# A passenger in the front seat of a car finds himself sliding toward the door as the driver makes a sudden left turn. Describe the forces on the passenger and on the car at this instant if the motion is viewed from a reference frame (a) attached to the Earth and (b) attached to the car.

Grade:upto college level

## 1 Answers

Deepak Patra
askIITians Faculty 471 Points
7 years ago
(a) From the reference frame attached to the Earth, when the car takes a left turn, the inertia of the passenger would maintain the state of motion of the passenger (in accordance with Newton’s first law of motion). This causes the passenger to move in the direction of velocity vector of car before car took a turn.
Therefore, to the observer at Earth frame, the passenger has the initial velocity equal to the velocity of the car before it takes the turn. The observer also see the car taking a turn, and accounts for an acceleration for the same. Thus, the observer would expect frictional forces to exist between the passenger and the seat.
Given that the passenger has moved towards the door when the car took a left turn, it is obvious that the passenger moves to the right. Therefore the frictional force would be in a direction opposite to the motion of the passenger, that is, towards the left.
If you assume that the frictional force between the passenger and seat is given by f , mass of passenger by m whereas the acceleration by a. Then the equation depicting the motion of passenger relative to the observer in Earth’s frame is:
f = ma
Therefore the magnitude of frictional force between the passenger and the seat is equal to the magnitude of the deceleration of the passenger.
(b) According to the observer in car’s frame, the car experiences a centripetal acceleration when it turns to left. Therefore a psuedoforce force will act on the passenger, accelerating him in the direction of the seat. But there is a friction between the seat of the car and the passenger, which decelerate the passenger in a direction opposite to the direction of its motion.
Thus the magnitude of net force acting on the passenger is the difference between magnitude the centrifugal force and magnitude the frictional force.
If you assume that the centrifugal force acting on passenger is F, the frictional force between the passenger and the seat is f , the mass of passenger is m whereas the acceleration is a. Then the equation depicting the motion of passenger relative to the observer in car’s frame is:
F – f = ma
Therefore one can see that the perceived acceleration for the observer in car differs from that of the observer on Earth.