DiscoverHover CURRICULUM GUIDE #7
NEWTON’S LAWS OF MOTION
© 2004 World Hovercraft Organization

Now that we understand how to measure the motion of a hovercraft, we can begin to investigate why hovercraft move as they do. Three of the most fundamental laws of motion, are Newton’s Laws of Motion, named after Sir Isaac Newton. Although they were formulated hundreds of years ago, these Laws work so well that they are still widely used to calculate the motion of everything from hovercraft traveling over a surface to planets traveling through space.

Sir Isaac Newton
1642 – 1727

Newton’s First Law, often called the Law of Inertia, states the following:

An object in motion tends to stay in motion, and an object at rest tends to stay at rest unless acted upon by an outside force.

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An object with no net force acting on it will move at a constant velocity (which may be zero).

This means that when an object is moving, it should keep on moving at the same speed and in the same direction unless some outside force is acting upon it. It also means that an object at rest (not moving) will stay at rest until some force causes it to start moving. If you’ve ever seen a video of astronauts in space, this law makes more sense. The astronauts can float without moving because there is no net force acting upon them. If they push off the wall of the space ship, they will float away at a constant speed and direction and won’t stop until they collide with or push off something else.

This law is often called the Law of Inertia, because it describes inertia, which is the term used to denote the tendency of a body to remain either at rest or in constant motion until acted upon by an outside force. This law is only valid in an inertial frame of reference. The acceleration of a body is always measured from a certain reference frame; if the object is in a frame that is accelerating relative to the frame in which the measurement is taking place, then the frame is not considered an inertial frame. For example, if a passenger in a hovercraft that is increasing in speed measures the acceleration of an object sitting on the seat of the hovercraft, the measured acceleration will be zero. However, if a person standing on the shore observes the same object, it will seem to be accelerating, even though the net force acting upon it in its frame of reference (the hovercraft) is zero.

In order to understand how an object will move, you need only know what forces are acting upon it. Let’s describe some of the most common forces. The first is a force that has been acting upon you your entire life: gravity. Earth’s gravity constantly pulls you down toward the center of the earth. When you jump into the air, you exert a force that pushes you up from the ground. Since this force is greater than gravity, you’re propelled upward. Once you’re in the air, gravity becomes the only force acting upon you and pulls you back down.

A second familiar force is contact force. When two objects are touching each other, they exert a contact force. When you push or throw something, you exert a contact force upon it. Think again of jumping: after you jump into the air and begin to fall back down due to gravity, the Law of Inertia says that you should continue that downward motion. If gravity had its way you’d keep falling toward the center of the earth, but you stop when you hit the ground because the ground exerts a contact force upon you. When you’re standing on the ground, Earth’s gravitational force pulls you down, but the ground exerts a contact that pushes you up. These two forces have the same magnitude, or strength, but act in opposite directions, so they cancel each other out. Even though both of these forces continue to act upon you, there is no net force because they cancel each other out. The term ‘net force’ refers to the directional sum of all the forces. When two forces act in the same direction, they add together. When they act in the opposite direction, one is subtracted from the other. If two forces that are equal in strength act in opposite directions, they cancel each other out completely.

A third force you constantly encounter, but may not realize, is friction. Friction is a force that opposes motion between two objects in contact. If you push a box across a floor and then stop pushing, it will slide for awhile but soon come to a stop because friction opposes the motion between the box and the floor. If you go to a skating rink and push the box across the ice, it will slide further because there is less friction between the box and the ice. It will still eventually come to a stop. Sometimes friction is a very useful force — walking would be impossible if there were no friction between the ground and the feet. You could jump up and down all you wanted, but there would be no way for you to move anywhere without anything against which to push. Often, though, friction works against people's goals, and new lubricants and other technologies are developed to minimize the effects of friction. Hovercraft, in fact, were invented as a way of reducing this sliding friction. Another form of friction is wind resistance. If you stick your hand out of a fast moving hovercraft, you feel a force pushing your hand back. This is caused by wind resistance, the friction between your hand and the air it’s moving through. Hovercraft are designed to have so little friction as they move that, when you stick your hand out to the side of the hovercraft, something interesting happens: the small amount of wind resistance on your hand is enough to make the hovercraft turn in that direction!

