Month: January 2015

How can you calculate the position of a falling ball?

Lou Bloomfield Leave a comment

When you drop a ball, its position changes in a complicated way. How would you calculate that position?

When you drop a ball, its altitude decreases by larger and larger increments as the seconds pass. If we call the altitude from which you drop it zero, then its altitude after 1 second is -4.9 m (-4.9 meters or about -16 feet), after 2 seconds is -19.6 m, and after 3 seconds is – 44.1 m. Here is one way to calculate those values.

First, note that the ball is accelerating downward steadily at 9.8 m/s2. The ball’s initial velocity was zero, so its velocity after falling for time t is 9.8 m/s2 * t downward.

Next, let’s find the ball’s average velocity while falling for time t. The ball’s velocity has been changing steadily from 0 when you dropped it to 9.8 m/s2 * t downward after falling for time t, so it’s average velocity is simply the average of those two individual values: 0 and 9.8 m/s2 * t downward. That average is 4.9 m/s2 downward.

Lastly, let’s determine how far downward the ball has traveled after falling for time t. Since it’s average velocity was 4.9 m/s2 * t downward and it has traveled for time t with that average velocity, its change in position is 4.9 m/s2 * t downward * t or simply 4.9 m/s2 * t2 downward. As you can see, its change in position is proportional to the square of its fall time t. With each passing second, it is moving downward faster and covering more distance. As stated above, its altitude after 1 second of falling is -4.9 m, after 2 seconds of falling is -19.6 m, and after 3 seconds of falling is -44.1 m.

If an object is moving, how could nothing be pushing on it?

Lou Bloomfield Leave a comment

How can an object with a constant velocity have zero net force acting on it? The object is moving, so how could nothing be pushing on it?

This important question is addressed by the concept and the observation of inertia. An object that is free of all external forces continues moving as it was. You don’t have to push on something to keep it moving. That is its nature. Left to itself, an object that’s moving will keep moving in a straight line at a steady pace. That’s ultimately the observation that’s called Newton’s first law of motion. Forces, therefore, don’t cause velocity. Velocity is a matter of history; if an object was already moving that’s what it’s going to tend to keep doing.

What forces cause are changes in velocity. In other words, they cause accelerations. So, if an object happens to be, at the point you are paying attention, moving to your right, at some particular velocity, in the absence of any pushes, that’s what it’s going to keep doing. That is its nature. That’s the observation of behaviors in our universe, without exception. The velocity they have is the velocity they keep. You don’t have to push on them to keep them moving; they do that for free. You have to push on them to bring them to a stop, to speed them up, or to change their direction.

 

Why do objects bounce when they fall on the floor?

Lou Bloomfield Leave a comment

Why do objects bounce when they fall on the floor? Does the floor push back up when an object hits it?

The answer is yes, the floor pushes up on the object and that causes the object to bounce. The floor and the object can’t occupy the same space at the same time, so they push each other away when they collide. The object pushes down on the floor and the floor pushes up on the object. Now, the object’s downward force on the floor affects the floor and may cause the floor to vibrate and has lingering influences on the rest of the room. But the floor’s push on the object affect the object and reverses its motion so that from going downward prior to the impact, the object ends up going upward after the impact.

For example, this baseball bounces on the table. When it hits the table, the ball and the table push on each other. Again, they can’t occupy the same space at the same time. So the ball pushes down on the table and that affects the table and the rest of the room. But the table pushes up on the ball and that upward push on the ball causes the ball to accelerate upward. It goes from heading downward, its velocity was downward and maybe even pretty fast, and that upward acceleration changes the velocity such that the ball ends up with an upward velocity, not all that big because baseballs don’t bounce very well. But that result comes from the upward push of the table on the ball.

So, objects bounce because, when they hit each other, they can’t occupy the same space; they push each other apart. Those two outward forces, one on each object, one on the object hitting the floor, for example, and one on the floor, they push each other apart and that causes the bouncing effects.

As a skater changes direction, is the skater accelerating?

Lou Bloomfield Leave a comment

When a skater changes direction, so that the skater’s velocity changes as a vector quantity, is the skater accelerating?

