Inclined Plane and Elevator with Acceleration

In summary, the conversation discusses the use of an inclined plane within an elevator to determine the acceleration of a sliding mass in different scenarios. The angle of the incline is taken into account and the concept of acceleration as a form of gravity is introduced. The equations for finding the acceleration in different situations are discussed and solved, with the conclusion that in free fall the acceleration is zero and with constant speed the acceleration is equal to the gravitational acceleration.
  • #1
harrinj4
27
0

Homework Statement



An inclined plane, fixed to the inside of an elevator, makes a 40 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





3. 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.

So lost though, how does the forty degree angle come into play?
 
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  • #2
harrinj4 said:
So lost though, how does the forty degree angle come into play?

Assume there's no acceleration, just gravity. Do you know how to split gravity into a component parallel to the incline and one perpendicular to it? (Hint: draw a vector diagram)

Now, if you're in an accelerating elevator in vacuum (no gravity), everything seems to accelerate downwards or upwards at the same rate regardless of their mass. That's exactly how gravity behaves: it accelerates all objects at the same rate, regardless of their mass. So acceleration can be considered to be additional gravity. Whereas gravity provides mg of force, acceleration provides ma; whereas gravity accelerates objects at g, acceleration does so at a. This is the equivalence principle, the central tenet of general relativity.
 
  • #3
ideasrule said:
Assume there's no acceleration, just gravity. Do you know how to split gravity into a component parallel to the incline and one perpendicular to it? (Hint: draw a vector diagram)

Now, if you're in an accelerating elevator in vacuum (no gravity), everything seems to accelerate downwards or upwards at the same rate regardless of their mass. That's exactly how gravity behaves: it accelerates all objects at the same rate, regardless of their mass. So acceleration can be considered to be additional gravity. Whereas gravity provides mg of force, acceleration provides ma; whereas gravity accelerates objects at g, acceleration does so at a. This is the equivalence principle, the central tenet of general relativity.

yeah so mgcos40 right?

.35mgcos40-mg? or am I way off? **** this is due in two hours
 
  • #4
No, it's mgsin40; mgcos40 is the component perpendicular to the incline.

Acceleration adds to or subtracts from gravity, net "force"=(mg+ma)sin40 or (mg-ma)sin40, depending on which way the elevator is accelerating. a=F/m, so a=(g+a)sin40 or (g-a)sin40
 
  • #5
ideasrule said:
No, it's mgsin40; mgcos40 is the component perpendicular to the incline.

Acceleration adds to or subtracts from gravity, net "force"=(mg+ma)sin40 or (mg-ma)sin40, depending on which way the elevator is accelerating. a=F/m, so a=(g+a)sin40 or (g-a)sin40

Alright, I figured it out!
 
Last edited:
  • #6
Just as a curious second question, what would the acceleration be if the elevator was falling freely?

or if it went upward at a constant speed?
 
  • #7
harrinj4 said:
Just as a curious second question, what would the acceleration be if the elevator was falling freely?

or if it went upward at a constant speed?

Use the same equations that you have derived alredy.

For free fall set a = g
For constant speed set a = 0

What do you get?
 
  • #8
kuruman said:
Use the same equations that you have derived alredy.

For free fall set a = g
For constant speed set a = 0

What do you get?

yeah I figured free fall would be zero!

THANKS!DSGHSDKGHDS
 

1. What is an inclined plane and how does it work?

An inclined plane is a simple machine that is a flat surface that is tilted at an angle. It allows an object to be moved from a lower position to a higher position with less force than lifting it straight up. This is because the force required to move the object is spread out over a longer distance along the inclined plane, making it easier to move.

2. How does acceleration affect an inclined plane and elevator?

Acceleration is a measure of how quickly an object's velocity changes. On an inclined plane, an object will experience a change in velocity due to the force of gravity. If the inclined plane is at an angle, the object will accelerate down the plane. In an elevator, acceleration can be felt as the elevator moves up or down. The greater the acceleration, the faster the object's velocity will change.

3. What factors affect the amount of force needed to move an object on an inclined plane?

The amount of force needed to move an object on an inclined plane depends on the angle of the plane, the weight of the object, and the coefficient of friction between the object and the plane. A steeper angle, a heavier object, and a higher coefficient of friction will all require more force to move the object up the inclined plane.

4. How does an elevator with acceleration affect the perception of weight?

In an elevator with acceleration, the sensation of weight can change due to the effect of acceleration on the object's mass. When the elevator is moving up and accelerating, the object's weight may feel heavier. When the elevator is moving down and accelerating, the object's weight may feel lighter. This is because acceleration affects the amount of force needed to support the object's mass.

5. How can inclined planes and elevators with acceleration be used in real life?

Inclined planes and elevators with acceleration are used in many aspects of daily life. For example, ramps and stairs are types of inclined planes that make it easier to move objects or people to different heights. Elevators with acceleration are commonly used in buildings to transport people and goods between floors. These machines make it easier to move objects vertically, and are essential in modern architecture and construction.

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