Solving the Elevator's Acceleration: Examining Newton's Laws

In summary, the conversation discusses the concept of weight and acceleration in an elevator. The elevator's scale shows a different weight when it accelerates, and the direction and magnitude of this acceleration are unknown. The conversation also touches on Newton's third law and its application in this scenario. The relevant equations used are F=MG and F=ma. The solution involves determining the direction of the lift's acceleration and using logic to calculate the actual acceleration. The formula for apparent weight is m(a+g).
  • #1
Vipercobra
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Homework Statement


An object is placed on a scale in an elevator which reads 8kg at rest. This scale shows 9.2kg when the elevator accelerates. What is the direction and magnitude of the elevator's acceleration.


Homework Equations


F=MA, F=MG, Fnormal=m(a-g)


The Attempt at a Solution


Can't really work out how to approach this equation as normally acceleration is given while in this case the change in weight is given. Tried substituing 8 into F=MG which gave 78.4 but I don't know how to process from here. I also tried using the formula Fnormal=m(a-g) but acceleration is unkown so I don't know how to proceed.

I also find Newton's third law confusing when applied to an accelerating lift. From what I have read each force has an action reaction pair in which both are equal. When an elevator accelerates upwards the upward force of the elevator is larger than the downwards force of an object, MG. What is the action reaction pair in this instance? The force upwards on the object isn't equal to the downwards force because if they were the object wouldn't be accelerating upwards.
 
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  • #2
Lets work from the bottom up

The action reaction pair.
Action: The force due to gravity and the force that cause acceleration
Reaction: the force from the scale keeping the object stationary

This action reaction (equal and opposite reaction) theory only applies to objects that are not accelerating i.e they are either stationary or traveling at constant velocity.

Now for your problem

A scale measure weight, which is a force, not mass.
I assume you know how to convert from mass to weight for calculation purpose.
I also assume you know that gravity is a force that causes acceleration when the is nothing to react to the force like when it is placed on a scale.

Given this information all you have to do is apply logic to determine what direction the lift accelerate for the object to press harder on the scale's surface. then you can determine the actual acceleration.

Relevant equations

F= mg
F=ma
 
  • #3
So then does that mean that the formula for apparent weight is simply m(a+g)??
 

FAQ: Solving the Elevator's Acceleration: Examining Newton's Laws

What are Newton's laws and how do they apply to elevators?

Newton's laws are three fundamental principles of physics that describe the behavior of objects in motion. The first law states that an object at rest will remain at rest and an object in motion will continue to move at a constant velocity unless acted upon by an external force. The second law states that the acceleration of an object is directly proportional to the net force acting on the object and inversely proportional to its mass. The third law states that for every action, there is an equal and opposite reaction. These laws apply to elevators because elevators are objects in motion that are affected by external forces such as gravity and the tension in the cables.

How does the acceleration of an elevator affect its passengers?

The acceleration of an elevator affects its passengers by creating a sensation of weightlessness or "floating" when the elevator is accelerating upwards, and a feeling of being heavier when the elevator is accelerating downwards. This is due to the fact that the passengers' bodies are also accelerating at the same rate as the elevator, causing a change in their apparent weight.

How does the weight of an elevator and its passengers affect its acceleration?

According to Newton's second law, the weight of an elevator and its passengers will affect its acceleration. The greater the weight of the elevator and its passengers, the greater the force of gravity pulling downwards, and thus the greater the net force acting on the elevator. This results in a greater acceleration downwards. On the other hand, if the weight is decreased, the acceleration will also decrease.

How do friction and air resistance impact the acceleration of an elevator?

Friction and air resistance can have a minor impact on the acceleration of an elevator. Friction between the elevator and the cables can slightly decrease the acceleration, while air resistance can slightly increase it. However, these effects are usually negligible and do not significantly affect the overall acceleration of the elevator.

How can we use Newton's laws to solve for the acceleration of an elevator?

To solve for the acceleration of an elevator, we can use Newton's second law, which states that the acceleration of an object is equal to the net force acting on the object divided by its mass. By analyzing the external forces acting on the elevator, such as the force of gravity and the tension in the cables, we can calculate the net force and use it to determine the acceleration of the elevator.

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