Acceleration in an Elevator
I was wondering which way is the screw is feeling the force on an elevator in the following equation:
While standing in an elevator, you see a screw fall from the ceiling. The ceiling is 3.0 m above the floor. How long does it take the screw to hit the floor if the elevator is moving upward and gaining speed at a constant rate of 4.0 m/s^2
I thought if the elevator is going up, it would be going down faster than usual. But do I simply add gravity to that acceleration?
Answer
I won't go deep into this, but this is actually a very important observation. Your instinct is correct that the elevator going up will cause the screw to seem faster. And while it may seem counterintuitive because they are in different directions, you can just add the acceleration due to gravity to the magnitude of the elevators acceleration to get an equivalent acceleration of the screw.
This is called a reference frame. Rather than looking at the elevator and the screw both moving, you can act as if the elevator is still (as it seems to anyone standing in the elevator) and subtract the acceleration of the elevator from the accelerations of every other object. (note here I said subtract the accelerations rather than add because I am talking about the acceleration as a vector rather than just the magnitude as I was before)
Customer support service by UserEcho
I won't go deep into this, but this is actually a very important observation. Your instinct is correct that the elevator going up will cause the screw to seem faster. And while it may seem counterintuitive because they are in different directions, you can just add the acceleration due to gravity to the magnitude of the elevators acceleration to get an equivalent acceleration of the screw.
This is called a reference frame. Rather than looking at the elevator and the screw both moving, you can act as if the elevator is still (as it seems to anyone standing in the elevator) and subtract the acceleration of the elevator from the accelerations of every other object. (note here I said subtract the accelerations rather than add because I am talking about the acceleration as a vector rather than just the magnitude as I was before)