chapter 2 forces

8/4/2019 Chapter 2 Forces

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2.1 Forces and Free-Body Diagrams

Forces

We define Force as any type of push or pull on an object (e.g. pushing a cart orpulling on a rope).

• Forces cause things to move, but they do not always give rise to motion. (e.g.Exerting force on a heavy, immovable desk).

• When a force is exerted on an object, the object changes shape, even on thesmallest scale. Some sort of deformation has occurred.

• Force has a magnitude and a direction and is therefore a vector quantity.

• Force is measured in newtons (N), and is equivalent to the force required toimpart acceleration of 1m/s2 to a mass of 1 kg.

Look at the forces listed on pages 72 and 73 in your text.

Free-Body Diagrams diagram of a single object showing all of the forcesacting on an object.

Sample problems 1, 2 and 3.

Try # 7 on page 73

Sample problems 4 and 5

Homework

p. 76 # 2, 3, 4, 6

2.2 Equilibrium and Newton’s First Law of Motion: Inertia

• The net force acting on an object, Fnet, is the vector sum of all the forces acting onthe object.

Sample 1

A young child exerts a force of 10 N to the right on a large sofa which has a mass of 100 kg. Static friction does not allow the sofa to move. Draw a FBD to illustrate theabove situation.



By calculating the vector sum of all of the forces, we will see that the net force actingon the sofa is zero.

The horizontal forces balance each other out, as do the vertical forces.

The object is said to be in a state of static equilibrium, since it has a net force of

zero and it is completely still, relative to the surface it is resting on.

Sample 2

An airplane with a mass of 1.6 x 104 kg is traveling with a constant velocity of 800km/h [E] while maintaining a constant altitude. Draw a FBD to illustrate the abovesituation.

In this case, the plane is in motion, but we see that the net force is still equal to zero. The plane is said to be in a state of dynamic equilibrium.

Since the velocity is constant, there is no acceleration.

In fact, any object in equilibrium experiences zero acceleration.

• In any case, Fnet (Σ F = 0).

That is, Σ Fx = 0, Σ Fy = 0, and Σ Fz = 0.



Inertia is a property of matter that causes a body to resist changes in its state of motion; it is directly proportional to mass.

• Objects at rest remain at rest unless acted upon by a net force• Objects in motion remain in motion unless acted upon by a net force• If the velocity of an object is constant, the net external force acting on it must be

zero• If the velocity of an object is changing either in magnitude, direction, or both, the

change must be caused by a net external force on the object.

Seatwork

p. 80-81 # 1, 3, 5, 7, 9

Newton’s Second Law of Motion

Suppose you have two small carts, with the respective masses m1 and m2;where m2 has twice the mass of m1.

To each cart, you attach a small fan which exerts equivalent amounts of force todrive its cart forward.

Which cart do you expect to accelerate away faster?Why?

Since m2 has twice the mass, it accelerates twice as slow as m1.

Newton’s 2nd law illustrates how mass, force and acceleration are related.

Force is measured in newtons (N), where 1 N is the force required to accelerate 1-kg

by a magnitude of 1m/s2.

1N = 1 kg (1m/s2), or 1 N = 1 kg • m/s2

• Remember that force is a vector quantity and has direction and its own respectivecomponents!

ΣFx = max and ΣFy = may

How does this relationship relate to Newton’s 1st Law?

Newton’s First Law: If the net force acting on an object is zero, theobject will maintain its state of rest or constant velocity

Newton’s 2nd Law:If the external net force on an object is not zero, the object accelerates in the direction of the force. The acceleration is directly proportionalto the net force and inversely proportional to the object’s mass. This law isrepresented by the equation: F net = ma



If acceleration is zero, the 2nd law implies that the net force should be zero also.

The first law is a special case of the 2nd law, where the net force is zero.Example Question

A box with a mass of 100 kg is pushed over a level surface to the right with anapplied force of 50 N [20˚ below the horizontal]. Kinetic friction is 20 N to the left.

a) Determine the magnitude of the normal force, FN

b) What is the acceleration of the box?c) What is the coefficient of kinetic friction?

Seatwork p. 83 # 10, 12, 14

Weight: is the force of gravity (Fg) acting on an object. It is also a vectorquantity measured in newtons.

