White water rafting is a popular summer activity.
1. The large rapids in a river usually occur in its narrowest sections. Compare the speed of the water in a wide section of the river to the speed in a narrow section.
Answer: The water will move faster through the narrow section.
Why: Since the same amount of water must flow through both sections of the river in a given time, the water must flow quickly through the narrow section.
2. In slow moving sections of the river you might decide to paddle to propel the raft forward. When you stop paddling the raft will quickly slow down to match the speed of the water. Why?
Answer: The drag forces of the water on the raft will slow it down.
Why: The drag forces, whether viscous or pressure, oppose an objects motion. When the motion (in this case the relative motion of the water and the raft) stops the drag forces are zero.
3. If there is a strong wind blowing up the canyon in which you are rafting your boat may actually stop moving forward. In this case there are four forces acting on the raft, which perfectly balance to keep the boat stationary. What are the four forces?
Answer: The forces are gravity, the buoyant force, the drag force of the water on the raft, and the drag force of the air on the raft.
Why: The forces of gravity and buoyancy cancel each other and the drag of the water, pointing downstream, cancels the drag force of the wind pointing upstream.
As you drive down the road in your car, it experiences many forces from the air around it. In answering the following questions assume that your car experiences no internal frictional forces to slow it down.
4. If you are driving very slowly so that the flow of air around your car is laminar your car will still slow down if you coast along a flat horizontal section of road. Why?
Answer: The air will provide a viscous drag force that opposes the direction of your motion.
Why: This force is very much like the force of sliding friction. The air near your car wants to move at the same speed as you car, whereas the air far from your car wants to remain stationary. As the layers of air in between these two regions slide past one another the air molecules bump into each other more than they would have if the layers were not sliding past one another. This wastes energy much like sliding friction does.
5. If you are coasting down a hill your car will eventually settle in at a constant velocity. How does the drag force compare to the car's weight?
Answer: The drag force is less than the car's weight.
Why: The support force of the road, which points normal to the road's sloping surface, cancels some of the car's weight. Only the portion of the car's weight that points along the road's slope is canceled by the drag force.
6. If you speed up so that the airflow around your car is no longer laminar, how does the pressure at the front of your car compare to the pressure at the back?
Answer: The pressure at the front of the car is higher than the pressure at the back.
Why: A turbulent wake will form at the back of the car where the pressure is lower. If you are driving in a snowstorm this turbulent wake becomes apparent in the erratically swirling motion of the snowflakes behind your car.
7. If you are driving fast enough that the airflow around you car is not laminar, your car will tend to get worse gas mileage if you drive faster than if you drive slower. Why?
Answer: The pressure drag force that your car experiences increases rapidly as your speed increases.
Why: As you drive faster, the pressure in front of your car gets larger. The turbulent wake behind your car also gets bigger producing a larger region of low pressure. Overall the force due to this imbalance in pressure gets larger so you must put in more energy to continue moving at this high speed.
8. Again assuming that the airflow around you car is not laminar, your car will tend to get worse gas mileage if you have a large pile of luggage strapped to the top than if there is nothing on you luggage rack. Why?
Answer: The pressure drag force increases as the cross-sectional area of the turbulent air pocket increases. Since the cross-sectional area of the car is larger with luggage than without, the turbulent air pocket will also be larger.
Why: An aerodynamically designed car top carrier may minimize the effects of pressure drag, but even this carrier experiences viscous drag.