Cases – Chapter 4
1.A one-wheeled cycle, or unicycle, is the ultimate in statically unstable vehicles.
a.Why does a unicycle always fall over when the rider doesn’t try to keep it upright?
b.To keep the unicycle from falling over, the rider continually tries to position the wheel so that the force the ground exerts on the wheel points toward a particular point. What is that point?
c.A person who is riding forward on a two-wheeled bicycle must lean left while making a turn toward the left. Does a person who is riding forward on a unicycle also have to lean left during a left turn?
d.While a unicycle doesn’t exhibit dynamic stability the way a two-wheeled bicycle does, there is a way to give it dynamic stability. If you spin the unicycle extremely rapidly about its vertical axis, it will act like a toy top and won’t fall over for a very long time. (Unfortunately, it’s hard to ride this way.) While gravity will exert a torque on this spinning unicycle about its point of contact with the ground, if its axis isn’t perfectly vertical, the unicycle doesn’t simply fall over. Instead, its axis of rotation changes directions. This behavior is an example of what?
2.While you usually consider the force of the earth’s gravity on you, you can also consider the force of your gravity on the earth. To do this, think of yourself as a very small planet. Since you’re a planet, you can consider things as being “near your surface.” But because your mass is relatively small, your gravity is extremely weak.
a.The only nearby object with a measurable weight near your surface is the earth. Explain why the earth has a substantial weight near you while other nearby objects do not.
b.What is the earth’s weight on your surface?
c.Imagine placing a scale on your surface and then placing the earth on top of that scale. Will the scale accurately report the earth’s weight near your surface? If not, what will it report?
d.If you suddenly push extra hard against the scale, it and the earth will begin to accelerate away from you, and you will accelerate away from them. As you push, will the scale read more, less, or the same as it did in c?
e.Which will accelerate more rapidly, the earth or you?
f.Suppose that you pushed hard enough that the earth and scale briefly left your surface completely (they stopped touching you). They will now begin to fall toward your surface. How will the acceleration due to gravity that they experience as they fall toward you compare to 9.8m/s2?
g.While the earth and scale are off your surface, will the scale read more, less, or the same as it did in c?
3.You are consulting for a screenwriter who is working on a science-fiction movie about the crew of a large, intergalactic spaceship. She wants the script to be realistic from a scientific perspective, so she has asked you to check her work so far. You read through the script, which includes descriptions of special effects, and quickly find several problems with it. Here are some of the scenes that have flaws.
a.In one scene, the spaceship must make an abrupt left turn to avoid hitting an asteroid. The crew members stand anxiously but motionlessly on the command bridge during this maneuver. In reality, what should happen to the crew members?
b.In another scene, a guard fires a projectile weapon at a massive alien creature. The guard remains stationary, but the creature is thrown backward by the weapon’s impact, even though the weapon doesn’t explode. In reality, what should happen to the guard as he fires the weapon?
c.The main spaceship carries several small fighter spacecraft that resemble high-tech modern military fighter aircraft. In the depths of space, these fighter spacecraft dodge and turn rapidly, even though the rocket exhaust is always sent straight out of the rear of each fighter. In reality, why couldn’t such spacecraft turn in space while similar looking aircraft can turn near the ground?
d.One small spacecraft secretly shuttles supplies from one earthlike planet to another, completing eight round trips without replenishing its chemical rocket fuel. You inform the writer that the spacecraft will barely be able to leave a planet even once using chemical rockets, unless that spacecraft is allowed to eject stages. Why are you right?
e.Near the end of the script, a main character falls from a cliff but is rescued only 2 m above the ground when she lands on the wing of a passing spacecraft. You inform the writer that the impact with the wing of the spacecraft would be just as fatal as one with the ground. Why is this the case?