Category: falling balls

What is the difference between mass and weight?

Mass is the measure of an object’s inertia. You have more mass than a book, meaning that you are harder to accelerate than a book. If you and the book were each inside boxes, mounted on wheels, I could quickly determine which box you were in. I would simply push on both boxes and see which one accelerated most easily. That box would contain the book and you would be in the box that’s hard to accelerate. Weight, on the other hand, is the amount of force that gravity (usually the earth’s gravity) exerts on an object. You weigh more than a book, meaning that the earth pulls downward on you harder than it does on the book. Again, I could figure out which box you were in by weighing the two boxes. You’d be in the heavier box. So mass and weight refer to very different characteristics of objects. They don’t even have the same units (mass is measured in kilograms, while weight is measured in newtons. But fortunately, there is a wonderful relationship between mass and weight: an object’s weight is exactly proportional to its mass. Because of this relationship, all objects fall at the same rate. Also, you can use a measurement of weight to determine an object’s mass. That’s what you do when you weigh yourself on a bathroom spring scale; you are trying to determine how much of you there is-your mass-but you are doing it by measuring how hard gravity is pulling on you—your weight.

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.

When you pushed the baseball and bowling ball with an equal force, the baseball went farther on the table because it has a smaller mass. If gravity also exerts an equal force on the 2 balls, like your push, then why do they fall at equal speeds?

The answer is that gravity doesn’t exert equal forces on the 2 balls! It pulls down harder on the bowling ball than it does on the baseball. Suppose the bowling ball has 10 times the mass of the baseball. Then gravity will also exert 10 times the force on the bowling ball that it exerts on the baseball. The result is that the bowling ball is able to keep up with the baseball! The bowling ball may resist acceleration more than the baseball, but the increased gravitational force the bowling ball experience exactly compensates.

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.

When you shoot a bullet straight upward, doesn’t it accelerate upward?

When you shoot a bullet upward, is does accelerate as long as it’s in the gun. The burning gases push upward on the bullet and it accelerates upward. But as soon as it leaves the gun, it’s a falling object, with the only force on it being gravity (and air resistance).

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.

When you throw a ball upward, what force pushes it upward?

To throw the ball upward, you temporarily push upward on it with a force greater than its weight. The result is that the ball has a net force (the sum of all forces on the ball) that is upward. The ball responds to this upward net force by accelerating upward. You continue to push upward on the ball for a while and then it leaves your hand. By that time, it’s traveling upward with a considerable velocity. But once it leaves your hand, it is in free fall. Nothing but gravity is pushing on it—it’s carried upward by its own inertia! In fact, it’s accelerating downward at 9.8 m/s^2. It rises for a while, but less and less quickly. Eventually it comes to a stop and then it begins to descend.

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.

While gravity supposedly makes all objects accelerate at the same rate, feathers do not seem to comply. What factors affect the feather’s acceleration, besides air resistance (which should affect all objects equally)?

Actually, air resistance doesn’t affect all objects equally. The feather has so much surface area that it pushes strongly on the air through which it moves and the air pushes back. For an object with very little mass and weight, the feather experiences an enormous amount of air resistance and has great difficulty moving through the air. That’s why it falls so slowly. If you were to pack a feather into a tiny pellet, it would then fall just about as fast as other objects. Similarly, you fall much more slowly when your parachute is opened because it then interacts with the air much more effectively.

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.