 Yes. Any change in a skater’s velocity involves an acceleration because acceleration is the change in velocity with time. So, if a skater is speeding up or slowing down, then it’s clear that the velocity changes because the speed part, the amount part a velocity, is changing. But when the skater’s velocity changes direction, so the skater is turning, even though the skater is traveling at the same speed, the skater is still undergoing acceleration and that acceleration still involves a net force on the skater, pushing the skater and bending the skater’s path.

How do you determine how much force you need to create a particular acceleration?

Lou Bloomfield Leave a comment

How do you determine how much force you need to create a particular acceleration?

The answer to that question is Newton’s second law of motion. That law relates the force you exert on an object, divided by the object’s mass, to the resulting acceleration of the object. For example, if I take this baseball, and I neglect all the other forces except for my force on it. So, for example, if we went out into deep space where there wasn’t gravity and there wasn’t air and life was simple, if I exert a force on the baseball. Well, we take that force, my force on the baseball, and divide it by the baseball’s mass, that ratio will tell us exactly how the baseball will accelerate. The baseball will undergo an acceleration that’s in the same direction as the force and that has the amount equal to the force I exert divided by the baseball’s mass.

The baseball has very little mass, so even gentle forces will cause significant accelerations in the baseball. If I double the force I exert on the baseball, I’ll consequently double the acceleration of the baseball. In contrast, my lead brick has a huge mass. Now, if I exert the same forces I did on the baseball, I’m going to be dividing those forces by a much larger mass and the brick’s acceleration will consequently be much smaller. It’ll still be proportional to my force, if I double my force I will double the acceleration, but it’ll be on a much smaller scale.

If you have a particular acceleration in mind, and you want to achieve it by exerting the right amount of force on the object, you just take that relationship between the force divided by the mass gives you acceleration, and you rearrange it algebraically so that you know what acceleration you want, a certain amount, multiply it by the mass of the object and that will tell you what force you need to achieve the acceleration you have in mind.

What forces act on you as you ride an elevator that’s in steady motion?

Lou Bloomfield Leave a comment

When you are standing in a constant-moving elevator, what forces act on you besides gravity pulling you down and the floor pushing you up?

There are no other forces acting on you; it’s just those two. and because the elevator is moving at constant velocity, the net force on you has to be zero. You are coasting and that means that the force of gravity downward, which is also called your weight, is exactly balanced by the upward push from the floor. Those two forces sum to zero, so the net force on you is zero and you move at constant velocity.

We don’t necessarily know what that velocity is though. It could be that you’re moving upward at constant velocity, or moving downward at constant velocity, or even motionless. But as long as the two forces exactly balance one another, the net force on you is zero and you don’t accelerate.

When you shake a massive object, why does your body shake, too?

Lou Bloomfield Leave a comment

When you shake a massive object, why does your body shake, too?

That’s because the massive object is shaking you. Forces always come in equal but oppositely directed pairs, an observation known as Newton’s third law of motion. So, if I push on this lead brick, and I shove it hard to your left, it pushes back on me equally hard toward your right. Two forces, in opposite directions; my force on the brick, the brick’s force on me. Now, this brick is pretty massive. It’s not as massive as I am, but it’s getting there. So I have to push very hard on it to make it accelerate away from me. It responds by pushing very hard on me, making me accelerate away from it. We’re shaking each other.

So, when you shake an object with very little mass, like this baseball, it’s pushing on you as well and shaking you as well, but it’s hardly noticeable. When you take something of comparable mass, like the brick, the shake is significant. I have to push very hard on it, so it pushes very hard on me.

What role does force play in a self-defense blow?

Lou Bloomfield Leave a comment

My self-defense instructor encouraged me hit the dummy with more force, so I exerted more force on my arm and it accelerated more rapidly. Yea for physics! But how does my increased force on my own arm cause me to hit the dummy with more force? — RL

Suppose you’re defending yourself against an attacker and you find that you have to hit them, either with your hand or with your fist. Two of the most important features of the impact between your hand and the person are how hard you push on the person and for how long.

The technical term for that push on the other person is a force; you exert a force on the other person. And a force is one of those physical quantities that has a direction to it. You can exert a force on someone toward the right or you can exert a force on someone toward left. Direction matters. Another thing about forces is that they’re always exerted between two thing, for example, you pushing on the other person. Forces don’t just exist by themselves; you can’t carry a force with you. You exert a force on something else.

