(18)  Newton's Second Law  

"From Stargazers to Starships" home page: ....stargaze/Sintro.htm
Lesson plan home page and index:             ....stargaze/Lintro.htm

• A version of Newton's laws of motion without the concepts of mass and force.

• How that formulation of Newton's laws allows mass and force to be defined, and about their units, the kilogram and the Newton.

• To apply and use F = ma to motion caused by gravity.

• The distinction between gravitational mass and inertial mass.

• That if an object is at rest, that does not mean no forces act on it--just that all forces on it add up to zero. If a book on the table does not fall, this does not mean gravity has stopped pulling it--just that the table also exerts a force, and that the sum of that force and the book's weight adds up to zero.

Starting out: (underlined statements below may be put on the blackboard, to be copied by students.)   We have so far discussed Newton's laws in a general, intuitive way. We have given:

--Their formal wording--3 laws

--The meaning of the 1st law

--"without the action of forces, motion in a straight line at constant speed continues indefinitely"

--The meaning of the 3rd law

--"Forces occur in pairs, same magnitude, opposite directions"

--The meaning of mass

--"Resistance to acceleration, inertia"

  We could of course define force by weight, using gravity. But if we do, all our calculations will depend somehow on the constant of gravity, on g--it could be done, but we are looking for a cleaner way.

  We have also discussed the idea of mass, but we still need a good way of measuring it. One could use the hacksaw-blade formula--but we have not yet reached the point where that formula can be derived!

(on the board) How do we measure mass?

  We will address these problems in the way of Ernst Mach, who lived two centuries after Newton. Here is what we will do:

(on the board)
Solution: Formulate Newton's laws using neither "force" nor "mass."

Continue with the "Stargazers" material.

Review:
What does Newton's first law say?
What does Newton's second law say?
What does Newton's third law say?

When two compact objects ("point masses") act on each other, they accelerate in opposite directions, and the ratio of their accelerations is always the same.

The newton is the force that can give 1 kg of mass an acceleration of 1 meter/sec².

When you jump from a high place, gravity gives your body an acceleration of g=10 m/s². Your weight is therefore 700 newtons.

This is a tricky question, related not only to F=ma but also to the concept of equilibrium, discussed at the end. An unthinking application of Newton's second law would give
a = F/m = 240,000/12,000 = 20 m/s2 = 2g

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

The total mass left is 3000 kg, the total weight is 30,000 newtons, so a = F/m = (240,000 - 3000)/3000 = 210,000/3000 = 70 m/s² = 7g.

Probably astrite. Balls of equal size and shape of the two materials are equally hard to lift, but astrite needs a greater force to get started and therefore delivers a greater force to the pins.