(18) Newton's Second Law
(Revised lesson plan, following a revision of section #18).
Part of a high school course on astronomy, Newtonian mechanics and spaceflight
by David P. Stern
This lesson plan supplements: "Newon's Second Law," section #18 |
Goals: The student will |
Follow the "Stargazers" material.
Forces can be opposed or unopposed.
-- What happens when a force acting on an object is opposed?
Or it may overcome the opposing force, and then work is performed, and energy is invested.
-- What happens when a force acting on an object is not opposed to any significant degree?
--What determines how big that acceleration will be?
[Any other word for "mass"? Yes, "inertia"]
--The weight of the object. [But weight is the result of gravity. Does gravity control the acceleration?
No, it does not, the "mass" or "inertia" does that. However, weight is also proportional to the mass, so "weighing" an object is one way of determining its mass. It does so, however, by using gravity.
--Can mass be determined without using gravity?
[Yes--the inertial balance used on "Skylab" did so, as does the experiment with a hacksaw blade.]
A big stone is many times heavier than a small pebble. It is pulled down by a much stronger force.
Yet stone and pebble fall at the same rate! Why doesn't the stone fall faster?
The MKS System-- All physical measurements depend on the units we use for 3 fundamental quantities. What are they?
1 mph = 0.469 meters/sec
600 mph = 268.17 meters/sec
An object undergoes "one unit of acceleration" if its velocity increases 1 meter/second each second. We therefore refer to it as "1 meter/second2" or in short "1 m/s2".
A freely falling stone accelerates at about 9.81 m/s2
The MKS unit of force is called the Newton.
It is the force which gives 1 m/s2 to 1 kg of mass.
--In the rest of this lesson we assume as an approximation g = 10 meter/sec2. If your body weighs 70 kilograms--and presumably, also has 70 kilogram of mass--what is your weight in newtons?
If bold face letters denote vectore, we can write Newton's 2nd law as
a = F/m
Both of course say exactly the same thing, each can be derived from the other. But if force is the cause and acceleration the resulting effect, the second form makes more sense--given the force, given the mass, we want to find the acceleration.
Note: the example below is also on the web page Snewt2nd.htm. It was placed there when the page was revised.
-- The V2 rocket in World War II had a thrust of about 240,000 newtons and a mass of 12 tons or 12,000 kilograms. What was its upward acceleration at launch? (Solve on the board, though a student may do the writing and participate in the solution.)
but is wrong.
Before launch, the rocket's weight is supported by the launching pad. Its weight is 12,000 g = 120,000 newton and since it does not move, an equal and opposite upward force of 120,000 newtons is exerted on it by the pad from below.
At the lift-off moment, that force ceases to act on the rocket: instead, the thrust of the engine now supports the rocket's weight (and if the engine generates a thrust smaller than the weight--less than 120,000 newton--the rocket will not lift off). So that force must be subtracted from what is available to accelerate the rocket. The result is
a = F/m = (240,000 - 120,000)/12000 = 10 m/s2 = 1 g
--At burn-out, the V2 has consumed 9 tons of fuel. What is its final acceleration just before that moment?
--In some weird alternate universe, weight and mass are not proportional. Two materials, astrite and barite, have the same weight per unit volume, but a volume of astrite has twice the mass of a similar volume of barite. Assuming the inhabitants play a game similar to bowling--which of the two would be a better material for bowling balls? (have a discussion).
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Author and Curator: Dr. David P. Stern
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Last updated: 10-15-2004