Notes on The Laws of Motion - University Physics I | PHYS 2050, Study notes of Physics

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Chapter 5

The Laws of Motion

Sir Isaac Newton  1642 – 1727  Formulated basic laws of mechanics  Discovered Law of Universal Gravitation  Invented form of calculus  Many observations dealing with light and optics

Newton’s First Law The Law of Inertia

An object in motion will stay in motion with

constant speed and direction, an object at

rest will stay at rest, unless acted upon by an

outside force.

Newton’s Second Law

the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass  The net force is the cause of change in motion, as measured by the acceleration  Mathematically (speeds much lower than the speed of light)

r

F = m

r

" a

Newton’s Third Law

If two objects interact, the force exerted by

object A on object B is equal in magnitude

and opposite in direction to the force

exerted by object B on object A

(Note on notation: is the force exerted by A on B) AB

F

r

AB

F

r

! r F AB = " r F BA ! r F BA

Classes of Forces Contact forces involve physical contact between two objects (a,b,c) Field forces act through empty space - No physical contact is required (d,e,f)

Units of Force  The SI unit of force is the newton (N)  1 N = 1 kg·m / s 2  The US Customary unit of force is a pound (lb)  1 lb = 1 slug·ft / s 2  1 N ~ ¼ lb

Inertial Frames  Any reference frame that moves with constant velocity relative to an inertial frame is itself an inertial frame  A reference frame that moves with constant velocity relative to the distant stars is the best approximation of an inertial frame  We can consider the Earth to be such an inertial frame, although it has a small centripetal acceleration associated with its motion

Inertia and Mass

 The tendency of an object to resist any

attempt to change its velocity is called inertia

 Mass is that property of an object that

specifies how much resistance an object

exhibits to changes in its velocity

More About Mass

 Mass is an inherent property of an object

 Mass is independent of the object’s

surroundings

 Mass is independent of the method used to

measure it

 Mass is a scalar quantity

 The SI unit of mass is kg

Weight

Weight is the gravitational force exerted on the

object

 Weight will vary with location

 Example:

 W

earth = 180 lb; W moon ~ 30 lb  m earth = 2 kg; m moon = 2 kg

More About Forces  A spring can be used to calibrate the magnitude of a force  Doubling the force causes double the reading on the spring  When both forces are applied, the reading is three times the initial reading

More About Newton’s 2 nd Law

is the net force

 This is the vector sum of all the forces

acting on the one mass of interest

Be careful to add only forces acting on that

object!

 Newton’s Second Law can be expressed in

terms of components:

 Σ F

x = m a x  Σ F y = m a y  Σ F z = m a z !

F

r

A baseball is struck by a bat. While the ball is in the air, what objects exert forces on the ball?

1. Earth
2. Bat
3. Air
4. Bat, Air
5. Earth, Bat
6. Earth, Air
7. Earth, Bat, Air
8. There are no forces on the ball.
9. The answer depends on whether the ball is going up, going down, or at its highest point.

Vector Nature of Forces Forces are vectors , so you must use the rules for vector addition to find the net force acting on an object

Vector Nature of Forces Two forces, 450 N at 10° and 400 N at 30° are applied to a car in an effort to accelerate it. What is the magnitude of the resultant of these two forces?

Find the direction of the resultant force

If the car has a mass of 3000 kg, what acceleration does it have? Ignore friction.

Consider the 3 forces shown in the diagram.

Gravitational Force

 The gravitational force, , is the force that

the earth exerts on an object

 This force is directed toward the center of the

earth

 From Newton’s Second Law

 we will refer to it as the Weight = F g = mg g F r g F = m g r (^) r

Normal Force  The normal force is always perpendicular to the surface (hence the name)  It resists an object pushing into the surface  We will be assuming our objects are completely rigid n r

Normal Force  Careful!! The normal force is not always equal to the gravitational force on the object  For example, in this case  may also be less than 0 and y g g F n F F n F F =!! = = + " n r

F

g

r

Free Body Diagrams

 Draw the object as a point mass

 Draw vectors for only the forces acting on

that mass

(do not include forces it exerts on other objects, do not include velocities, accelerations etc..)

 Try to indicate relative magnitudes by the

length of the vectors when possible,

 label angles

Draw a free body diagram for the man when the elevator is at rest. What is the reading on the scale? 1)n S

mg 2)n S =mg 3)n S <mg