forces. force – a push or a pull contact – a force acting on a body by touching it long-range...
TRANSCRIPT
Forces
Force – a push or a pull
• Contact – a force acting on a body by touching it
• Long-range – force exerted on a body w/o contact (gravity, magnetic force, electrical force)
Newton’s 2nd Law
• The acceleration of an object is directly proportional to the force acting on it, and inversely proportional to its mass.
F = ma a = F/m m = F/a
Units: kg m/s2 = Newton (N)
Newton's Second Law of Motion
Plot Force Vs. Acceleration for the following carts:cart 1 = m
cart 2 = 2mcart 3 = 3m
Net Force – vector sum of all forces acting on a body
acceleration = Fnet/m
Only net forces cause accelerations!!
Free-Body Diagrams
• Include all forces acting on the body
• Include weight (Wt), the normal force (Fn), or tension if necessary (FT)
• Then identify the net force and its direction
• The direction of the net force indicates the direction of the acceleration of the body
Equilibrium
• Equilibrium = balance = the sum of all of the forces acting on a body is zero (net force is zero)
• Static equilibrium = the object is at rest
• Dynamic equilibrium = the object is moving at constant velocity
• In each case the net force is zero (there is no acceleration therefore no net force)
Mass versus Weight
• Mass is the amount of matter in an object and is measured in kilograms
• Weight is the gravitational force exerted by a large body (Earth) on a mass and is measured in Newtons
• Wt = m(a)
• Weights may vary, but mass remains constant
Newton’s 2nd Law: The Elevator Ride
Fnet = FT + (-Wt)
Where FT = the tension force acting upwards and Wt = weight that acts
downwards
At rest:
Fnet = 0 so: 0 = FT + (-Wt)
FT = Wt
Accelerating Upward:Fnet = m(a) so: m(a) = FT + (-Wt)
FT = m(a) + mg
Constant VelocityFnet = 0 so: 0 = FT + (-Wt)
FT = Wt
Decelerating UpwardsFnet = m(-a) so: m(-a) = FT + (-Wt)
FT = m(-a) + mg
Weightlessness & Apparent Weight
• Apparent weight – the weight of an object that is sensed as a result of contact forces on it.
For instance, if you were on a scale and someone pushed down on you, the scale would read more
If you and the scale attached were freefalling, it would read zero b/c both would be accelerating in the same direction….ie.: astronauts on the space shuttle orbiting the Earth…the shuttle is freefalling while the astronauts freefall…they “float” b/c of the “apparent forces”
• Weightlessness- apparent weight is zero. There are no contact forces pushing up on you
Newton’s 1st Law
Newton’s 1st law states: “an object that is at rest will remain at rest or an object that is moving will continue to move in a straight line with constant speed” unless acted upon by an unbalanced force.
Inertia - the tendency of an object to resist change
Examples of Inertia
• Turning a corner sharply in a car…
• The Scrambler at the amusement park…
• Pulling a tablecloth off of a table without disturbing the dishes…
• The potato on the knife…
Friction
Friction – the force that opposes the motion between two surfaces that are in contact. This force is caused by the electromagnetic force b/t the two surfaces.
All surfaces, even smooth are rough at the microscopic level. When surfaces start to move, a weaker kinetic friction results.
The details of this process are still unknown! We simplify our calculations using a model
Model of Friction
This model makes two assumptions:
1.Friction depends on the surfaces in contact
2.Friction does not depend on the area of surfaces in contact
Example: a block of wood flat on the desk vs. on its side
Static Friction
Static Friction (Starting Friction) – the force that opposes the start of relative motion between two surfaces in contact
***these are maximum values***
When the magnitude of the force exerted exceeds the maximum value of static friction, the object will move
• Once the object starts to move, the force of friction DECREASES
Kinetic Friction
Kinetic Friction (Sliding Friction) – the force exerted on one surface by the other when surfaces are in relative motion
***these values are always less than static friction***
Ff kinetic < Ff static
Other examples:
Rolling Friction- less than sliding friction
Fluid Friction- friction in a fluid body (gas or liquid)
Force of Friction
• The magnitude of the frictional force (Ff) is proportional to the magnitude of the force pushing one surface against the other
Ff kinetic = μk FN Ff static = μs FN
Coefficient of Friction = μ (mu) – proportionality
constant for surfaces in contact
Air Resistance ~ Drag
When objects move through the air, they experience fluid friction or air resistance
As the object accelerates (freefall), air resistance INCREASES
Air resistance depends on:1. Velocity of the object2. Surface area3. Shape4. Density of the fluid
• As velocity increases, so does the drag force
• Eventually, the weight = drag
• At this point, the body no longer accelerates ~ terminal velocity
TERMINAL VELOCITY – the constant velocity that is reached when drag force equals the force due to gravity (dynamic equilibrium)
Newton’s 3rd Law
Newton’s 3rd Law – all forces come in pairs; equal in magnitude, opposite in direction
Interaction Pair (action-reaction pair) = two forces that are in opposite directions and have equal magnitudes
***common misconception*** action-reaction forces act on different objects therefore, equilibrium does not result
(the normal force and weight are not action-reaction forces!)
YouTube - Newton's 3rd Law - Science Theater 09
Inclines
Hanging Signs
Solving using the component method:
x = F cos θ y = F sin θ
• Add the x and y components • Use Pythagorean Theorem to find R• The magnitude of R is the magnitude of the
weight of the sign• The direction of the weight is down