Relative Acceleration in Noninertial Reference Frames

[Bipolarity]

Homework Statement

Suppose you have a spaceship and in the spaceship is a block on an frictionless incline. Initially, the spaceship is at rest on the Earth's surface. The astronaut in the spaceship observes the block sliding down the incline with acceleration $Mgsinθ$.

Now consider that the spaceship is accelerating upwards with an acceleration of A. What will be the acceleration of the block relative to the astronaut in this situation? (assume gravity is still equal to g)

Homework Equations

The Attempt at a Solution

My answer:
Even though the spaceship is accelerating upwards, the astronaut has no way of detecting whether or not the spaceship is accelerating through experiments on the block. Thus, the acceleration measred by the astronaut must be the same as before, i.e. $Mgsinθ$. If this were not the case, the astronaut could conclude that the spaceship is accelerating in some direction, but that is impossible from experiments done only within the spaceship.

Could someone confirm my answer. Thanks.

BiP

 

[BruceW]

That's not right. It looks like you have tried to use the equivalence principle. I am guessing you have been learning about how a man in an elevator cannot tell whether the elevator is accelerated upwards with zero gravity, or whether the elevator is stationary, and there is a gravitational field downward.

The important thing to remember from this is that we are swapping between non-inertial reference frames, so this means that 'gravity' is going to be different, as perceived by those different frames.

You have two situations: 1) spaceship 'at rest' on the Earth's surface. 2) spaceship accelerating with respect to the earth. Now, using the example of the man in the elevator, what will happen to the block?

 

[mfb]

The astronaut cannot feel gravity itself, but it can feel the thrust required to accelerate the spaceship - and this depends on gravity, as you fix the acceleration relative to the surface of earth.
On the ground, the spaceship does not feel gravity itself either - it feels the force from the ground, keeping the spaceship at rest relative to the surface. If the spaceship uses its engines, you just increase that force.