Kevin has edited encyclopedias, taught history, and has an MA in Islamic law/finance. He has since founded his own financial advice firm, Newton Analytical.
Have you ever had to push a broken-down car? Hopefully, the answer is no but if you have, you definitely know that the lighter the car, the easier the job. In this lesson, we learn why that is the case.
Trucks and Sports Cars
Imagine for a moment that you had your dream car. For many people, chances are that your dream car is either a little sporty coupe from a German or Italian manufacturer, or a much more solid vehicle, like a truck or an SUV.
Now, imagine that your dream car has broken down on the side of the road. There is a service station 300 yards away, and you and your friends feel foolish calling a tow truck for such a short distance. Plus, the towing company said it would be $300, which no one wants to pay. Reluctantly, you and your friends get out and start to push. Which car do you want now? The tiny little sports car or the heavy, giant truck?
Most people would choose the smaller car at this moment, as it is easier to push. Why is that? The answer is relatively simple, according to Isaac Newton. In fact, it's his Second Law of Motion: Force = Mass * Acceleration. What does that mean? Let's find out.
Acceleration and Mass
First, let's examine what is meant by two of those words: mass and acceleration. Mass is probably the easier of the two to define, as it means the total amount of material present. Mass is different from weight, in that weight is the effect of gravity on an object. As such, due to differences in gravity, a 220 pound man on earth would only weigh about 37 pounds on the moon, but his mass of 100 kilograms would be identical anywhere. In our example, the sports car had a much lower mass than the SUV.
So what about acceleration? Acceleration is the term given to the measure of the change of velocity over time. This is why you'll often hear scientists call it 'meters per second per second,' or 'meters per second squared.' We are tracking how the force increases. Someone who goes the speed limit consistently on the highway will have a much lower acceleration than someone who speeds up, slows down, and slams on the brakes.
Multiplying acceleration and mass gives us the force of an object. Force is measured in a unit known as a newton, which is a kilogram meter per meter squared. In other words, it's simply the units of acceleration and mass pushed into one unit.
Think about it like this. A baseball on a shelf is unable to exert any force, but when thrown it will exert a force due to the fact that it has gone from not moving to moving at more than 100 kilometers an hour!
So, back to your broken down car. What we are trying to find is the force needed to cause your car to change its velocity; in other words, to accelerate. If you put the mass of the sports car at 500 kg and the mass of the SUV at 2,000 kg, you will need four times the acceleration to get the same amount of force.
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Still standing by that choice of the SUV? In any event, we can manipulate the formula of Force = Mass * Acceleration in some pretty interesting ways. Let's say that you and your friends get out of the car and push with a combined force of 1,000 newtons, a considerable effort indeed! By what margin would your vehicle accelerate?
In any event, you set up the equation as Acceleration = Force / Mass. For the sports car, that means that acceleration is equal to 1,000 newtons over a mass of 500 kilograms. Doing the math, that means that your car is lurching towards the service station at an acceleration of 2 meters per second squared. In other words, it may be worth it to put someone up front to steer and hit the brakes if necessary!
On the other hand, if you are still standing by your 2,000 kilogram SUV, the equation is very different. Your acceleration is equal to 1,000 newtons divided by 2,000 kilograms. Your car lurches forward at only half a meter per second squared. Slowly, you start making your way to the station.
In this lesson, we looked at Newton's Second Law of Motion, defined as Force = Mass * Acceleration. Remember, mass is the total amount of matter present in an object, while acceleration is the rate at which velocity changes. Using the example of a broken down sports car and a broken down SUV, we saw how changes to mass created differences in acceleration.
Newton's Second Law of Motion: defined as Force = Mass * Acceleration
mass: the total amount of material present
acceleration: the measure of the change of velocity over time
Using the Second Law of Motion will help you determine how much force is needed.
Upon reviewing this lesson, you should be able to:
Define Newton's Second Law of Motion
Describe acceleration, mass, and force
Manipulate the Second Law of Motion to find acceleration
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