Lesson - Space Ship Pilot

Lesson Outline:

• Newton's First Law
• Velocity and Acceleration
• Newton's Second Law
• Motion in 2 Dimensions
• Vectors

Newton's first law states that an object in motion tends to remain in motion, unless acted on by an external force. This tends to be at odds with our everyday experience of reality, in which when we stop pushing something, it slows down. What is often not as obvious to us is the number of external forces that can act on an object. Dissipative forces such as air resistance and friction can slow a body, without it being obvious to the observer that there are forces actually at work.

Without any external force, an object just moves at its current speed. If it is sitting still, it continues to sit still. If it is moving, it continues moving at the same speed and in the same direction.

Something else which is not obvious is the how acceleration and velocity are related. Velocity is the speed and direction of motion. Acceleration is the rate at which that velocity changes. If I push a book across a desk at a constant speed, I am applying a force, and the book moves with a constant velocity, so doesn't that violate Newton's first law? Once again, we have to consider that sometimes there are more forces acting than we realize. In the case of pushing your book across a table, you push the book, but the friction between the book and the table pushes back. If the force that you apply is greater than the frictional force, the book speeds up, or accelerates. Remember, acceleration is the rate at which velocity changes, so slowing down and changing direction are also example of acceleration.

So, the force that is applied changes the velocity, but does not directly determine the velocity. This is expressed by Newton's second law which says, in effect, that when you push something you make the velocity change. The exact way of saying it is that the acceleration (a) produced by a given force (F) on a mass (m) is given by F=ma.*

Acceleration and velocity are easy for a drag car racer, with the only things to consider being speeding up and slowing down. For the rest of us, we have to deal with more than one direction. When dealing with motion in 2 dimensions, we can either give magnitude and direction, or we can give the magnitude along pre-specified directions, such as along the x and y axis.

Exploration Activity:

To consider an example of a situation in which there would be no external forces, we have to remove air resistance, friction, and even gravity. Consider a spaceship far from our planet, trying to dock with a space station. An applet of this model is provided for you here. The only force that acts on the ship is the ship's thruster, and we can see what happens as we apply and remove a force on the ship.

As we apply a force, the ship has a resultant acceleration, which according to Newton's second law, is exactly proportional to the force applied.

Exercises:

0. Accelerate the ship in one direction. Now slow the ship down to a halt. What direction did you have to accelerate the object in order to slow the ship down?
1. Is it possible to bring the ship to a halt using any other direction of acceleration other than what you found in exercise 1?
2. Accelerate the ship in one direction. What happens when you change the acceleration by 90 degrees? (i.e. start off moving forward, then accelerate directly to the left of the screen)
3. In question 3, when you change the acceleration so that the ships thrusters are moving it left, does the speed at which the ship approached the top or bottom of the screen change?
4. Get the ship moving, and turn the thrusters off. Does the ship slow to a stop?
5. Answer the following questions true or false:
1. Velocity and acceleration are always in the same direction
2. The velocity is proportional to the force that is applied to an object.
3. Accelerating an object produces a change in the velocity.
4. Accelerating an object speeds the object up.
5. When the applied force on an object ceases, the motion of the object ceases.
6. Satellites orbiting the Earth have no air resistance or friction to slow them down, but they do not travel in a straight line path, instead they circle around the Earth. How can you explain this in terms of Newton's first law?

*Remember that when a variable in Physics is boldfaced, it means that the variable represents a vector, that is, the object has both a magnitude and a direction associated with it. Sometimes you will see this written as a right-pointing arrow positioned above the variable instead.