Why do two objects of unequal mass fall and hit the ground at the same time?

Why do two objects of unequal mass fall and hit the ground at the same time?

If one object has twice the mass of the other, then it is twice as hard to accelerate. To make it keep pace with the other ball, it must experience twice the force. Fortunately, gravity pulls on it twice as hard (it has twice the weight of the other ball), so in falling, it does keep pace with the other ball. The two fall together. Just for fun, imagine stepping off the high diving board with two friends. The three of you have essentially identical masses and weights and also fall at the same rate. Now imagine that two of you hold hands as you fall. You are now a single object with twice the mass of your other friend. Nonetheless, you still fall at the same rate. So an object with twice the mass of another falls at the same rate as that other object.

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.

Is it possible for a ball to fall to earth at a different angle from the one at …

Is it possible for a ball to fall to earth at a different angle from the one at which it rose?

If the ground is level and there were no air resistance, the answer would be no. The flight of the ball is perfectly symmetric. It rises to a maximum height in a parabolic arc and then returns to the ground as the continuation of that same parabolic arc.

However, if the ground isn’t level, then the angle it hits the ground at might be different. For example, if you toss a ball almost horizontally off a cliff, it will hit the ground almost vertically. Horizontal and vertical are two very different directions.

Air resistance also tends to slow a ball’s motion and it’s particularly effective at stopping the downfield component of its velocity. Gravity makes sure that the ball descends quickly, but there is no force to keep the ball moving downfield against air resistance. The result is that balls tend to drop more sharply toward the ground. When you hit a baseball into the outfield, it may leave your bat at a shallow angle but it will drop pretty vertically toward the person catching it.

Finally, if the ball is spinning, it can obtain special forces from the air called lift forces. These forces can deflect its path in complicated ways and are responsible for curve balls in baseball, slices and hooks in golf, and topspin effects in tennis.

Why do you feel no acceleration in free fall, even though you are accelerating?

Why do you feel no acceleration in free fall, even though you are accelerating?

This wonderful question has many answers. The first, and most direct, is that you do feel the acceleration. You feel an upward fictitious force (not a real force at all, but an effect of inertia) that exactly balances your downward weight. The feeling you experiences is “weightlessness.” That’s why your stomach feels so funny. You’re used to having it pulled downward by gravity but the effect of your fall is to make it feel weightless.

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.