Calculate Velocity & Time of Pencil Dropped from Elevator Moving at 5m/s

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This means that the motion of the pencil is independent of the elevator's motion. In summary, using this principle, you can calculate the time it takes for the pencil to drop from 1m to the elevator floor and its velocity regardless of the elevator's speed.
  • #1
lytien
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A pencil is dropped from inside an elevator moving 5m/s upward. Calulate the time it takes to drop from 1m to elevator floor and its velocity.


I approached as a velosy problem. Is this more of a Force problem ? I could calculate the velocity and time it took while the elevator was at a standstill, but got stuck when its in motion. Can someone please guide me in the right direction? THanks!
 
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  • #2
maybe show some working so we can see where you went wrong

note the pencil will initially be moving up at 5m/s the same speed as the elevator & have a think about equivalence of inertial reference frames
 
  • #3
lytien said:
I could calculate the velocity and time it took while the elevator was at a standstill, but got stuck when its in motion. Can someone please guide me in the right direction? THanks!

The concept you should apply is Galilean relativity; the laws of physics are the same in all inertial frames.
 

FAQ: Calculate Velocity & Time of Pencil Dropped from Elevator Moving at 5m/s

How do you calculate the velocity of a pencil dropped from an elevator moving at 5m/s?

To calculate the velocity of the pencil, we can use the formula v = u + at, where v is the final velocity, u is the initial velocity (in this case, 5m/s), a is the acceleration due to gravity (9.8m/s^2), and t is the time the pencil takes to reach the ground. By plugging in the values, we can find the final velocity of the pencil.

Can the velocity of the pencil change if the elevator is moving at a constant speed?

Yes, the velocity of the pencil will change as it falls due to the acceleration of gravity. However, the elevator's constant speed will not affect the velocity of the pencil.

What is the time it takes for the pencil to reach the ground?

To find the time it takes for the pencil to reach the ground, we can use the formula t = sqrt(2h/g), where h is the height from which the pencil is dropped and g is the acceleration due to gravity. By plugging in the values, we can calculate the time it takes for the pencil to fall.

How does the velocity and time change if the elevator is moving at a higher speed?

If the elevator is moving at a higher speed, the initial velocity (u) will be greater, and therefore the final velocity (v) will also be greater. However, the acceleration due to gravity and the height from which the pencil is dropped will remain the same, so the time it takes for the pencil to fall will not change.

Is the velocity of the pencil affected by air resistance?

The velocity of the pencil will be slightly affected by air resistance, which is a force that opposes the motion of an object in the air. However, for the purposes of this calculation, we can assume that the effect of air resistance is negligible and can be ignored.

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