are equal, the person remains motionless in this frame.
Read More:
| Related Topics | ||
|---|---|---|
| Impulse Units | Centripetal and Centrifugal Force | Banking of Roads |
| Types of Friction | Centripetal Acceleration Derivation | Coefficient of Static Friction |
Things to Remember
[Click Here for Sample Questions]
- A pseudo force is a fictitious force that appears to act on a mass whose motion is described using a non-inertial frame of reference.
- For frames accelerated in common ways, four pseudo forces are defined.
- The four forces are Rectilinear acceleration, Coriolis force, Centrifugal force, and Euler force.
- Some examples of pseudo forces are cars accelerating forward, lifts accelerating upward, etc.
- Pseudo force is given by the formula Fp = - ma
- Although appearing to act on the body, work done by the pseudo force is zero.
Get Live Updates on Board Exams 2023: https://t.me/class_10_12_board_updates
Previous years questions
- The resultant of these forces is three times the first force… [KEAM]
- The tension in the string P is… [KEAM]
- If the resultant force is equal to 40√3, the magnitude… [KEAM]
- lf a force of 6 N is applied on the heavier mass… [KEAM]
- A truck is stationary and has a bob suspended by a light string… [NEET – 2019]
- An object flying in the air with velocity … [NEET – 2019]
- Which one of the following statements is incorrect … [NEET – 2018]
- A man weighing 60 kg is in a lift moving down with an acceleration… [KCET – 2018]
- The speed of the bullet after it emerges horizontally from the block … [NEET – 2016]
- A car is negotiating a curved road of radius R… [NEET – 2016]
Sample Questions
Ques. What is the definition of a pseudo-force? (2 Marks)
Ans. A fictional force that acts on all masses whose motion is described using a non-inertial frame of reference, such as a rotating reference frame, is known as a pseudo force. It is also known as a fictitious force, inertial force, or d'Alembert force.
For example: Assume two bodies, A and B, are riding on a speeding bus, and C is watching them from the ground. C will have a net force that causes acceleration if it draws a free-body diagram of B. However, if A draws a free-body diagram for B, B is at rest for him, thus he needs a fake force in his frame to counteract the force depicted by A. This fictional force is known as pseudo force.
Ques. Is centrifugal and centripetal force always equal? (2 Marks)
Ans. Both centrifugal and centripetal forces will be equivalent in a frame of reference where the body is at rest as far as the radial direction is concerned. However, if a body experiences radial acceleration concerning a frame, centripetal force will not equal centrifugal force in that frame.
Ques. Is the work performed by these forces relevant to the work-energy theorem? (1 Mark)
Ans. Yes, work done by pseudo forces is accounted for when applying the work-energy theorem from a non-inertial frame of reference.
Ques. What is the role of these forces in problem-solving? (2 Marks)
Ans. The role of pseudo forces in problem–solving are as follows:
- It helps to determine the time at a specific rate.
- I7t also helps to easily analyze the situation in the frame of reference.
Ques. A rough inclined plane is placed on a cart moving with a constant velocity u on horizontal ground. A block of mass M rests on the incline. Is any work done by force of friction between the block and incline? Is there then a dissipation of energy? (3 Marks)
Ans. Consider the diagram according to the situation where the wedge is moving with velocity u. As the block Mis at rest concerning the inclined plane. There is no pseudo force acting on the block because the wedge is moving with constant velocity. So,
f = frictional force = Mg sinθ
As the block rests on the incline, the force of friction acting between the block and the incline opposes the tendency of sliding the block. Since the block is not in motion concerning the incline, therefore, work done by the force of friction between the block and the inclined plane is zero. Also due to this reason, there is no dissipation of energy.
Ques. A body is being raised to a height h from the surface of the earth. What is the sign of work done by (a) applied force and (b) gravitational force? (5 Marks)
Ans. (a) External force is applied on the body to lift it in an upward direction against its weight, therefore, the angle between the applied force and displacement is = 0°
Work done by the applied force
W= F. S =Fs cos = Fs cos 0° = Fs ( cos 0° = 1)
i.e., the sign of work done by applied force is positive.
(b) As shown in the figure the gravitational force acts in a downward direction and displacement in an upward direction, therefore, the angle between them is = 180°.
Work done by the gravitational force
W = Fs cos 180° = -Fs (cos 180° = -1)
Ques. Calculate the work done by a car against gravity in moving along a straight horizontal road. The mass of the car is 400 kg and the distance moved is 2 m. (2 Marks)
Ans. The weight of the car (mg) acts vertically downward and the car is moving along the flat road, so the displacement of the car is horizontal, i.e. angle between them is 90°.
Work done by weight of the car
W = Fs cos 90° = 0 (cos 90° = 0)
Hence, the work done by the car against gravity will also be zero.
Ques. Give an example of a situation in which an applied force does not result in a change in kinetic energy. (2 Marks)
Ans. Assume a ball is tied to a string and is moving in a vertical circle. Work done by tension force will be zero and hence tension force will not cause any change in the KE of the ball. Because at any instant of time, the displacement is tangential and the force is central, i.e., the tension in the string and the small displacement at any instant are perpendicular to each other.
Ques. Two bodies of unequal mass are moving in the same direction with equal kinetic energy. The two bodies are brought to rest by applying a retarding force of the same magnitude. How would the distance moved by them before coming to rest compare? (3 Marks)
Ans. According to the work-energy theorem, Change in KE is equal to work done by all the forces acting on the body. Let us assume that only one force (retarding force) is acting on the body, therefore,
KE of the body = Work done by retarding force KE of the body = Retarding force x Displacement
As the KE of the bodies and retarding forces applied to them are the same, therefore, both bodies will travel equal distances before coming to rest.
Read More:
Comments