Acceleration of Body in Elevator & Earth with 0.5g Rise

In summary: Inside the elevator, the "effective" gravitational force that is felt by the passengers (and any masses involved in an experiment) is just ##g_{\text{eff.}} = g+ 0.5 \timesg = 1.5\, g.## So you weigh more inside the elevator than you do standing on the ground, and dropped objects fall to the elevator floor faster as well.Of course, if you filmed that from outside, through the transparent glass walls of an elevator, you would see a dropped object just traveling as usual using... well, the laws of gravity.
  • #1
Eitan Levy
259
11

Homework Statement


A slope is inside an elevator. A body with the mass of m is on the slope. θ=30°.
What would be the acceleration of the body in relative to the elevator if the elevator rises with an acceleration of 0.5g?
What would be the acceleration of the body in relative to the Earth if the elevator rises with an acceleration of 0.5g?

Homework Equations


ma=F

The Attempt at a Solution


This question got me really confused. When am I supposed to add the fictitious force? When looking at the body in relative to the elevator or in relative to the earth?
The calculation itself is simple, but I can't figure in what case do I need to add the fictitious force. Thanks a lot.
 

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  • #2
Eitan Levy said:
When am I supposed to add the fictitious force?
Fictitious forces are used when viewing things from an accelerated frame. So use it in the frame of the elevator.
 
  • #3
Doc Al said:
Fictitious forces are used when viewing things from an accelerated frame. So use it in the frame of the elevator.
And when looking at the elevator in relative to the EARTH. I shouldn't add this?
 
  • #4
Eitan Levy said:
And when looking at the elevator in relative to the EARTH. I shouldn't add this?
Correct. For the purposes of the question, the Earth frame is near enough inertial.
 
  • #5
Eitan Levy said:
And when looking at the elevator in relative to the EARTH. I shouldn't add this?
Right. In the inertial frame of the Earth (close enough, as haruspex says), only "real" forces appear: the normal force and gravity.

You could solve the problem in both frames, but you may find it easier to solve it in one frame then simply transform your answer to the other frame.
 
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  • #6
haruspex said:
Correct. For the purposes of the question, the Earth frame is near enough inertial.

Doc Al said:
Right. In the inertial frame of the Earth (close enough, as haruspex says), only "real" forces appear: the normal force and gravity.

You could solve the problem in both frames, but you may find it easier to solve it in one frame then simply transform your answer to the other frame.

I if have a body on an accelerating wagon (the body doesn't move in relative to the wagon), with acceleration equals to a (horizontal).
If I look at it in relative to the Earth without adding such force, how does it make sense. I get just the normal and gravity, but the body does move with that acceleration, without having any forces acting that way.
 
  • #7
Eitan Levy said:
I get just the normal and gravity,
If it is staying with the accelerating wagon then the wagon is exerting a horizontal force on it.
 
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  • #8
Eitan Levy said:
I get just the normal and gravity, but the body does move with that acceleration, without having any forces acting that way.
For the body to accelerate there must be a force. For example, friction. (If the wagon surface were frictionless, the body could not accelerate.)
 
  • #9
Doc Al said:
For the body to accelerate there must be a force. For example, friction. (If the wagon surface were frictionless, the body could not accelerate.)
It was never stated (that I see) if the situation in the elevator had any friction associated with the ramp. Is the wagon just another idea to try to figure it out?
 
  • #10
scottdave said:
It was never stated (that I see) if the situation in the elevator had any friction associated with the ramp. Is the wagon just another idea to try to figure it out?
It was another scenario introduced by Eitan in post #6.
 
  • #11
scottdave said:
It was never stated (that I see) if the situation in the elevator had any friction associated with the ramp.
The ramp, presumably, is frictionless.

scottdave said:
Is the wagon just another idea to try to figure it out?
A different scenario.
 
  • #12
Eitan Levy said:

Homework Statement


A slope is inside an elevator. A body with the mass of m is on the slope. θ=30°.
What would be the acceleration of the body in relative to the elevator if the elevator rises with an acceleration of 0.5g?
What would be the acceleration of the body in relative to the Earth if the elevator rises with an acceleration of 0.5g?

Homework Equations


ma=F

The Attempt at a Solution


This question got me really confused. When am I supposed to add the fictitious force? When looking at the body in relative to the elevator or in relative to the earth?
The calculation itself is simple, but I can't figure in what case do I need to add the fictitious force. Thanks a lot.

Inside the elevator, the "effective" gravitational force that is felt by the passengers (and any masses involved in an experiment) is just ##g_{\text{eff.}} = g+ 0.5 \times
g = 1.5\, g.## So you weigh more inside the elevator than you do standing on the ground, and dropped objects fall to the elevator floor faster as well.

Of course, if you filmed that from outside, through the transparent glass walls of an elevator, you would see a dropped object just traveling as usual using the standard Earth's acceleration of gravity, ##g##, but you would also see the elevator floor rising up to meet the object. From inside the elevator it looks like the object is falling faster.

I realize that your problem does not involve a dropped object, but the same downward forces are acting on the object as would be the case if the object were dropped. The ramp is opposing those forces and re-directing the direction of acceleration.
 
Last edited:
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  • #13
Ray Vickson said:
Inside the elevator, the "effective" gravitational force that is felt by the passengers (and any masses involved in an experiment) is just ##g_{\text{eff.}} = g+ 0.5 \times
g = 1.5\, g.## So you weigh more inside the elevator than you do standing on the ground, and dropped objects fall to the elevator floor faster as well.

Of course, if you filmed that from outside, through the transparent glass walls of an elevator, you would see a dropped object just traveling as usual using the standard Earth's acceleration of gravity, ##g##, but you would also see the elevator floor rising up to meet the object. From inside the elevator it looks like the object is falling faster.

I realize that your problem does not involve a dropped object, but the same downward forces are acting on the object as would be the case if the object were dropped. The ramp is opposing those forces and re-directing the direction of acceleration.
That was really helpful! Thanks.
 

Related to Acceleration of Body in Elevator & Earth with 0.5g Rise

What is acceleration?

Acceleration is the rate at which an object's velocity changes over time. It is measured in meters per second squared (m/s²).

How is acceleration related to the elevator and Earth?

In the context of an elevator and Earth, acceleration refers to the change in an object's velocity as it moves vertically. When the elevator accelerates upwards, the object experiences a positive acceleration, and when it accelerates downwards, the object experiences a negative acceleration.

What does 0.5g rise mean?

0.5g rise refers to an acceleration of 0.5 times the acceleration due to gravity, which is 9.8 m/s² on Earth. This means that the object in the elevator is experiencing an upward acceleration of 4.9 m/s².

How does acceleration affect the body in an elevator?

When an elevator accelerates upwards, the body experiences a sensation of being pushed downwards due to the force of gravity. This can result in a feeling of weightlessness or lightness. On the other hand, when the elevator accelerates downwards, the body experiences a sensation of being pushed upwards, resulting in a feeling of heaviness or pressure.

Is acceleration of body in an elevator different from acceleration on Earth?

Yes, the acceleration experienced by the body in an elevator is different from the acceleration due to gravity on Earth. In an elevator, the acceleration is caused by the motor moving the elevator, while on Earth, the acceleration is due to the force of gravity pulling objects towards the center of the planet. Additionally, the direction of acceleration in an elevator can change, while the acceleration due to gravity on Earth is always downwards.

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