Newton s Laws of Motion

Transcription

1 Newton s Laws of Motion Background If you are driving your car at a constant speed when you put it in neutral and turn off the engine, it does not maintain a constant speed. If you stop pushing an object and simply let it go on its own, eventually it comes to a stop. So is ``being at rest" the natural state of motion of things? The problem is that in the cases described above, there is friction between the object and the road. Therefore, we really didn't leave the object alone. That is, we never removed all forces acting on the object, even if we thought we did. So, suppose that the car was moving over a truly frictionless road. If you can remove all forces acting on the car, so that no forces act on it after the engine is turned off, describe the motion of the car. In the next experiment, you will use a computer simulation of a spaceship in order to study an object that is in space, far from any large planets or stars to pull on it. You will be able to fire thrusters that exert forces on the spaceship. Procedure: 1. Find the file CanonicalSpaceship.jar that you saved on your computer and double-click to run it. When you do this, you should see the following window pop up.

2 2. This is called the control window. In the control window, click the Initialize button. Another window will pop up that looks like this: 3. We will call this the Animation Window. In the control window, notice that the Initialize button has disappeared and in its place is a Start button. Click the Start button. 4. Click on the animation window so that it has focus, meaning that the window has been selected and is the top-level window. 5. You are now ready to operate the spaceship. The spaceship has a right engine (F key), a left engine (D key), a top engine (K key), and a bottom engine (J key). At the beginning, the spaceship is at rest. 6. Make the spaceship speed up to the right by pressing and holding the D key for about 5 seconds (just count to 5 by saying ``one thousand 1, one thousand 2,..."). a. What direction is the force on the spaceship and how does the force affect the motion of the spaceship as the thruster is firing? b. What is the force on the spaceship after the thruster stopped firing? Describe the motion of the spaceship in this case.

3 7. The spaceship is now moving to the right. In what direction must a force be applied to the spaceship in order for it to slow down? 8. Press the F key for 10 seconds to fire a thruster that pushes to the left on the spaceship. Describe what you observe for the motion. 9. Fire the appropriate engine to make the spaceship come to a stop and remain stopped. Describe what is required to get the spaceship to stop. 10. Get the spaceship moving in any direction. Next, fire two opposite engines simultaneously. 11. What did you observe about the motion of the spaceship when opposite thrusters are firing simultaneously? 12. Write the most general statement possible that describes the motion of an object if there are no forces on the object. Your statement should be something like ``If there are no forces on an object, then..."

4 13. Two students are discussing the so-called natural state of things. Student 1: The natural state of things is to be at rest. If there are no forces on an object, then it will be at rest or at least eventually come to rest. Student 2: ``The natural state of things is to maintain their velocity. If there are no forces on an object, then it will either be at rest or will move in a straight line with a constant speed." Do you agree or disagree with each student? Explain. This simulation has allowed you the opportunity to see how an object would move in the absence of any resistive forces (friction, air resistance). Strange as it may seem, if an object is already moving, it will continue moving forever. It does not naturally run down and stop. This is what Newton s First Law tells us. When the spaceship was at rest and you fired one of the thrusters, you noticed that the spaceship s speed increased. This change in velocity is what we call acceleration. This is what Newton s Second Law tells us will happen. If a constant force is exerted on an object, that object will accelerate. That is the object s velocity will change. When you stop firing the thruster, there are no longer any forces acting on the ship. Therefore, the ship stops accelerating, meaning that it stops speeding up and just maintains its velocity as Newton s First Law tells us. Go to the control window and click the stop button. Click the New button. Click the Initialize button. Finally click the Start Button. Now, click on the animation window to give it focus. This puts the ship back in the center of the window at rest. What do you think would happen if you fire one thruster for a few seconds, and then, while continuing to hold that thruster down, you fire the opposite thruster? Will the ship continue to speed up, will it continue moving at a constant speed, or will it slow down? Give it a try.

5 These two forces cancel each other out. That is to say that having both forces acting at the same time is equivalent to having no forces acting on the ship at all. Note that, in this case, the ship just continues to move in a straight line at a constant speed, just as Newton s First Law tells us. It is not possible to see Newton s Third Law directly with this simulation. However, we can think about it somewhat indirectly. When you watch a rocket or space shuttle launch, you see hot gases escaping from the rocket downward. It can be natural to think that the rocket lifts off because the engine exhaust is pushing off the ground, in much the same way that you would jump upward using your feet to push off the ground. But, this is not what is happening. As you can tell in the simulation, when you fire a thruster, there is no ground for the gases to push off of, but the ship experiences a force. For example, when you press the D key, you see hot gases coming out of the left side of the ship. This causes the ship to accelerate to the right, which means there is a force acting to the right on the ship. What is causing this force? Down inside the thruster, as the fuel burns it produces rapidly expanding gases. This particular thruster is designed to have an opening on the left side, and so the gases are pushed out the opening to the left. As the thruster exerts a force on the gas to the left, the gas exerts an equal force on the thruster to the right (Newton s Third Law). This is the origin of the force that causes the ship to move to the right. This is the same principle as we saw in the video of the man sitting on the cart and throwing balls. The man pushed on the balls to the left, and the balls pushed back on the man to the right. It might be hard to think of a gas as being able to exert a force on the ship in the same way that a ball exerts a force on a person, but this is what happens.