Chapters 2 & 4: Newton’s Laws
Newton’s Laws introduce two new ideas, the ideas of force and inertia or mass. Forces are how we interact with or influence other objects. Intuitively, forces are pushes or pulls on objects. Forces are vectors, they have a magnitude and a direction in space. If you push something, you push it in a certain direction. Like other vectors we represent forces by arrows with the length representing the magnitude and the direction of the arrow representing the direction of the force. If two or more forces act on an object the net or total force is the vector sum of the individual forces. For example if a force of 30N acts to the right (+ x direction) and 20N acts to the left (- x direction) the net force is 30N – 20N = 10N (to the right). The 20N force acting to the left is represented as – 20N because it is in the – x direction.
If the two forces were in the same direction, i.e. both toward the right, the net force would be 50N to the right. (Note that it is the direction of the arrow, not the side that indicates the direction of the force. One might be pushing toward the right and the other pulling toward the right.)
An object maintains a constant velocity unless acted on by a (net) external force. This means that if its velocity is zero (it is at rest) it stays at rest if no net external force acts on it. If it is moving with a speed in a certain direction, it will continue to maintain its speed in the same direction if no net external force acts on it. This law can be viewed as a consequence of the 2nd law.
If a net force acts on an objects it will cause the object to accelerate and the acceleration is given by
The arrow over the F and the a indicate that they are vectors, i.e. have a magnitude and point in a particular direction. M represents the mass or inertia of the object. The mass is a measure of the object’s inertia, i.e. how hard it is to accelerate it. We also associate the mass with the quantity of matter in the objects, e.g. the number of electrons, protons and neutrons in it. Mass is measured in kilograms (kg). On the earth, 1kg will weigh about 2.2 pounds. Force is measured in Newtons (N) or kgm/s2, 1N = 1kgm/s2. A pound is a measure of force in English units. 1 pound = 4.4N.
The direction of the force is also the direction of the acceleration. A force of 10N toward the east applied to a mass of 2kg will produce an acceleration of 5m/s2 toward the east.
The force in Newton’s second law is the total or net force on the object. If the total force is zero, the acceleration is zero and visa versa, if a = 0, Ftotal = 0. That does not mean there are no forces on the object, but it means that if there are forces, they have to cancel each other.
If mass is a measure of an objects inertia, what is weight? Weight is actually a force due to gravity. Beware of Hewitt's definition of weight. He starts out right in chapter 4 page 61, but then changes it in chapter 9 pp. 166-67 in a way most physicists would not like. Use the definition I've given. The earth exerts a gravitational force on all objects because they have mass. The farther you are from the center of the earth, the less the gravitational force the earth exerts on you. Also the gravitational force the earth exerts on you depends on your mass, so the gravitational force on you is written as
where M is your mass and g is the gravitational field, in this case the field due to the earth. The gravitational field g is about the same everywhere on the surface of the earth where g = 9.8m/s2. I usually round this off to 10m/s2. (If you go to the moon, the g of the moon is about 1/6 the g on the earth, so even though you would have the same mass on the moon, you would weigh less.)
On the earth, a person of mass 70kg would weigh 70kg × 10m/s2, or 700N. On the moon they would weigh about 117N.
Note that if an object is in free fall, i.e. gravity is the only force acting on them, then the net force on them is F =Mg and the acceleration is a = F/M so
and all objects in freefall have the same acceleration, even though the forces on them are not the same. Since the force is proportional to the mass, the masses cancel.
