Free Fall

Free fall describes the motion of an object under the influence of only gravity.

Examples of free fall:

• a ball dropped in a complete vacuum - no air particles to provide air resistance
• a satellite orbiting Earth - nothing, but gravity, would affect the motion of the satellite. 
• a ball launched or thrown upwards in a vacuum - once the ball is launched, gravity is the only thing affecting its motion

Not examples of free fall:

• a ball dropped under normal conditions on Earth - the ball would experience air resistance
• a space shuttle (in space) which has its engines turned on - the engines would provide thrust, which would affect the motion of the space shuttle

Because of the negative acceleration of gravity, the position of an object dropped into free fall changes at increasingly larger rate. This is just like an object accelerating in linear motion. However, if the object is launched into the air, the position of the object will change at a smaller and smaller rate until it reaches the peak of its motion (zero velocity). After the peak, the position changes at an larger and larger rate.

In terms of velocity, the negative acceleration of gravity causes the velocity to steadily decrease whether the object is dropped or thrown.

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In class, we tried to demonstrate free fall as best as we could by dropping balls off of a staircase. It wasn't a "perfect" demonstration of free fall because we weren't dropping the balls in a vacuum, but we tried. :)

We recorded the dropping of a medicine ball using iPads and used an app to track the motion of the ball. We then created graphs based on the tracking information. Here are the results:

Video:

Tracking:

Graphs:

With best-fit line drawn in

These graphs demonstrate the motion described earlier. For instance, the slope of the position vs. time graph (top) becomes steeper as the ball drops. This shows that the ball is falling faster and faster, which means that the position is changing more and more.

The velocity vs. time graph shows the steadily decreasing velocity due to the negative acceleration. The slope of this graph also describes the acceleration of the ball which would be gravity in this case. Using the graphing app, we were able to create a best-fit line for the slope, and calculate the slope (acceleration of gravity). This yielded -9.708 (m/s^2), which is actually quite close to the known acceleration of gravity on Earth, -9.8 m/s^2. How close?

Percent error = |theoretical - actual yield|/(theoretical) * 100% = |9.8 - 9.708|/9.8 * 100% = 0.94% error

That's a very small percentage error despite the multiple potential sources of error. These include: 

• air resistance (goes against gravity --> smaller acceleration rate)
• video (doesn't show the whole drop, camera motion --> affect acceleration rate)
• accuracy of the tracking (we had to manually track the ball frame-by-frame --> affect acceleration rate)
• best-fit line (manually selected region --> affects how acceleration rate is calculated)

We also dropped a few other kinds of balls including a big tennis ball and a beach ball. Here are the acceleration rates of those:

• tennis ball: -9.795 m/s^2
• beach ball: -6.234 m/s^2

As you can see, the acceleration of the tennis ball is almost exactly the same as the acceleration of gravity. However, the beach ball's acceleration rate is off by quite a bit (~36% error). This is due to the higher air resistance experienced by the beach ball which creates a force opposite of the acceleration of gravity.

Overall, this demonstration was quite fun to experience, and I thought the tracking/graphing apps were pretty cool.