DiscoverHover CURRICULUM GUIDE #9
MOMENTUM
© 2005 World Hovercraft Organization

When a hovercraft turns, it continues to travel in the same direction for a while before it finally changes direction. This is due to its momentum. Momentum is defined as the mass of an object multiplied by its velocity.

Momentum = Mass × Velocity

Newton’s First Law states that an object in motion tends to stay in motion. The momentum of an object is a way to describe just how much the object tries to stay in motion. Let’s say there are three objects coming toward you, and you have to try to stop them. The first is an empty shopping cart rolling at 8 km/hr [4.97 mph], the second is a small DiscoverHover hovercraft traveling at 8 km/hr [4.97 mph], and the third is an identical small hovercraft traveling at 80 km/hr [49.7 mph]. If we calculate the momentum of each one, the shopping cart would have the least momentum because it has the lowest mass times velocity. The 8 km/hr [4.97 mph] DiscoverHover craft would be second, and the hovercraft going 80 km/hr [49.7 mph] would have the greatest momentum. We can imagine that the shopping cart would be easy to stop. Stopping the hovercraft going 8 km/hr [4.97 mph] would be much harder, but we could probably get it stopped after pushing it for a while. It’s safe to say that the hovercraft going 80 km/hr [49.7 mph], however, would push you out of its way!

Newton’s First Law can now be rewritten to say the following: An object’s momentum tends to stay the same. Remember that velocity is a measure of both speed and direction, so when the object’s momentum tries to stay the same, its velocity tries to stay the same. This means that the direction of travel also tries to stay the same. This explains why the DiscoverHover hovercraft initially keeps going in the old direction when you try to turn it. Its momentum is carrying it in the old direction and wants to keep it going in the old direction. Only after exerting enough thrust to push it in the new direction will the momentum finally change.

Figure 9-1: Turning hovercraft
Image ©2005 DiscoverHover

Rewrite Newton’s Second Law using momentum. Remember that Newton’s Second Law states that:

Force = Mass × Acceleration.

It was stated earlier that acceleration can be defined as a change in velocity, so we restate Newton’s Second Law:

Force = Mass × Rate of change of Velocity

Since momentum is mass times velocity, let’s go one step further:

Force = Rate of change of Momentum

Any time we want to change an object’s momentum, we have to exert a force on it. The greater the change, the more force is required.

So far we’ve rewritten Newton’s First and Second Laws to include momentum. If we do the same with Newton’s Third Law, the result is known as the Law of Conservation of Momentum. Remember that Newton’s Third Law states that for any action there is an equal and opposite reaction. This also means that for any force, there is an equal force acting in the opposite direction. Since we know that forces lead to changes in momentum, we can also say that changing the momentum of one object means that the momentum of a neighboring object will change by an opposite amount.

Imagine a DiscoverHover hovercraft moving toward a second hovercraft that is stationary. The first hovercraft has momentum as it travels toward the other, but the second hovercraft isn’t moving, so it has no momentum. After they collide, the momentum of the second hovercraft is increased as it moves away, but the momentum of the first is decreased as it slows down or even stops. During the collision, the momenta of both hovercraft change. If you add the momenta of the two hovercraft before and after the collision, you’ll find that the total momentum doesn’t change during the collision. The second hovercraft’s momentum increases by the same amount that the first hovercraft’s momentum decreases. The momentum of the system, or everything involved in the collision, remains the same. This is what is meant by Conservation of Momentum.

Figure 9-2: Turning hovercraft
Image ©2005 DiscoverHover

As a hovercraft turns, the momentum of the hovercraft is changing. The Law of Conservation of Momentum says that the total momentum of everything involved in the system stays constant. Can you think of what else is changing its momentum in order to balance the hovercraft’s change in momentum? Remember that in a turn, the rudders change the direction of the airflow blowing out behind the hovercraft. The rudders are essentially changing the momentum of the air. When you add the change in momentum of the air to the change in momentum of the hovercraft, the total momentum again stays the same.

When turning in a hovercraft, you often feel a force that pulls you toward the outside of the turn. Although this outward pull is often called centrifugal force, it’s actually not a force at all. It is the Law of Inertia at work. Remember that an object in motion tends to stay in motion. When the hovercraft turns, your body wants to keep going straight. Refer to the diagram of the hovercraft on a tether spinning around in a circle. The inertia of the hovercraft tries to make the hovercraft travel in a straight line, but the tether pulls on the hovercraft, making it travel in a circle. The inward force on the hovercraft due to the tension in the tether is called centripetal force. A constant centripetal force keeps the hovercraft traveling in a circle. If the string were to break, the hovercraft would instantly start to travel in a straight line according to the Law of Inertia.

Figure 9-3: Centripetal force
Image ©2005 DiscoverHover

The same thing occurs when riding in a hovercraft as it goes around a curve. Instead of the tension in the string, part of the thrust, supplemented by the friction between the skirt and the surface, provides the centripetal force that pushes the hovercraft around the curve. Your body, however, wants to continue traveling in a straight line. Although it seems like your body is being pushed to the outside of the hovercraft, it is actually the hovercraft being pushed inward while you try to continue traveling straight. This is why the outward centrifugal force doesn’t really exist. The wall of the hovercraft must push against you in order to accelerate you around the turn with the hovercraft.

In a hovercraft, there isn’t enough friction between the craft and the surface it’s hovering over to provide the centripetal force necessary to turn it in the same way an automobile turns. The centripetal force must instead be provided by directing the hovercraft’s thrust partially toward the inside of the curve. This is why in the pictures of the turning hovercraft, they appear to be moving sideways. The hovercraft must turn toward the inside of the curve and use its thrust to provide the centripetal force necessary to push it around a curve. This is called vector thrust. Some of the thrust is used to keep the hovercraft moving while the remainder is used to turn the craft or to overcome the craft’s tendency to continue in a straight line. Also, the pilot of a turning hovercraft will often try to bank or roll the hovercraft into a turn. Since the cushion pressure exerts a force on the underside of the hovercraft, the tilt on the underside results in a tilt in the force. One component of this force acts in the direction of the turn.

Figure 9-4: Cushion Pressure Provides Turning Force
Image ©2005 DiscoverHover

Quiz Questions.

1. What are the sources of the centripetal force when you turn the hovercraft?
2. If centripetal force is given by m × v² / r, where m is the mass, v is the velocity of the hovercraft and r is the turning radius of the hovercraft, calculate the turning radius of the hovercraft with centripetal force equal to 900 N [202.3 lb], mass equal to 145 kg [9.94 slugs] and a speed of 9 m/s [29.5 ft/s] during the turn.

Answers are in the Answer Key