Inclined Plane Inside an Elevator

In summary: So the inertial force has to act downwards to balance out the forces and account for the relative acceleration.In summary, the problem involves a block sliding on an inclined plane inside an elevator. The angle of the plane is 25° and there is no friction. The question asks for the acceleration relative to the block in three scenarios: when the elevator is accelerating upwards at 0.35g, accelerating downwards at 0.35g, and at a constant speed. To solve this, we need to find the net force on the block in the y direction by considering the elevator's acceleration. In the accelerating reference frame of the elevator, there will be an additional inertial force acting on the block opposite to the direction of the acceleration.
  • #1
rwx1606
32
0

Homework Statement


An inclined plane, fixed to the inside of an elevator, makes a 25 angle with the floor. A mass m slides on the plane without friction. What is the acceleration relative to the block if the elevator is a)accelerating upwards .35g b)accelerating downwards .35g? c)constant speed


Homework Equations



F=Ma

The Attempt at a Solution


I know there's two accelerations I have to take into the account. The acceleration as the block slides down the incline, and the acceleration of the elevator. Combining these two, I can find the relative acceleration. I chose the reference frame to be titled so that the x-axis is along the incline. The thing I can't figure out is how the motion of the elevator affects the motion of the block. For example, when the elevator is accelerating upwards. Does the block accelerate upwards with it? From the block's force diagram I only have the normal force and mg down. the weight provides the acceleration down the incline but I have no clue what the elevator's acceleration does to the system. Any help would be appreciated.
 
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  • #2
Okay so the first thing you want to do is find the net force on the object in the y direction. There is obviously mg pointing down, however the elevator is accelerating up at 0.35g.

therefore net force y = 0.35mg - mg.
Now you can treat the question as a normal inclined plane question where the only y force acting on it is -0.65mg.

You can figure out the rest with this.
 
  • #3
View the problem from the accelerating reference frame of the elevator. In that frame there will be an additional inertial force acting on the block equal to [itex]-ma[/itex] (where "a" is the acceleration of the elevator).
 
  • #4
why does this inertial force act downwards on the block?
 
  • #5
rwx1606 said:
why does this inertial force act downwards on the block?
It acts opposite to the direction of the acceleration. When the elevator accelerates upwards, the inertial force acts downwards.
 
  • #6
You can look at it simply like this, the elevator is accelerating upwards, therefore, relative to the elevator, the block is accelerating downards.
 

1. What is an inclined plane inside an elevator?

An inclined plane inside an elevator is a type of mechanical system that is used to move objects or people between different levels of a building. It consists of a flat surface that is tilted at an angle, allowing for easier movement up or down the incline.

2. How does an inclined plane inside an elevator work?

An inclined plane inside an elevator works by using a motor to move a platform up or down the incline. The angle of the incline reduces the amount of force needed to lift the platform, making it easier to transport heavy objects or people.

3. What are the advantages of using an inclined plane inside an elevator?

Some advantages of using an inclined plane inside an elevator include its ability to transport heavy objects or people with less effort, its space-saving design, and its versatility in different types of buildings. It also requires less maintenance compared to other types of elevators.

4. Are there any safety concerns with using an inclined plane inside an elevator?

Inclined planes inside elevators are generally safe to use, as long as they are properly maintained and operated. However, it is important to follow safety protocols, such as not overloading the platform and ensuring that the incline is not too steep for the intended use.

5. How is an inclined plane inside an elevator different from a traditional elevator?

An inclined plane inside an elevator differs from a traditional elevator in its design and operation. While traditional elevators use a vertical shaft and cables to move the platform, an inclined plane elevator uses an angled surface and a motor to transport objects or people. Inclined plane elevators are also typically smaller and more compact, making them a popular choice for buildings with limited space.

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