Objects that are in free fall are objects moving in one dimension, just doing so vertically.
Objects that are in free fall are objects moving in one dimension, just doing so vertically. We ignore air resistance unless told otherwise, and we don’t worry about what happens before and after the object is in freefall (1:15). If on earth, the acceleration we should use is -9.81 m/s2.(1:50) Episode 6 recaps 3 key aspects of free-fall problems (4:47). Throw a ball into the air at 30 m/s to follow along with our example problem (5:49).
The Question of the Day asks:(8:38) A t-shirt is launched straight upward from a canon at a basketball game, what is the t-shirt’s acceleration at the peak?
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Hi and welcome to the APsolute Recap: Physics 1 Edition. Today’s episode will focus on objects in free-fall.
Lets Zoom out:
Unit 1 – Kinematics
Topic 1.1 – Position, velocity, and acceleration
Big Idea – Force Interactions
A lab cart rolled up a hill will eventually stop and roll back down. How is a tennis ball thrown upward in the air different? In many ways they are the same. They both start with positive velocity, stop, and finish with negative velocity. We say that the tennis ball thrown in the air is in free fall. What does that mean? What is causing the freely falling ball to change its velocity? What if we threw a bowling ball or soccer ball into the air?
Lets Zoom in:
We say that objects are in free-fall whenever the speed of the object is only changed by gravity’s effects. In many cases, free-fall problems will state that the effects of air resistance are negligible or so small that we don’t need to focus on them. On the AP exam, it is expected that you ignore the effects of air resistance unless otherwise indicated. You also do not want to focus on the moments before or after the object is freely falling. For a ball thrown upward and caught at the same height, we want to evaluate it the moment after it leaves the throwers hand until the moment just before it is caught.
Since only gravity acts on a freely falling object, all objects accelerate downward at the same rate, 9.81 m/s/s. On the AP exam , it is ok to round this value to 10 m/s/s for the sake of simplicity in calculations. Assuming that you are using the convention of positive is upward, then this acceleration should be used as a negative vector whenever calculating with it. But, what does it mean? To accelerate means that the velocity of an object changes over time. So, on Earth, objects change their speed by -10 m/s every second that they are in free-fall. A ball thrown upward at 30 m/s will spend 3 seconds moving in the upward direction. It’s velocity will change by -10 m/s every 1 second. It will slow to 20 m/s, then 10 m/s then 0 m/s. At this instant, the object is at its peak height, and will now begin to speed up in the negative direction by… you guessed it! -10 m/s every second! The entire trip - the object is being accelerated uniformly at -10 m/s/s.
This may leave you wondering, well not all objects are thrown upward. What about objects thrown downward? Well, they too enter into free-fall and will continue to accelerate at the tried and true -10 m/s/s. A ball thrown downward at -30 m/s will spend 1 second speeding up to -40 m/s and then another second to speed up to -50 m/s, and so on. The beauty of all of this is that the good ole’ kinematic equations can be used and solutions for free-fall problems can be organized in the same way as 1-D horizontal motion problems.
Some key aspects to look out for…
· If it is stated that an object is “dropped”- then it is expected you realize that means the initial velocity is 0 m/s
· If an object is at its peak height, it is expected that you know it momentarily has a velocity of 0 m/s at that point in time
· If the object is launched on Earth, then the acceleration due to gravity or “g” (little g) is -10 m/s/s.
You may find yourself wondering, well sure we can find the velocity of objects in free-fall, but what about finding out how far they fall downward? or what maximum height they reach? or how long they spend in the air? Whoah whoah whoah! Slow down! We are getting to that. Again, the good news is… they are moving in one dimension, so all of the kinematic equations still work to solve algebraically AND… so do all graphing applications!
Let’s think about that ball thrown upward at 30 m/s. If we imagine the velocity vs time graph for that object, it will have an initial velocity of 30 m/s and it will reach a velocity of 0 m/s after 3 seconds. Grab a pen and a piece of paper, a napkin, anything and sketch this out. Well, that would make a triangular shape between the graphed velocities and the x-axis with an area that would equal the upward displacement, in this case the maximum height. AND! The slope of the v-t graph would just be the acceleration of -10 m/s/s. Since gravity doesn’t turn off at the top, the ball would continue with this acceleration into the negative space of our graph and we would have an inverted triangle as it falls down. Since the ball is freely falling, it continues with its -10 m/s/s acceleration and an additional 3 seconds later it is back in the thrower’s hand for a total of 6 seconds of hangtime. That makes sense, because now we have two triangles, one for the positive displacement on the way up to the peak position, and one for the negative displacement on the way down and this would be graphed below the x-axis since it is negative.
And, if you prefer equations, then initial velocity (vy0) is +30 m/s, acceleration is -10 m/s2 and time in the air is 6 seconds. We can find the final position by setting the initial position (y0) as 0 m. Voila! Using the equation for final position we get ½ (-10m/s2)(6 s)2 + (30m/s*6s) and we see that we get a final position of 0 m, right where it left! Not too bad right?
To recap……
Objects that are in free fall are objects moving in one dimension, just doing so vertically. If on earth, the acceleration we should use is -9.8 m/s2 or -10 m/s2. We ignore air resistance unless told otherwise, and we don’t worry about what happens before and after the object is in freefall. Every bit of physics that works in the horizontal direction still works in the vertical direction. That’s kind of beautiful don’t ya think? Physics works!
Coming up next on the APsolute RecAP Physics 1 Edition, we will take a break to review some critical skills with trigonometric functions and learn how their use can help us to solve a wider variety of problems.
Today’s Question of the Day is about objects in freefall.
Question: A t-shirt is launched straight upward from a canon at a basketball game, what is the t-shirt’s acceleration at the peak?