Question

someone plz explain:
1.what happens to the weight(and normal reaction)of something, in an elevator that accelerates upward.plz explain
also,are action reaction forces still equal?
2.What happens when a coin is dropped in an elevator accelerating downward/decending?
3.What happens to the tension in a rope wound over a pulley with one of its ends attached to an object of weight 75N when the object moves upward with a) increasing b) decreasing speed.

plz xplain as im totally confused

Answer 1

The old elevator problem!

Number 1: If the elevator accelerates upwards, the elevator floor must exert a force upwards on the object such that the object also accelerates upwards with the elevator. Now, the force exerted by the elevator on the object is dubbed \(F_e\) and acts upwards. Summing forces, we can observe that\[F_e = N- mg\]where N is the normal force. Solving for N realizes that N will be greater if \(F_e\) acts upwards (positive sign). The opposite occurs if the elevator accelerates downwards.

This can be observed easily at home. Take something and put it in your hand. Raise your hand upwards quickly. Notice how the object appears to be heavier?

Number 2: Since the coin is separate from the elevator, the only force acting on it is gravity. However, since the elevator is moving away from the coin, the coin will remain in the air longer. If the elevator is moving upwards, the elevator is "chasing" the coin, and the time it spends in the air decreased relative to the case when the elevator is not accelerating.

Consider making a pass to another player on a football or soccer field. If the player is stationary the ball will take t seconds to reach the player. If the player is running towards you (elevator moving up), the time it takes (t') will be less t'<t. If the player is running away from you (elevator moving down) the time it takes (t') will be greater t'>t.

Number 3: Consider the FBD of a mass with a rope attached to itwhere T is the tension, mg is the force of gravity, and a is the acceleration of the mass (it can be either upwards or downwards). Let's consider a case when a =0. Summing forces yields.\[\sum F = 0 \rightarrow T - mg = 0 \rightarrow T = mg\]Consider a case when the mass is accelerating upwards\[\sum F = ma \rightarrow T - mg = ma \rightarrow T = ma + mg\]Observe that this INCREASES the tension. The opposite occurs if we accelerate downwards.