## When you push someone on a swing, why don’t the forces cancel?

### If you push someone on a swing with 50 N of force and they push back with 50 N of force, then why does the person still move? Shouldn’t they stay motionless if all the forces are cancelled out?

You’re struggling with the most common misconception about Newton’s third law of motion — the law stating that for every force object A exerts on object B, there is an equal but oppositely directed force exerted by object B on object A. The pair of forces described in Newton’s third law always act on different objects and therefore never cancel one another. Object A’s force on object B acts only on object B and can cause object B to accelerate. Object B’s force on object A acts only on object A and can cause object A to accelerate.

When you push someone on the swing, your force on the person affects that person and will affect their swinging motion. The person does indeed push back equally hard on you, but that force affects you! If you are wearing roller skates, you will accelerate backward and drift away from the swing.

## Is deceleration something different from acceleration?

### Is deceleration something new or just acceleration in the opposite direction?

Deceleration is simply a special case of acceleration. An object decelerates by accelerating in the direction opposite its current velocity. For example, if your car is heading toward Washington at 60 mph (100 km/h) and you push on the brake pedal, your car will begin to accelerate in the direction pointing away from Washington and your forward velocity (toward Washington) will decrease with time. Since an object that accelerates in the direction opposite its velocity always slows down, it has become conventional to say that it is decelerating.

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

### 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.

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

### 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?

### 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?

### 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 does it mean to coast?

#### If something is coasting or moving at a steady pace, is it experiencing a net force of zero? — NP

That’s exactly right! Coasting and zero net force go hand-in-hand: when an object is experiencing zero net force, it doesn’t accelerate and thus it coasts. A coasting object is an inertial object, meaning that it moves at a steady pace along a straightline path. And if the coasting object is at rest, it stays at rest.

To clarify the term “net force,” note that when an object is experiencing several separate forces, it doesn’t accelerate in response to each one individually. Instead, it accelerates in response to the sum of all the forces acting on it: the net force. Remember that forces have directions associated with them (forces are vector quantities), so when you sum them you must consider their directions carefully. The proper force to consider in Newton’s second law is actually the net force on the object. If you know both the net force on the object and the object’s mass, you can predict the object’s acceleration. And if the net force is zero, then the object doesn’t accelerate at all — it coasts.