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Frame of Reference

A reference frame in which Newton’s first law is valid is called an inertial reference frame. In an inertial reference frame, a body subject to no net force will either stay at rest or move at constant velocity. Any frame moving at constant velocity relative to a known inertial frame is also an inertial frame. If the acceleration of a particle is zero in one inertial frame, it is zero in all inertial frames.

An accelerated frame of reference is called a non-inertial frame. Objects in non-inertial reference frames do not obey Newton’s first law.

Suppose a ball is on the frictionless floor of a car and the brakes are applied. Since there is no net force on the ball an observer on the ground will see the ball continue to move at the velocity of the car just before the brakes were applied. However, relative to an observer in the car, the ball accelerates in the forward direction, even though there is no net force on it. To explain the acceleration of the ball with respect to the car (non-inertial frame) one has to invent a fictitious force called the pseudo force. It is an imaginary force which acts on all the occupants of an accelerated frame. The direction of the force is opposite to the direction of the acceleration. FP = -ma

This pseudo force is real enough to throw you forward when a bus suddenly stops. It is fictitious in the sense that it has no physical origin, that is, it is not caused by one of the basic interactions in nature. Its action does not have the reaction required by the third law.

direction of force

Fig. (a) A ball is dropped inside a car which is initially at rest but has an acceleration a to the right A person on the ground observes that the ball is falling vertically downward under gravity.

direction of force

Fig. (b) A person in the accelerated car observes that the ball falls down and towards the left of the car. According to him the backward acceleration is caused by the pseudo force.

The force exerted by the man on the scale is equal and opposite to N and determines the reading on the scale or the apparent weight. Thus, when the elevator accelerates up, the apparent weight of the block is greater than its true weight by Ma0.

(b)When the elevator accelerates downward with a0 the free body diagrams can be drawn as shown in the figure.

free body diagram of man with respect to ground

Applying Newton’s Second Law
Mg N = Mao
N = M(gao)

ree body diagram of man with respect to elevator
with respect to the elevator
N + Mao – Mg = 0
Or N = M(gao)

Thus, when the elevator accelerates down, the apparent weight of the man is lesser than his true weight by Ma0. If a0 = g, as it would if the elevator were in free fall, the man would be apparently weightless.

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