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 Force, Mass, and Acceleration

 F = M x A

Basic Concepts

A vehicle in deep space has its rocket engine turned off but loses no speed. Yet, if we put a car in neutral on the freeway, it'll slowly lose its speed, requiring us to again power it. The air and the roadway both tug at the car, trying to lower its speed. Without those two influences, the car would stay at it original speed just like the space vehicle.

A physics person wouldn't say "Tugging at the car"; they'd say a "force was applied to the car". So this doesn't sound too academic, recall that you "apply a force" to a car when you push an out-of-gas vehicle off the roadway with your hands. If you've ever done this, you'll recall: - the car feels very heavy. It often takes a strong push to even budge it. In fact it helps to have 2-3 people pushing. - After pushing hard for about a minute, even with several people, the car will be traveling only about walking speed.

The combined pushing your group applied was probably about 200 lbs of force. Yes, if directed upwards, you could have lifted 200 lbs. Any force applied to a movable object produces a change in speed, an "acceleration", which was small in the example just mentioned. The dead car originally was at a speed of 0 and you changed it to 2 mph over 1 minute of pushing. Thus your acceleration was "two miles per hour per minute" (2 mph / min). If you had a super tow truck apply the same force to the car for 30 minutes, the resultant speed would be 30 times larger. The acceleration in this case would still be 2 mph/min but, applied for a half hour, the resultant speed is 60 mph. Note that this '2 mph/min' could also be called '60mph per half hour" or even '120 mph / hour"

Now imagine a dead car weighing only half as much as the first. Your 200 lb force will accelerate the light car at twice the rate; that is, after one minute of pushing, the car will be traveling at 4 mph. The same force resulted in double the acceleration (4 mph/min) just because the car was lighter.

The connections between force, acceleration, and weight are summed up very tersely by a very old, frequently used equation:

    F = M x A
or "force equals mass times acceleration" so 'm' means 'mass' (like weight), 'a' is acceleration, and 'F' is force.

Details, units, etc

'M' is mass and, while it's similar to 'weight', it isn't quite the same thing. In fact, it's defined to be Weight/AccelerationDueToEarth'sGravity.

So F = M x A is
   F = Weight/G x A
and if you examine the units, the G and A units cancel and F gets whatever
units Weight had - so it makes sense.
<-- TODO====== mention slugs vs weight. TODO. systems of units. our chosen units. using car's wt, can quickly get equivalent forces decel = 5 mph / _ secs. F = M x A = weight / G x decel so 1st order of business is to get G and 'decel' into the same units. G is typically given as 9.8 meters/secSquared but that's also equal to 21.8 mph/sec . F = car'sWeight x (decel_mph/sec) / (21.8 mph/sec) F = car'sWeight x (5 mph/measurement secs) / (21.8 mph/sec) -->