## If you had an object in an empty sphere with a radius of a few miles, surrounded…

#### If you had an object in an empty sphere with a radius of a few miles, surrounded by equally distributed and very concentrated mass, what effects of gravity would the object feel?

As long as the mass isn’t so concentrated that the laws of general relativity become important, the object won’t feel any gravity at all. The forces from opposite sides of the surrounding mass will cancel exactly. For example, if you were at the center of the earth in a large spherical opening, you would be perfectly weightless. The force from the north side of the earth would balance the force from the south side. This effect is quite remarkable and depends on the fact that gravity becomes weaker as the inverse square of the distance separating two objects. That way, even if you aren’t in the exact center of the earth, the forces still cancel.

## If you fire a bullet horizontally and drop an identical bull at the same moment,…

#### If you fire a bullet horizontally and drop an identical bull at the same moment, will they both hit the ground at the same time?

Yes. The fired bullet may travel farther, but it will fall just as quickly as the dropped bullet and they’ll hit the ground at the same moment. This effect explains why you must aim above the target when shooting at something far away. The faster the bullet travels to the target, the less it will drop. An arrow travels slowly enough that it will fall a considerable distance en route. You must aim quite high when shooting an arrow.

## If you dropped a bullet and at the same time, fired a bullet directly at the gro…

#### If you dropped a bullet and at the same time, fired a bullet directly at the ground, wouldn’t the bullet fired at the ground hit the ground first?

Sure it would. The fired bullet will only hit the ground at the same time as the dropped bullet if the fired bullet is shot exactly horizontally. If you fire the bullet at the ground, then it starts out with an enormous downward component to its velocity. The falling bullet doesn’t have this initial downward component to its velocity and never catches up.

## If you drop a penny from the Empire state building – could it really puncture a …

#### If you drop a penny from the Empire state building – could it really puncture a hole in a car because of its constant acceleration?

Probably not. If the penny were to fall sideways, so that it had as little air resistance as possible, it would reach about 280 km/h (175 mph). That speed ought to be enough to drive the penny into the car if its top were thin enough. However, studies have shown (see http://www.urbanlegends.com/science/penny_falling_impact.html) that coins tumble as they fall and experience substantial air resistance. As a result, you could probably catch a falling penny in your hand, although it might sting a bit. A falling ballpoint pen, because of its aerodynamic shape, is another matter.

## If the Space Shuttle is always falls toward the center of the earth, how does it…

#### If the Space Shuttle is always falls toward the center of the earth, how does it get to outer space? If something accelerates, doesn’t it go faster and thus have its speed increase?

The second question first: no, an object can accelerate without going faster. In fact, a stopping object is accelerating! If an accelerating object can speed up or slow down, it can certainly maintain a constant speed. If you swing a ball around in a circle on a string, that ball is accelerating all the time but its speed isn’t changing.

Now the first question: for the space shuttle to reach orbit, it needs an additional force in the upward direction. It obtains that force by pushing exhaust gas downward so that the exhaust gas pushes it upward. During the time when it’s heading toward orbit, it’s not falling because it has an extra upward force on it. However, the Space Shuttle can leave its orbit and head off into outer space by traveling faster than it normally does. It acquires this increased speed by firing its rocket engines again. Its usual speed keeps it traveling in a circle near the earth’s surface. If it went a bit faster, its path wouldn’t be bent downward as much and it would travel more in a straight line and away from the earth. It would still be falling toward the earth (meaning that it would still be accelerating toward the earth), but its inertia would carry it farther away from the earth. If the Shuttle had enough speed, it would travel to the depths of space before the earth had time to slow its escape and bring it back.

## If force causes only acceleration and not velocity, does a machine (i.e. an engi…

#### If force causes only acceleration and not velocity, does a machine (i.e. an engine) that causes a constant velocity in an adjacent object not exert a force?

If that adjacent object is free of any other forces, then no, the machine does not exert a force on it! This is a wonderful question, because it points toward many of the issues concerning energy and work. The bottom line is this: if some object is truly free moving (no other forces on it), it will move along at constant velocity without anything having to push on it. For example, if your car were truly free moving (no friction or air resistance), then it would coast forever on a level surface and the engine wouldn’t have to do anything. You could even put the car in neutral and turn off the engine. The only reason that you need an engine to keep pushing the car forward is because friction and air resistance push the car backwards.

## If a projectile released or hit at a 45° angle above horizontal should go th…

#### If a projectile released or hit at a 45° angle above horizontal should go the farthest, then why, in the game of golf, does the three iron (20° loft) hit a golf ball so much farther in the air than, say, a seven iron (approximately 45° loft) if the same technique and force are produced by the golfer? Is it backspin, shaft length, etc.?

It’s backspin! Air pushes the spinning ball upward and it flies downfield in much the same way as a glider. When you throw a glider for distance, you concentrate your efforts on making it move horizontally because the air will help to keep the glider from hitting the ground too soon. Similarly, the air holds the spinning golf ball up for a remarkably long time so that giving the ball lots of downfield speed is most important for its distance. That’s why a low-loft club like a three iron sends the ball so far.

## I don’t understand the relationship between mass, acceleration, and force in New…

#### I don’t understand the relationship between mass, acceleration, and force in Newton’s second law.

First off, force causes acceleration. The stronger that force, the more the acceleration. In fact, the two are exactly proportional to one another: double the force and you double the acceleration. Secondly, mass resists acceleration. The more mass an object has, the less it accelerates. The two are exactly inversely proportional to one another: double the mass and you halve the acceleration. These two ideas can be combined into one observation: the force you exert on an object is equal to the product of its mass times the acceleration it experiences. Look at that relationship: if you double the force you exert on an object, you double its acceleration, so that part checks out. If you double the object’s mass and leave the force unchanged, then the acceleration must be halved, so that part checks out. Thus Newton’s second law is simply a sensible relationship between the force you exert on an object, its mass, and its acceleration.

## I don’t understand the horizontal component of a ball thrown downfield. Does it …

#### I don’t understand the horizontal component of a ball thrown downfield. Does it have constant velocity and/or acceleration, even at the start?

Until you let go of the ball, you are in control of its velocity and acceleration. During that time, it does accelerate and its velocity isn’t constant. But as soon as you let go of the ball, everything changes. The ball’s motion in flight can be broken up into two parts: its vertical motion and its horizontal motion. Horizontally, the ball travels at a constant speed because there is nothing pushing or pulling on it horizontally (neglecting air resistance). Vertically, the ball accelerates downward at a constant rate because gravity is pulling down on it. Thus the ball travels steadily forward in the horizontal direction as it fall in the vertical direction. Of course, falling can begin with upward motion, which gradually diminishes and is replaced by downward motion.

## I can accept that weight is a force, but it doesn’t seem to follow common sense …

#### I can accept that weight is a force, but it doesn’t seem to follow common sense to me.

It would seem like a force if you had to lift yourself up ladder. Imagine carrying a friend up the ladder; you’d have to pull up on your friend the whole way. That’s because some other force (your friend’s weight) is pulling down on your friend. But when you think of weight as a measure of how much of you there is, then it doesn’t seem like a force. That’s where the relationship between mass and weight comes into play. Mass really is a measure of how much of you there is and, because mass and weight are proportional to one another, measuring weight is equivalent to measuring mass.