How Does Gravity Affect the Motion of a Falling Box from an Elevator?

[Violagirl]

Homework Statement

A box falls from an elevator that is ascending with a velocity of 2 m/s. It strikes the bottom of the elevator shaft in 3 seconds. A) How long will it take the box to reach its maximum height?
B) How far from the bottom of the shaft was the box when it fell off the elevator? C) What is the height of the elevator when the box is at its highest point?

Homework Equations

v(t) = v0 + at
x(t) x0+v0t+1/2at²
v²-v0²=2aΔx

The Attempt at a Solution

I know that the elevator will reach a maximum height when the velocity is 0. So v = 0, v0 = 2 m/s, a = 9.8 m/s^-2, t=3 sec.

For A) (the one I'm concerned with for now), I set it up as V-V0/a = t. Plugging everything in, t = 0 - (2 m/s)/9.8 m/s^-2 to get an answer of -.204 s. I know that must not be right as I don't believe t can be negative. However, since the box is falling off the elevator, shouldn't it be measured as a positive value since it's falling down?

 

[Hypersphere]

In which direction is the acceleration?

 

[Violagirl]

In which direction is the acceleration?

In this problem, acceleration is defined as a constant, which would be gravity measuring out to be 9.8 m/s². I know that if an object is moving "up", gravity is typically negative in that situation. However, since the box is falling off the elevator and moving towards gravity, it should have a positive value, right?

 

[Hypersphere]

I know that if an object is moving "up", gravity is typically negative in that situation. However, since the box is falling off the elevator and moving towards gravity, it should have a positive value, right?

OK, suppose you throw a ball up in the air. Is the sign of the acceleration negative while it is moving upwards and positive when it is moving downwards then?

 

[Violagirl]

OK, suppose you throw a ball up in the air. Is the sign of the acceleration negative while it is moving upwards and positive when it is moving downwards then?

Oh I did not think about it in that context, so I know that the ball's velocity decreases as it's tossed up and then reaches a max velocity of zero and then it's velocity increases as it falls back to earth, which would represent a positive and increase in acceleration.

 

[azizlwl]

For A) (the one I'm concerned with for now), I set it up as V-V0/a = t. Plugging everything in, t = 0 - (2 m/s)/9.8 m/s-2 to get an answer of -.204 s. I know that must not be right as I don't believe t can be negative. However, since the box is falling off the elevator, shouldn't it be measured as a positive value since it's falling down.
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You are taking upward as positive as given to v.
The gravity is pointing downward.
So it must be opposite sign to v.

You can assign a as positive and it will make v of negative sign.

 

[Hypersphere]

Oh I did not think about it in that context, so I know that the ball's velocity decreases as it's tossed up and then reaches a max velocity of zero and then it's velocity increases as it falls back to earth, which would represent a positive and increase in acceleration.

Well, let us take this carefully.
1. The ball loses speed as it moves up. Thus the acceleration is in the opposite direction of the velocity, i.e. downwards. (Think of it as vectors.)
2. The ball reaches a max height, where it has a minimum speed of zero. The acceleration continues to point in the same direction, having the same value. (Gravitation continues to exist even if you don't move.)
3. The ball starts to move down, with increasing speed. Thus the acceleration is in the same direction as the velocity, i.e. downwards.

Basically, the gravitation always points towards the ground. What sign does it have? It depends on your coordinate system. Say that your axis points upwards (as you have, since you say that upwards velocities are positive), then the gravitational acceleration is indeed a=-g.

 

[Violagirl]

Ok, got it! So just all depends on how your choose to set up your coordinate system and keeping it consistent. That makes sense, I must not have been had a consistent system in that case. Thanks a lot!

Well, let us take this carefully.
1. The ball loses speed as it moves up. Thus the acceleration is in the opposite direction of the velocity, i.e. downwards. (Think of it as vectors.)
2. The ball reaches a max height, where it has a minimum speed of zero. The acceleration continues to point in the same direction, having the same value. (Gravitation continues to exist even if you don't move.)
3. The ball starts to move down, with increasing speed. Thus the acceleration is in the same direction as the velocity, i.e. downwards.

Basically, the gravitation always points towards the ground. What sign does it have? It depends on your coordinate system. Say that your axis points upwards (as you have, since you say that upwards velocities are positive), then the gravitational acceleration is indeed a=-g.