Speaker A
Mr. P: Good morning. If I'm sitting in a canoe holding a ball with a large mass, I throw the ball to the left, and it lands in the canoe, what do you think will happen to the positions of the objects?
Demonstration of center of mass in a canoe-ball system using Newton's laws and projectile motion.
Ask about this video. Answers come from its transcript only — with the timestamp, so you can check them.
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Key Takeaways
- The center of mass of a closed system with no external forces remains stationary relative to Earth.
- Internal forces between objects in a system do not cause net acceleration of the system.
- When the ball lands inside the canoe, the canoe moves to conserve the center of mass position.
- If the ball leaves the system, external forces cause the canoe and Mr. P to move at constant velocity.
- Newton's Third Law pairs explain the equal and opposite forces within the system.
What the video covers
- Mr. P throws a ball to the left while sitting in a canoe and discusses expected movements of the ball, canoe, and himself.
- The system is defined as the ball, canoe, and Mr. P, with no net external force acting on it.
- Newton's Third Law explains internal forces between the ball and canoe, resulting in no net acceleration of the system.
- The center of mass of the system remains stationary relative to the Earth even as the ball moves left and the canoe moves right.
- When the ball lands in the canoe, all motion stops to maintain the center of mass position relative to Earth.
- If the ball lands outside the canoe, the canoe and Mr. P continue moving right due to an external force on the system.
- Masses and positions of the ball, Mr. P, and canoe are used to calculate the center of mass before and after the throw.
- Calculations show the center of mass shifts relative to the system but stays fixed relative to Earth, causing the canoe to move.
- The demonstration confirms the physics principles and Newton's laws governing the system's motion.
- Mr. P emphasizes the importance of understanding internal vs external forces and the conservation of momentum.
Chapters
- 00:00Introduction and initial question
- 00:27Discussion on movement of canoe and ball
- 00:44Clarifying system and forces
- 01:16Newton's laws and center of mass explanation
- 02:38Motion of ball and canoe relative to Earth
- 03:42Forces when ball lands inside canoe
- 03:47Forces when ball lands outside canoe
- 05:05Masses and positions defined
- 06:08Calculating initial center of mass
- 07:09Calculating final center of mass
Full Transcript — Download SRT & Markdown
Speaker A
"Flipping Physics" Intro Bo: Nothing is going to happen. The ball lands in the canoe, so everything just stays where it is.
Speaker A
Bobby: Well, but the ball moves to the left, obviously. Bo: Right, but nothing else moves.
Speaker A
Billy: Won't the canoe and Mr. P move to the right because the ball moves to the left?
Speaker A
Bobby: Sure, the ball moves to the left and the canoe moves to the right.
Speaker A
And then I would think everything keeps moving to the right at a constant velocity after the ball lands in the canoe.
Speaker A
Bo: No, I don't think anything moves. Bobby: Except the ball to the left. Bo: Except the ball to the left.
Speaker A
Mr. P: Okay, let's watch what actually happens. Mr. P: As you can see, the ball does move to the left and the canoe and I move to the right when the ball is in projectile motion.
Speaker A
But notice what happens when the ball lands in the canoe. Everything stops moving. Bobby: Everything stops?
Speaker A
Billy: Why is that? Mr. P: Well, first off, let's define the ball, the canoe, and me as "the system."
Speaker A
Notice that the net external force acting on the system is zero. Yes, I apply a force on the ball and, according to Newton's Third Law, the ball applies an equal but opposite force on me.
Speaker A
But those two forces are internal to the ball, canoe, Mr. P system. Therefore, there is no net external force acting on the system.
Speaker A
If there is no net external force acting on the system, the system does not accelerate.
Speaker A
Because the system was initially at rest, the system will remain at rest. Bo: But then, why does anything move?
Speaker A
Mr. P: Right, okay. So, we have to be careful here. The system remaining at rest means the center of mass of the system will not move.
Speaker A
In terms of Newton's Second Law, because the net force acting on the system is zero, the acceleration of the system is zero. Therefore, because the system starts out at rest, the velocity of the system will not change, it will stay zero, and the center of mass of the system will remain at rest.
Speaker A
However, as the ball moves to the left, the center of mass of the system moves to the left relative to the boat.
Speaker A
To be clear, the center of mass of the system moves to the left relative to the boat, but it does not move relative to the planet.
Speaker A
Because the center of mass of the system does not move relative to planet Earth, as the ball moves to the left, everything else in the system must move to the right in order to keep the center of mass of the system in the same location relative to planet Earth.
Speaker A
Billy: I get that, but why does everything stop when the ball lands in the boat?
Speaker A
Bobby: Oh, I know. That is because the boat stops the ball from moving to the left.
Speaker A
If the canoe and Mr. P kept moving to the right, the center of mass of the system would move to the right.
