Constructing Physics

Elementary Physics Course Notes

Adam Johnston
Department of Physics
Weber State University

 

Gravitation

What happens when you drop something?  It falls down.  This is a nice feature of the world we live in.  Notice also that it falls at the same rate, always going faster and faster, no matter what the mass of the falling object is.  (This is weird, but something that we'll try to justify in our discussion of gravity.)  All things fall downwards accelerating at a rate of 10 m/s/s, or 32 ft/s/s.  We often refer to this rate of acceleration (usually 'a') as g.

You can see this with the ball machine III virtual demo.  (It is found on the projectile motion animation list.)  You can turn the air resistance on or off to see its effect.  Notice what the acceleration of gravity is, and how it does not change.

After this demonstration, Adam started scribbling a diagram on the board.  As students began to realize what was happening, their murmurs grew louder: "He's got to be kidding!  A cardboard box/elevator hanging by a thread?!  Surely he's kidding . . . "

But he wasn't.  Adam continued to describe and draw on the chalkboard the individual who travels up and down in a cardboard elevator.  Many different instances of motion were analyzed, varying both the velocity and the acceleration.  What we found was that the net force acting on the individual in the box was always in the same direction and proportional to the acceleration.  So, you could be moving upwards, but without any acceleration (change in velocity), no net force would be felt.  Or, you could be moving upwards but slowing down, signifying a downward acceleration, and thus making you feel "lighter" since there was a net force in the downward direction.  Adam even considered what would happen if the thread attached to the elevator broke.  We figured that the poor bloke in the box would feel "weightless," and Adam demonstrated this by tossing a can of water with a hole in it.  We noticed that the water never leaked while the can was accelerating downward (even if it was tossed upwards!) because the can and its water all accelerated at the same rate.  

"Wow," we said to ourselves.  "Now I know what will happen if I throw a holey can of water up into the air -- and I thought physics wouldn't apply to my everyday life," noted one astute student.

 

What about when an object is thrown?  In that case, it is both falling and moving from left to right at the same time.  If we look closely at left to right kinds of motion, we realize that it can continue without any outside forces, so without any acceleration.  (It would be a strange world if there were accelerations and forces that naturally happened to you from the left or right!)  So if an object is thrown, does its freefall motion and its left to right motion just simply get added together?  Or, does something more complicated happen?  Does an object's motion from left to right affect its rate of freefall?

To test this, we simultaneously dropped a ball and launched a ball (from the same height).  The ball that dropped hit the ground at exactly the same time that the ball which was launched from left to right hit the ground.  Therefore, it seems that the falling motion is consistent, independent of how an object moves from left to right.

You can see this for yourself with the ball machine II virtual demo.  (Set the initial angle to 0 degrees.)  It is found on the projectile motion animation list.

We used this principle to shoot at some falling objects, such as Squeeky the (blindfolded) Monkey.  Even though the target fell from his perch at the same time that a projectile was shot at him, because the projectile and the target fall at the same rate, they intersect at the same place at the same time. 

Don't believe it?  You can try a virtual demonstration in which you throw a banana at a monkey, in the projectile motion animation list.

 

 

 

later . . .

Adam was flippantly building solar systems and letting go of planets.  We all watched in horror as the Earth plunged into the flames of the Sun.  Numerous students would later report nightmares.  Everyone was quite shaken up.

Then we imagine a giant cannon, just like Newton himself imagined.  Placing the cannon on a round Earth, we see that shooting the projectile at faster velocities gets it to travel farther around the Earth.  If we were to fire it too fast, it would actually launch off the Earth.  But, if we fire it with just the right velocity, it's rate of fall will be exactly right to match the curvature of the Earth (at its given velocity), and it will maintain an orbit.

Adam began by tossing a ball up into the air again.  Pointing out (for something like the 435th time) that the ball always falls back down, Adam also revisited the issue of what the ball was doing at the top of its path.  While most could see that it must be stopped (v=0) at that instant, it is harder to prove that its acceleration still exists.  One way to do this, now that we have the tools, is to think of the gravity involved.  The gravitational force is still acting on the ball at the top of its path (and there are no other prominent forces), and Newton's second law says that where there is a net force, there must be an acceleration.  Unless you just turned gravity off (oh, wouldn't that be neat), the force is still there, so the ball must still be accelerating, even when it isn't moving.

 

 

Going 'round in circles

Author's note: We didn't dedicate an entire class period to this material, but there are similar treatments to our brief introduction of orbital motion. Don't panic if this doesn't look familiar.

The major focus of today's discussion was on freefall, projectiles, and the execution of Barney the Dinosaur  (Rated PG-13).  There were no small children in the audience, and most seemed to agree that the violent nature of the demonstrations were necessary.

Before this, however, we discussed a giant, hollowed out bagel.  What if this bagel were in the middle of space, where presumably there is no gravity?  (Is that really true?  We'll cover gravity in more detail during the next class session.)  To keep yourself upright (rather than floating around), you could get the bagel spinning at just the right rate.  If you are spinning with the bagel on its inside (standing on the outside wall), the bagel needs to accelerate you centripetally to keep you going around in circles.  Otherwise, you want to move in a straight path.  In order to do this, the "floor" of the bagel (the inside of the outside wall) must push on you towards the center of the bagel.  You feel a similar force by the floor right now.  So, gravity would be simulated inside this rotating bagel.  You stay in place for the same reason that the water in the bucket stayed in place (last lecture).

Everyone started getting hungry for bagels.

What happens when you drop something?  It falls down.  This is a nice feature of the world we live in.  Notice also that it falls at the same rate, always going faster and faster, no matter what the mass of the falling object is.  (This is weird, but something that we'll try to justify in our discussion of gravity.)  All things fall downwards accelerating at a rate of 10 m/s/s, or 32 ft/s/s.  We often refer to this rate of acceleration (usually 'a') as g.

You can see this with the ball machine III virtual demo.  (It is found on the projectile motion animation list.)  You can turn the air resistance on or off to see its effect.  Notice what the acceleration of gravity is, and how it does not change.

What about when an object is thrown?  In that case, it is both falling and moving from left to right at the same time.  If we look closely at left to right kinds of motion, we realize that it can continue without any outside forces, so without any acceleration.  (It would be a strange world if there were accelerations and forces that naturally happened to you from the left or right!)  So if an object is thrown, does its freefall motion and its left to right motion just simply get added together?  Or, does something more complicated happen?  Does an object's motion from left to right affect its rate of freefall?

To test this, we simultaneously dropped a ball and launched a ball (from the same height).  The ball that dropped hit the ground at exactly the same time that the ball which was launched from left to right hit the ground.  Therefore, it seems that the falling motion is consistent, independent of how an object moves from left to right.

You can see this for yourself with the ball machine II virtual demo.  (Set the initial angle to 0 degrees.)  It is found on the projectile motion animation list.

We used this principle to shoot at some falling objects.  These included Barney the Dinosaur and Squeeky the (blindfolded) Monkey.  Even though these targets fell from their perch at the same time that a projectile was shot at them, because the projectile and the target fall at the same rate, they intersect at the same place at the same time. 

Don't believe it?  You can try a virtual demonstration in which you throw a banana at a monkey, in the projectile motion animation list.

Have happy weekends, but please do not go shooting animals out of trees!