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Momentum Moving objects have a quantity that objects at rest don’t have. More than a hundred years ago, this quantity was called impedo. A boulder at rest had no impedo, while the same boulder rolling down a steep incline possessed impedo. The faster it moved, the greater the impedo. The change in impedo depended on force and, more importantly, on how long the force acted. Apply a force to a cart and you give it impedo. Apply a long force and you give it more impedo. But what do we mean by “long?” Does “long” refer to time or distance?

When this distinction was made, the term impedo gave way to two more precise ideas momentum and kinetic energy. And these two ideas are related to a cluster of other concepts including work, power, efficiency, potential energy, and impulse. What are the distinctions and relationships among these quantities?

How can they be used to analyze matter in motion, the workings of machines, and even such complex phenomena as the energy sources that power modern industry and the “machinery” of living organisms?

We all know that a heavy truck is more difficult to stop than a small car moving at the same speed. We state this fact by saying that the truck has more momentum than the car. By momentum, we mean inertia in motion or, more specifically, the product of the mass of an object and its velocity; that is,

Momentum = mv

Or, in shorthand notation,

Momentum = mass x velocity

When direction is not an important factor, we can say momentum = mass x speed, which we still abbreviate mv. We can see from the definition that a moving object can have a large momentum if either its mass or its velocity is large or both its mass and its velocity are large. A truck has more momentum than a car moving at the same velocity because it has a greater mass. We can see that a huge ship moving at a small velocity can have a large momentum, as can a small bullet moving at a high velocity. A massive truck moving down a steep hill with no brakes has a large momentum, whereas the same truck at rest has no momentum at all.

Changes in momentum may occur when there is a change in the mass of an object, or a change in its velocity, or both. If momentum changes while the mass remains unchanged, as is most often the case, then the velocity changes. Acceleration occurs. And what produces acceleration? The answer is force. The greater the force acting on an object, the greater will be the change in velocity and, hence, the change in momentum.

But something else is important also: time how long the force acts. Apply a force briefly to a stalled automobile and you produce a small change in its momentum. Apply the same force over an extended period of time, and a greater momentum change results (Figure4.2). A long sustained force produces

more change in momentum than the same force applied briefly. So, for changing an object’s momentum, both force and the time interval during which the

force acts are important. impulse. The quantity “force x time interval” is called impuls

If you wish to produce the maximum increase in the momentum of something, you not only apply the greatest force, you also extend the time of application as

much as possible (hence the different results obtained by pushing briefly on a stalled automobile and by giving it a sustained push).

Long-range cannons have long barrels. The longer the barrel, the greater the velocity of the emerging cannonball or shell. Why? The force of exploding gunpowder in a long barrel acts on the cannonball for a longer time, increasing the impulse on it, which increases its momentum. Of course, the force that acts on the cannonball is not steady it is strong at first and weaker as the gases expand.

Most often the forces involved in impulses vary over time. The force that acts on the golf ball in Figure 4.3, for example, increases rapidly as the ball is distorted and then decreases as the ball comes up to speed and returns to its original shape. When we speak of any force that makes up impulse in this chapter, we mean the average force.

Imagine that you are in a car that is out of control, and you’re faced with a choice of slamming either into a concrete wall or into a haystack. You don’t need much physics knowledge to make the better decision, but knowing some physics aids you in knowing why hitting something soft is entirely different from hitting something hard. Whether you hit the wall or the haystack, your momentum will be decreased by the same amount, and this means that the impulse required to stop you is the same. The same impulse means the same product of force and time, not the same force or the same time. You have a choice. By hitting the haystack instead of the wall, you extend the time of impact you extend the time during which your momentum is brought to zero. The longer time is compensated for by a lesser force. If you extend the time of impact 100 times, you reduce the force of impact to a hundredth of  what it might have been. So, whenever you wish the force of an impact to be small, extend the time of the impact. And, conversely, if the time over which the force acts is short, the force itself will be comparatively large, for a given change in momentum. Going back to the example of the car, you can see why you are in much more trouble if you hit the concrete wall rather than the haystack. Your time of impact is short, so the force on you is large, as your momentum decreases to zero.