Which Coin Hits the Bottom of the Lift Shaft First?

  • Thread starter AllenHe
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In summary: This is because Coin A has a greater potential energy at the point of release, which is converted into kinetic energy upon impact, giving it a greater speed. However, due to its initial upward velocity, it will take longer to reach the ground. Coin B, on the other hand, has no initial velocity and therefore will reach the ground first, but with a lower speed.
  • #1
AllenHe
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Homework Statement


A lift is traveling upwards at constant speed. As it passes the second floor,a passenger frops coin A through an old-fashioned gate grille. At exactly the same time, a person standing on the second floor landing drops coin B through the gate grille at the landing. Which coin, A or B(if either),reaches the bottom of the lift shaft first?Which if (either) has the greater speed on impact?


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The Attempt at a Solution

 
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  • #2
I think everyone would like to hear your thoughts about the this. I.e. you should make some effort to solve it!
 
  • #3
My teacher told me that when the passenger on the lift drops the coin, the coin is still experiencing an upward acceleration.So its velocity will be slower than the person who drops the coinB on the second floor landing.
But I checked the answer at the back of the book, it says that Coin B will have a greater speed on impact,but it also said that Coin A will reach the bottom first.That's a bit confusing.
 
  • #4
AllenHe said:
My teacher told me that when the passenger on the lift drops the coin, the coin is still experiencing an upward acceleration.So its velocity will be slower than the person who drops the coinB on the second floor landing.
But I checked the answer at the back of the book, it says that Coin B will have a greater speed on impact,but it also said that Coin A will reach the bottom first.That's a bit confusing.
Let's clear up a few things. The coin in the lift is not accelerating, since the lift is traveling at constant speed. At the point of release, coin A will have some non-zero upward velocity and so will continue to move vertically upwards for some time. Coin B in contrast, is initially stationary and therefore will fall straight down. Upon release, both coins will experience the same acceleration (-g) and therefore will accelerate at the same rate. Therefore, coin B will hit the ground first. Try it yourself, throw a ball upwards and at the same time drop another ball - which hits the ground first?

As for which coin has the greatest velocity, when coin A reaches the peak of its trajectory (i.e. when it stops before falling back to earth), it will be higher than where coin B began its fall to earth. Therefore, coin A will have more potential energy than coin B. When both coins hit the floor, their potential energies will be equal, with the change being converted to kinetic energy. Therefore, coin A will have greater speed on impact.
 
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  • #5
Im getting it.But in the book, it said that CoinA will reach the bottom first, and coin B has the greatest speed on impact.
 
  • #6
AllenHe said:
Im getting it.But in the book, it said that CoinA will reach the bottom first, and coin B has the greatest speed on impact.
Then the book is incorrect. It is precisely the opposite: Coin A has the greatest speed on impact and Coin B will reach the bottom first.
 

1. What is motion?

Motion refers to the change in position of an object over time.

2. What are the different types of motion?

The three types of motion are linear motion (movement in a straight line), rotational motion (movement around an axis), and oscillatory motion (back and forth movement).

3. What factors affect an object's motion?

The factors that affect an object's motion include its mass, speed, direction, and any external forces acting upon it (such as gravity or friction).

4. How is motion measured?

Motion is typically measured using units of distance (such as meters or feet) and time (such as seconds or minutes). The most common way to measure motion is by calculating an object's speed, which is the distance it travels divided by the time it takes.

5. What are the laws of motion?

The laws of motion were established by Sir Isaac Newton and describe how objects move. They include the law of inertia (an object will remain at rest or in uniform motion unless acted upon by a force), the law of acceleration (the force acting on an object is directly proportional to its mass and acceleration), and the law of action and reaction (for every action, there is an equal and opposite reaction).

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