Chapter 6, Problem 68A

Drop a sheet of paper and a coin at the same time. Which reaches the ground first? Why? Now crumple the paper into a small, tight wad and again drop it with the coin. Explain the difference observed. Will the coin and paper fall together if dropped from a second-, third-, or fourth-story window? Try it and explain your observations.

To determine

If a sheet of paper and a coin is dropped from a height at the same time, which will reach first on the ground and why?

Answer to Problem 68A

The coin will reach the ground first.

Explanation of Solution

Introduction:

Objects in a freefall will experience equal gravitational forces. But, more the mass, less air resistance is applied to it.

To calculate the time taken by an object to reach the ground.

  $t=\sqrt{2d/g}$

t= time taken

d= height of the fall

g= gravitational force

As compared to the sheet of paper, the coin will reach the ground first. The key is the frictional resistance due to air. If the test is conducted in a vacuum chamber then both will take the same amount of time to reach the ground.

Conclusion:

Coin will reach the ground first comparatively sheet of paper.

To determine

If a small, tightwad crumpled sheet of paper is dropped with a coin from a height at the same time, which will reach first on the ground and why?

Answer to Problem 68A

Crumpled sheet of paper and coin both will reach at the ground together.

Explanation of Solution

Introduction:

Equal masses will equal air resistance in free falling.

Now, after crumpling the paper into a small, tightwad, and then dropping it along with the coin would result in the same time taken by both the objects. Because the mass of crumple of paper is now comparatively equivalent to the mass of the coin. Thus, both objects will experience the same amount of air resistance and reach the ground at the same time.

Conclusion:

Both will fall down on the ground at the same time.

To determine

Will coin and paper fall together if dropped from a second-, third-, or fourth-story window?

Answer to Problem 68A

The coin will reach first each time. The only difference would be that time taken in dropping from a second-, third-, or fourth-story window to reaching ground would increase respectively.

Explanation of Solution

Introduction:

Greater the mass lesser will be air resistance experienced by the object in free falling.

Even if, the test is conducted from a second-, third- or fourth-story window, the result would have been the same. The coin will reach first. The only difference occurs in the time taken by the objects. As more the height, more will be the time taken.

Conclusion:

Coin will reach first but time duration will increase as height increases.