Speaker A
There is still zero net external force acting on the system. So, the center of mass of the system needs to stay at rest, so the canoe and Mr. P have to stop moving to the right.
Speaker A
Mr. P: Absolutely. There is a Newton's Third Law pair here. The ball applies a force on the canoe and the canoe applies an equal but opposite force on the ball.
Speaker A
Both the ball and the canoe are a part of the system. So those two forces are internal to the system.
Speaker A
So the net external force is still zero. Now, what do you think will happen if I throw the ball, but it does not land in the canoe, it instead lands outside of the canoe?
Speaker A
Bobby: Well, clearly nothing changes from the first example while the ball is in projectile motion.
Speaker A
Bo: But the ball is not a part of the system because it does not land in the boat, right?
Speaker A
Billy: Right. So, in this case, the system is actually just the canoe and Mr. P.
Speaker A
Therefore, there is a net external force acting on the system, which means, after the ball leaves Mr. P's hands, the canoe and Mr. P will continue to move to the right at a constant velocity.
Speaker A
Bobby: Just like before, there is a Newton's Third Law pair here. The force Mr. P applies on the ball is equal and opposite to the force the ball applies on Mr. P.
Speaker A
Bo: Right, but the ball is no longer a part of the system. So, the two forces do not cancel one another out and the net force on the system is not zero.
Speaker A
Mr. P: All right. Let's see if you are correct. Will you look at that?
Speaker A
The canoe and I do continue to move to the right even after the ball lands outside the canoe.
Speaker A
Unlike when the ball landed in the canoe, when the ball lands outside the canoe there is a net external force acting on the system, the canoe and me.
Speaker A
And therefore, we continue to move to the right even after the ball lands. Now let's go back to the ball landing in the canoe and actually calculate how far the canoe and I move.
Speaker A
Let's define some known values. The mass of the ball is 6.5 kilograms. The mass of Mr. P is 72 kilograms.
Speaker A
The mass of the canoe is 33 kilograms. We have set the x-position zero location at the center of the canoe, so all x-position measurements will be relative to the center of the canoe.
Speaker A
Notice we are not concerning ourselves with the y-position center of mass because we are only discussing horizontal movements in this example.
Speaker A
Because I do not move relative to the canoe, the initial and final positions of Mr. P are both 133 centimeters to the right of the center of the canoe.
Speaker A
Both the initial and final positions of the canoe are 0 because the canoe does not move relative to itself and we are assuming the center of mass of the canoe is directly in its center.
Speaker A
The initial position of the ball is 108 centimeters to the right, and the final position of the ball is 157 centimeters to the left, of the center of the canoe.
Speaker A
Bo, please determine the initial x-position of the center of mass of the system. Bo: Okay. The initial x-position of the center of mass of the system equals the mass of the ball times the initial position of the ball plus the mass of Mr. P times the initial position of Mr. P,
Speaker A
plus the mass of the canoe times the initial position of the canoe, all divided by the total mass of the system.
Speaker A
Substituting in numbers gives us 6.5 times 108 plus 72 times 133 plus 33 times 0, all divided by the quantity 6.5 plus 72 plus 33, which equals 92.179 centimeters.
Speaker A
Actually, the final x-position of the center of mass of the system calculation is almost the same.
Speaker A
Do you want me to do that one too? Mr. P: Sure, Bo. Go ahead.
Speaker A
Bo: The final x-position equation is similar to the initial, just replace the initial with final.
Speaker A
Also, the only value that changes is the x-position of the ball. The initial position was positive 108, but now the final position is negative 157.
Speaker A
That gives us 76.731 centimeters for the final x-position of the center of mass of the ball, canoe, and Mr. P system.
Speaker A
Mr. P: Remember our goal here is to determine the change in position of the center of mass of the system.
Speaker A
Change in, or delta, is always final minus initial. So it is 76.731 minus 92.179, which equals negative 15.448 or negative 15 centimeters with two significant digits.
Speaker A
In other words, the center of mass in the system moves 15 centimeters to the left relative to the system.
Speaker A
In order for the center of mass of the system to stay in the same location relative to the rest of the planet, the zero reference point of the system, the center of the canoe, needs to move 15 centimeters to the right
Speaker A
relative to the planet. As you can see in the video, our prediction matches the demonstration and again, THE PHYSICS WORKS!!
Speaker A
The physics works on a ha ha ha, the physics works... Bo: It's not my fault this time.
Speaker A
Bobby: I can still think you are completely responsible for this. Mr. P: The physics works! The physics works ha ha ha, the physics works! The physics works (snaps)!
Speaker A
Thank you very much for learning with me today. I enjoyed learning with you.
Topics:center of massNewton's lawsprojectile motionconservation of momentumphysics demonstrationcanoe and ballinternal and external forcesFlipping Physicsmass calculationsystem motion