That leaves this intuitive notion that you carry something with you during the wind up to an impact a little fuzzy. What is it you’re caring if you’re not carrying a force? Well, there is something you’re carrying: it’s known as momentum and momentum is a conserved physical quantity. That means you can’t create momentum or destroy momentum; all you can do is move it from one object to another.

In this respect momentum resembles money. Money is a conserved quantity, too, assuming that you don’t print it up in your basement (you are a law-abiding citizen) or you don’t destroy it (you’re not goofy). Money is conserved and goes from person to person to person. It is the conserved quantity of finance. Correspondingly, momentum is the conserved quantity of motion.

If you want to start moving to the right, you I have to accumulate some rightward momentum. Momentum, like force itself, has a direction to it. There’s momentum to the right; there’s momentum to the left. They are different, so if you want to move to the right, you have got to accumulate rightward momentum. The same is true of your hand or your fist, when you’re going after that attacker. If you want your fist to be really quick and move to the right rapidly, you have to invest a lot of rightward momentum into your fist.

To do that, you have to get that momentum from somewhere because you can’t make it. You can’t just cooking it up from nowhere. It comes from the ground and from the rest of your body. You pour rightward momentum—let’s suppose the bad guys are over to your right—you pour rightward momentum into your own fist. That momentum comes out of the rest of you and you do this how? By exerting a rightward force on your own fist.

You can do this—you can think of yourself as two separate parts: (1) your overall body and maybe your shoulder, and (2) the rest of you, your arm and your hand. So you’re pouring rightward momentum into your fist, at the expense of everything else. You actually can end up going backwards if you’re not careful

So you pour the rightward momentum into your hand and the amount of rightward momentum your hand accumulates is equal to the force you exert on your hand times the time over which you exert that force. The harder you push your hand and the longer you push your hand, the more rightward momentum it accumulates. If you want a fierce impact, You want to put a lot of rightward momentum into your hand. That means you push hard and you push long. You don’t go gently; you get going! You pour the momentum in so that its all accumulated.

This is this is the case not just for for punching somebody. It’s also the case for throwing a baseball. If you really want it to go fast, you need to take a long windup and you pour the rightward momentum into the baseball over as long a distance and with as much force as you can summon. Pack it full of rightward momentum, and off it goes. The same with a hammer. You pour rightward momentum into it, get it going and pack it full of momentum. When it hits the nail, its going to pack a wallop.

Okay, so now on to the impact. You have invested momentum in your hand; now when your hand hits something, it invests momentum in what it hits: the other guy, the bad guy. Your hand, which is chock-full of rightward momentum impacts that other person and transfers much or maybe even all its rightward momentum to that person by way of a force for a time. It’s passing along that momentum and it turns out that it can pass all of its momentum in a variety of different patterns. It can either pass along all its momentum with a gentle force over a long time, by pushing the person as they go away, or it can transfer all its momentum with a giant force for a short time.

If you hit knuckles to jaw, that impact is fierce and involves a big force, but not for very long. All the moment goes over in a jiffy. So a momentum transfer, it turns out, the amount of momentum you the put into something or transfer to something, is just this product of force times time. You can use a little force for a long time, or a big force for a short time; both of them can transfer the same momentum.

Well, if you really want to stun somebody, you want to make the transfer quick—short time, big force—and so that’s the bare-knuckle fight. It hurts. On the other hand, if you put on big fluffy gloves and delay or prolong the impact, it’s a little force for a big time. It more pushes you, but it doesn’t have that peak impact force that hurts.

So there you have it: if you’re trying to defend yourself against an attacker and you punch them, you do it by accumulating as much momentum toward the bad guy as possible. Use a big force for a big time, whatever you can do to get a lot of forward momentum into your knuckles and into hand. At the impact point—the moment when when you touch the other person—you want to transfer all that momentum to the other person, perhaps by way a big force for a short time. That’ll hurt everybody involved, you included, but, in any case, hopefully it will have the desired effect of getting the bad guy to go away and leave you alone.