4 Ch. - Newton's 2nd Law
force, mass, and acceleration,
What causes acceleration?
A "push" or "pull" applied to an object causes the object to move. The "push" or "pull" is a FORCE. The change in velocity (rest to moving) is an ACCELERATION.
Force is proportional to Acceleration F~a
Force and acceleration
a~F 2a ~ 2F 3a ~ 3F
m
What relates the two terms? MASS
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Newton's Second Law
The acceleration of an object is directly proportional to the net force applied and inversely proportional to the mass.
F = Fnet = ma a = Fnet /m
Mass, m - kilograms (kg) Acceleration, a - m/s2 Force, F - kg-m/s2 1 kg-m/s2 = 1 N (Newton)
Forces in Nature
Forces: cause a "push" or "pull" on an object. There are FOUR fundamental forces in nature: Electromagnetic (force between charged particles) nuclear strong (force between nuclear components) nuclear weak (another force between nuclear components) gravitational (very weak force between all matter) Most of the "forces" we encounter in our common experience are EITHER gravitational or electromagnetic in nature (e.g., weight, friction, drag, traction, tension, etc.).
"New" forces?
Modern physics theories suggest that when the universe was very young (<< 1 second), these four forces were combined into a single force. One goal of physics research is to find a single theory that describes this state of the universe (see String Theory). Question: Do physicists understand all the forces?? NO!! In late 1990's, there was evidence the universe was expanding at an accelerating rate - an "anti-gravity" force?? This is now referred to as "dark energy"!
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Acceleration due to gravity
In the absence of drag or buoyant forces (i.e., in vacuum), all objects falling near the earth's surface have an acceleration due to gravity. This acceleration is given its own symbol, g.
a = g = 10 m/s2
g = 10 m/s2
Mass vs. Weight
Mass provides a measure of the inertia. However, in common use, the terms mass and weight are used interchangeably. In physics, these are
not the same concept.
MASS - the quantity of matter associated with an object; a measure of inertia. Mass is a "fixed" quantity independent of location. WEIGHT - the force on an object due to gravity. Fgrav = W = mg
Units Mass Weight Metric kilogram (kg) Newton (N) English slug pound (lb) 1 kg -> 2.2 lb -> 10 N -> 0.067 slugs
Mass vs. Weight (m = 70 kg) Earth Accel. 10 m/s2 Weight 700 N 154 lbs Moon 1.7 m/s2 119 N 26 lbs Jupiter 25 m/s2 1750 N 386 lbs
Friction
Friction is any action (force) that opposes the motion of an object. As a rule, friction has very peculiar properties. When first pushing an object, it requires a large force to get the object to begin moving. Once motion has begun, there is an initial "jerk", then the object requires a much force smaller to keep it moving. For solids, the friction force is independent of speed or area of contact. For fluids (gases or liquids), friction is also present, but the friction force IS dependent upon both the speed and the surface area. Eg., Air Drag!
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Application of Forces
APPLIED FORCES F1 = 20 N F1 = 20 N m F2 = 10 N m F2 = 10 N F1 = 5 N F3 = 10 N m F2 = 5 N F1 = 20 N m m = 10 kg; a = Fnet/m
a) b) c) d) e)
0 m/s2 1 m/s2 2 m/s2 -1 m/s2 3 m/s2
NET FORCE m a = 2 m/s2
Fnet = 20 N
Fnet = 30 N
m
a = 3 m/s2
Fnet = 10 N
m
a = 1 m/s2
Fnet = 0 N
m
a = 0 m/s2
Question: For this last case, can the box be in motion??
Application of Second Law: Case 2 - Free Fall Vertical motion with a = g
Consider the two balls A and B. A B Ball A: Ball B: mA = 1 kg mB = 3 mA = 3 kg
Find the acceleration of each ball.
There is only one force acting on each ball, the gravitational force (its own weight). Ball A: W = mA g = (1 kg)(10 m/s2) = 10 N Ball B: W = m B g = (3 kg)(10 m/s2) = 30 N
Compute the acceleration of each ball: Ball A: a = FA/m A = 10 m/s2 = g Ball B: a = FB/mB = 10 m/s2 = g
Application of Second Law: Case 3 - Non-Free Fall Vertical motion with a < g
In many "real" vertical systems, there is also a friction force present - air resistance or air drag. This drag force is dependent upon: (a) Surface area of the object; (b) speed of the object In all cases, Newton's laws apply -> Remember, it is the NET FORCE that determines the acceleration
a= Fnet mg ! R = ; R - resistive force (drag) m m
Since the resistive force R is dependent upon the speed, v: R increases and a decreases until a = 0 m/s2 air drag (R) There is a critical speed at which a 0 Speed is a constant at this point!! This is the terminal velocity.
weight (mg)
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Application of Second Law: Case 1 - Equilibrium (a = 0)
We now apply the Second Law to a variety of physical systems in an attempt to determine the resulting motion. 1 a) Static Equilibrium: a = 0; v = 0 (system at rest) normal force Example: A book on a table top. Are there forces? "Normal" - upward force from table YES! Weight - downward force of gravity weight
Example: Hanging from a rope tension Tension - stretching of the material in the rope weight Weight - downward force of gravity
Application of Second Law: Case 1 - Equilibrium (a = 0)
We now apply the Second Law to a variety of physical systems in an attempt to determine the resulting motion. 1 b) Dynamic Equilibrium: a = 0; v 0 (system in motion at constant velocity) Example: Pushing a box across a rough floor at a constant speed "Pushing" force F = 50 N "Resistive" force F = 50 N Here, the resistive forces (e.g., friction) are completely balanced by the "pushing" force of the person. Consequently, the net force is ZERO! However, while the acceleration is zero, there is still motion - at a constant velocity.
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