Until Newton presented his laws in 1686, most philosophers accepted the theory developed by the Greek philosopher Aristotle, which claimed that it was the natural state of objects to be at rest, and that unless a force acted upon an object, the object would slow down gradually until it came to rest. However, it was noted that on slippery surfaces, objects slowed down much more slowly. Newton eventually took this trend to its logical conclusion and found that in an environment lacking any slowing influences, an object would keep moving steadily in a straight line until an outside force caused it to do otherwise.

We now have a better concept of what forces are, and we know from Newton’s First Law that if there is no net force on an object, its velocity doesn’t change. Exactly how the velocity changes if there is a net force acting upon the object is described by Newton’s Second Law, which is most easily stated with the following formula:

F = m × a

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Force = Mass × Acceleration

Any time a net force acts upon an object, that object will accelerate. Newton’s Second Law also states that more massive objects require more force to achieve the same acceleration as less massive objects. This is why you have to push harder to move a large hovercraft than a smaller one.

Given what we know about velocity and acceleration, Newton’s Second Law agrees with his first law. The equation for the Second Law states that a force leads to an acceleration, therefore, if no net force is acting on an object, that object will not be accelerated. No acceleration means that the velocity doesn’t change, so it follows that no force equals constant velocity … just as the First Law states. From this it may appear that the First Law is merely a special case of the Second Law, therefore unnecessary, but keep in mind that the First Law also serves to define an inertial frame of reference.

Knowing the relationship between force and acceleration means we can clear up one of the most common misconceptions in all of science: the relationship between mass and weight. It’s very common to believe that kilograms are just the SI (System International) equivalent of pounds and vice versa, but this isn’t the case. The pound is a measure of weight in the Imperial unit system, and its equivalent in SI is the Newton, named after Sir Isaac Newton. Weight is actually a measure of the force that gravity exerts on an object. The kilogram is a unit of mass in SI. Although rarely used, the unit for mass in the Imperial system is called a slug. Refer to the unit conversion sheet to see exactly how these units are related.

The pound is therefore a measure of force exerted by gravity while the kilogram is a measure of the mass of an object. When you convert between pounds and kilograms, you’re essentially using Newton’s Second Law. We can easily convert because of the manner in which gravity acts. On Earth, gravity acts to accelerate all objects the same, regardless of their mass. If you drop a bowling ball and a pebble from a bridge, they will hit the bottom at the same time because gravity accelerates them the same. This point was illustrated in 1971, when Apollo 15 Commander David Scott dropped a hammer and a feather at the same time. Since there is no air on the Moon to slow down the feather, both objects fell at the same speed and hit the ground at the same time. If acceleration is constant for all masses and forces, then you can easily interchange between the two. Keep in mind, however, that mass and weight are different concepts. If you’ve seen a video of astronauts on the moon you’ve noticed that they seem to weigh very little as they almost float around on the surface of the moon. This happens because they really do weigh less on the moon than on the Earth. Their mass, on the other hand, stays exactly the same.

We can now conclude with Newton’s Third Law, which states:

For every action there is an opposite and equal reaction.

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When one body exerts a force on another, the body acted upon always exerts a force equal in magnitude and opposite in direction to the first force.

This means that for every force that is exerted on an object, the object exerts back an equal force in the opposite direction. This can be demonstrated with two hovercraft. If a larger hovercraft collides with a DiscoverHover One, it will exert a force on the DiscoverHover craft, causing it to accelerate away. At the same time, the DiscoverHover One will exert an equal amount of force on the larger hovercraft in the opposite direction, which causes the larger hovercraft to decelerate. Essentially this means that all forces exist in pairs. If you push against a wall, the wall pushes back. If you bang your head against a wall, you’re exerting a force on the wall. Keep doing this and the headache you’ll get will demonstrate the wall’s force exerting back on you! When a rifle is fired from a stationary hovercraft it forces the bullet forward, but the bullet, in turn, pushes back on the rifle, which pushes through your body and accelerates the hovercraft backward. You can see this in the way the gun recoils after a shot, and you can feel it in your shoulder. It may be difficult to believe, but gravity acts in the same way. The Earth pulls you with a force due to your mass, but you also gravitationally pull back on the Earth with the same force. However, the Earth doesn’t really notice this; in accord with Newton’s Second Law, its mass is so huge that the Earth’s acceleration caused by your gravitational pull is very small.

Quiz Question:

1. If the thrust exerted by your DiscoverHover One hovercraft is 180 N [40.5 lb force] and it’s mass is 125 kg [8.57 slugs], at what rate will your hovercraft accelerate?

Continue to Experiment 6.1