Pseudo, the word means false. Therefore, pseudo force is a false or an imaginary force. Pseudo force is a force that does not actually exist, but it appears to be present when the frame of reference is accelerating. It is also known as a fictitious force, inertial force, or d’Alembert force. It means that in the frame of every accelerating body, a pseudo force appears to be acting on all the objects contained in the frame. The direction of the pseudo force is always opposite to the direction of acceleration of the frame. The acceleration with which the objects in the frame appear to be moving is the same as that of the acceleration with which the object moves. The magnitude of the pseudo force is equal to the product of the mass of the object and the acceleration of the frame. The frame that is not accelerating is known as the inertial frame, whereas the frame that is accelerating is known as the non-inertial frame.
1. Railroad Cart
Suppose a person is standing on a railroad cart, while another person is standing on the ground near the railway track. When the cart starts to accelerate in a forward direction, the observer standing on the ground sees the cart moving and finds no motion in the rocks present around him. However, the person standing on the cart sees the rock present on the ground to be moving with the same acceleration, whereas the railroad cart appears stationary to him. As per the person standing on the cart, the rocks move in a backward direction without any application of force. The rocks appear to be moving due to the motion of the cart itself. A force appears to be present in the frame that pulls the rocks in the backward direction. This fictitious force is known as the pseudo force.
2. Pulling a Box with a Brick in it
Suppose a brick is kept in a box, and the box is put into motion with the help of a rope or a string. In reference to the ground, i.e., the inertial frame, the box, and the brick accelerate in an upward direction. Whereas, in reference to the box, i.e., the non-inertial frame, the brick appears to be at rest and the box accelerating in the upward direction. The gravitational force acts on the brick in a downward direction, while a normal contact force acts in the upward direction. The reference frame is accelerating therefore, a pseudo force must act in the direction opposite to the direction of acceleration of the box. The magnitude of the pseudo force is the product of the mass of the brick and the acceleration of the frame. The brick is at rest; therefore, the net force acting on it must be equal to zero or the upward force must be equal to the downward force. Hence, the magnitude of the net force is equal to the sum of the magnitude of the pseudo force and gravitational force.
3. A Bob Suspended in a Truck
When a bob is suspended in a truck that is moving in a forward direction, the string with which the bob is hung gets taut, and the bob moves in the backward direction. If the chosen reference frame is with respect to the road, which is the inertial frame, then no pseudo force exists. When the reference frame is shifted to the truck or the non-inertial frame, a pseudo force is said to be present. A gravitational force pulls the bob in the downward direction, and a tension force is said to be acting along the string. The truck accelerates in the forward direction, and a pseudo force acts in the opposite direction with a magnitude equal to the product of mass and acceleration. The bob appears to be in a state of rest; therefore, the net force present on it must be zero. The vertical component on tension is equal to the gravitational force, whereas the horizontal component is equal to the pseudo force. These forces acting on the bob are perfectly balanced.
When a car is accelerating in the forward direction, all the other objects present in the frame of reference tend to be moving in the opposite direction to the observer who is present in the car. For example, the moon, the sun, the tree, or the other objects, and people present outside the car tend to move in the direction opposite to the direction of acceleration of the car. This is due to the existence of the pseudo force
While going down in a lift, a strong force is felt that pulls our body in the upward direction. This imaginary force makes the objects present outside the moving lift appear to be in motion with the same amount of acceleration as that of the lift but in the opposite direction. The force that causes this to happen is the fictitious force that is called the pseudo force.