Acceleration acting on a block lying on a wedge (non-inertial frame)

In summary: It will have the acceleration you found in the wedge frame of reference plus the acceleration of the wedge.
  • #1
Homework Statement
Consider this situation: there's a wedge, where a block is lying on it. There's no friction. A horizontal acceleration is applied to the wedge. This acceleration may cause three cases: the block doesn't move with respect to the wedge; the block slides up; the block slides down.
Relevant Equations
Newton's equation
I have some difficulties trying to understand non-inertial frames.

I have problems to notice the acceleration in these cases, from an inertial reference frame and from non inertial refrence frame.

Consider the first case, if I'm on the wedge, I see that the block doesn't move so there's no acceleration, all the forces add up to zero. But what about if I'm on an inertial frame? Which acceleration would the block have? Just horizontal acceleration, right? (Because I would see that it is moving to the right, so if I consider non inclined axis, the acceleration would be just in ##x##)

And what about the case where it is sliding up? From the non inertial frame, I would see just ##x## acceleration (if I consider inclined axis). And what if I saw it from the ground? What components would it have?
 
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  • #2
Say the contact is frictionless. If the wedge slides to the right with acceleration ##\vec a## in the inertial frame, an observer in the non-inertial frame will see the block experience a fictitious force ##-m\vec a##. If the block is at rest relative to the wedge in the non-inertial frame, the observer will conclude that the fictitious force is just enough to keep the block from sliding down. This situation is equivalent to the one in which the block is not accelerating in an inertial problem, but is prevented from sliding down by a real force, e.g. a finger, holding it in place. Sliding up or sliding down means that the fictitious (or real) force is greater or less than what is needed to keep the block from sliding.
 
  • #3
kuruman said:
Say the contact is frictionless. If the wedge slides to the right with acceleration ##\vec a## in the inertial frame, an observer in the non-inertial frame will see the block experience a fictitious force ##-m\vec a##. If the block is at rest relative to the wedge in the non-inertial frame, the observer will conclude that the fictitious force is just enough to keep the block from sliding down. This situation is equivalent to the one in which the block is not accelerating in an inertial problem, but is prevented from sliding down by a real force, e.g. a finger, holding it in place. Sliding up or sliding down means that the fictitious (or real) force is greater or less than what is needed to keep the block from sliding.
Yes, I understand that. But I don't understand the acceleration of the block in the second case. From an inertial frame, it will just have ##x## acceleration? Or ##x## and ##y##? And from non inertial? Will it have just ##x## acceleration?
 
  • #4
Like Tony Stark said:
Yes, I understand that. But I don't understand the acceleration of the block in the second case. From an inertial frame, it will just have ##x## acceleration? Or ##x## and ##y##? And from non inertial? Will it have just ##x## acceleration?
It will have the acceleration you found in the wedge frame of reference plus the acceleration of the wedge.
 
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1. What is acceleration acting on a block lying on a wedge in a non-inertial frame?

The acceleration acting on a block lying on a wedge in a non-inertial frame is the rate of change of velocity of the block in relation to the wedge. It is caused by the non-inertial forces acting on the block, such as the normal force and friction.

2. How is the acceleration of the block affected by the angle of the wedge?

The acceleration of the block is directly affected by the angle of the wedge. The steeper the angle of the wedge, the greater the acceleration of the block will be. This is because the component of gravity acting down the incline increases as the angle increases, causing a larger non-inertial force on the block.

3. What is the difference between the acceleration of the block and the acceleration of the wedge?

The acceleration of the block is caused by the non-inertial forces acting on it, while the acceleration of the wedge is caused by the external forces acting on it. These two accelerations may be different, as the wedge may have a different mass and angle than the block, resulting in different forces acting on each.

4. Can the acceleration acting on the block be negative?

Yes, the acceleration acting on the block can be negative. This means that the block is slowing down, either due to an opposing non-inertial force or a decrease in external forces acting on the wedge.

5. How does the presence of friction affect the acceleration of the block?

The presence of friction can decrease the acceleration of the block, as it acts in the opposite direction of the block's motion. This means that the non-inertial force caused by friction will need to be overcome by a greater external force in order for the block to accelerate.

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