One way of measuring a person's body fat content is by "weighing" them under water. This works because fat tends to float on water, it is less dense than water, while muscle and bone tend to sink, they are more dense. Knowing your "weight" under water as well as your real weight out of water, the percentage of your body's volume that is made up of fat can easily be estimated. This is only an estimate since it assumes that your body is made up of only two substances, fat (low density) and everything else (high density). Compare the "weight" measured by an underwater scale under the following circumstances. Quotes are placed around weight to indicate that the measurement read on the scale is not your true weight, the force applied to your body by gravity, but a measurement of the net downward force on the scale.
1. If a large percentage of your body's volume were fat compared to a small percentage?
Answer: The underwater "weight" would be less if the person's body contained more fat.
Why: By increasing the relative volume of fat the average density of a person goes down so the buoyant force is larger and cancels more of the gravitational force.
2. If you were fully immersed in the water compared to being partially immersed?
Answer: You would "weigh" more if you were only partially immersed.
Why: The buoyant force is equal to the weight of the volume of fluid displaced. With less fluid displaced the buoyant force is also less.
3. If you were fully immersed at the shallow end of a pool compared to being fully immersed at the deep end?
Answer: You would "weigh" the same amount.
Why: Since liquids are incompressible you will displace the same amount of water (you will not be compressed by the increased pressure at the deep end), and this water will weigh the same amount (it will have the same density), so the buoyant force will be the same.
4. If your lungs were full of air compared to when all of the air has been blown out of your lungs?
Answer: If your lungs were full of air you would "weigh" less.
Why: Air has a much lower density than anything else in your body does so the buoyant force would be greater. In fact, you may even float on the surface of the water and not be able to "weigh" yourself at all.
5. Salt water is more dense than fresh water. Would you "weigh" more if you were fully immersed in salt water or fresh water?
Answer: You would "weigh" less in salt water than in fresh water.
Why: You would displace the same volume of fluid if immersed in salt water, but that fluid would weigh more since it has a higher density. This would lead to a larger buoyant force.
The brakes on most cars make use of a hydraulic system to transfer the force applied by your foot at the brake pedal to the brake pads at the car's wheels, which slow you down. The hydraulic system consists of a fluid filled tube connected at both ends to pistons. The piston at one end is attached to the brake pedal and the piston at the other end is attached to the brake pad. When the brakes are applied the brake pad, which is fixed relative to the car's body, pushes against a disk (the rotor) that spins with the wheel. The sliding friction between the brake pad and the disk slows the car down.
6. Why is the fluid used to fill such a hydraulic system a liquid rather than a gas?
Answer: Liquids are incompressible, while gases are compressible.
Why: If a compressible fluid were used then much of the work you do in pushing on the brake pedal would go into compressing the gas rather than pushing the piston on the other end.
7. When you push on the brake pedal what happens to the pressure of the hydraulic fluid?
Answer: The pressure increases.
Why: As the brake pedal moved down under your foot it pushes on the piston and starts the fluid moving. This requires a higher pressure near the brake pedal than at the other end of the line. Since the liquid in the brake lines is incompressible, the piston attached to the brake pad also begins to move. Now the pressure inside the line is constant; the fluid moves along at a constant velocity. Once the pad presses against the rotor there is another acceleration which causes the pad to stop moving. This acceleration required the pressure near the pad to be higher than the pressure near the pedal. Once both the pedal and the pad have stopped moving the pressure is again constant throughout the fluid, but can be quite high since it is being pushed on from both ends of the line.
8. The sliding friction between the brake pad and the disk slows the car down. Where does the car's kinetic energy go in this process? Assume you are driving on a flat horizontal stretch of road.
Answer: The sliding friction between the pad and the disk cause both to heat up. Most of the energy is converted into this heat.
Why: Some energy will also be removed by air resistance and you may even be able to hear the brakes indicating that energy is being used to make noise.