Weight = Fg = mg g represents the acceleration due to gravityg = 9.8 m/s2

Seatwork p. 84 # 16-19

Newton’s Third Law of Motion

• Is sometimes referred to as the action-reaction law

• Involves forces that act in pairs on two objects at a time. (example, helicopterblades spin quickly, exerting an action force downward on the air. The airexerts a reaction force upward on the blades, sending the helicopter in adirection opposite to the motion of the air.)

2.4 Exploring Frictional Forces

Recall that friction is a contact force that resists the motion of an object and isperpendicular to the normal force acting on the object.

Friction is defined by the expression

Static frictional forces from the interlocking of the irregularities of two surfaces willincrease to prevent any relative motion up until some limit where motion occurs.

It is the threshold of motion which is characterized by the coefficient of static friction.

The coefficient of static friction is typically larger than the coefficient of kineticfriction.

Ff = μFN



Fluid Friction and Bernoulli’s Principle

A fluid is a substance that flows and takes the shape of its container.It can be either a liquid or a solid.

Newton’s laws of motion can be applied to analyze relative fluid motion. This helps

us understand the factors that affect air resistance, minimize turbulence and controlthe motion of objects moving through fluids (aerodynamics and hydrodynamics).

As a fluid flows, there are attractive forces that hold the molecules together. Thesecohesive forces cause internal friction or viscosity .

Honey has a high viscosity, because its cohesive internal forces do not promote easyflow.

Likewise, water has a low viscosity, as it flows quite readily.

Let’s look at the flow of water through a pipe…

• As the water flows through the pipe, the water closest to the pipe wallsencounters the most friction, and is the slowest.

• Water in the center of the pipe flows the fastest, as it experiences the leastresistance.

• This is an example of a laminar flow

Laminar Flow – stable flow of a viscous fluid where adjacent layers of a fluid

slide smoothly over one another. This type of flow can alsooccur when a fluid passes around a smooth object (like airflowover the nose of a plane)

Turbulent Flow- occurs when that fluid has to make its way around a non-efficiently shaped object (i.e. a box), causing a high externalresistance, or when the fluid is highly viscous.

Drag- Is the forces that act against an object’s motion through a fluid



• With respect to energy efficiency, turbulence (or drag) is not a good thing, askinetic energy is lost due to heat created by the friction

To combat turbulence, engineers started streamlining their respective designs.

Tools used to accomplish this are large wind tunnels in which models are placed toobserve airflow around vehicles or other objects. A wind tunnel creates an artificialand controlled environment in which detailed observations can be made.

Homework p. 106-107 # 1-7

Streamlining is the process of reducing the turbulence experienced by anobject moving rapidly relative to a fluid.

Nature, over time, has allowed animals to evolve into more streamlined creatures.• Fish and birds are shaped the way they are so that they could move quickly

through their environment without expending any extra energy.

One might think that the smoothest surface would create the least “drag”.

This isn’t always the case.

Sometimes the fluid sticks better to a smooth surface. This “stickiness” actually increases drag and decreases efficiency.

A shark may look like a smooth, torpedo bolting through the water.

Up close, however, the shark’s skin is rough.

• The roughness of a shark’s skin causes tiny eddies that add a little barrierbetween the surface of the shark and the water in which it is swimming.

• This allows for the water to quickly flow around the body of the shark.

http://emu0.emu.uct.ac.za/gallery/shark.gif



You might have seen this property applied to thesurface of golf-balls.

• The golf-ball is dimpled in order to decrease thedrag as it travels through the air.

Bernoulli's principle states that a rise in pressure ina flowing fluid must always be accompanied by adecrease in the speed.

Conversely an increase in the speed of the fluid resultsin a decrease in the fluid’s pressure.

An example is provided by the functioning of aperfume bottle: squeezing the bulb over the fluidcreates a low pressure area due to the higher speed of the air, which subsequently draws the fluid up. This is illustrated in the followingfigure.

Venturi Tube

Label on the diagram below the areas of high and low velocity and the correspondingareas of high and low pressure.

http://www.ce.utexas.edu/prof/KINNAS/319LAB/Applets/Venturi/venturi.html

http://www.ce.utexas.edu/prof/KINNAS/319LAB/Applets/Venturi/venturi.html



Bernoulli’s principle also tells us why windows tend to explode, rather than implode inhurricanes: the very high speed of the air just outside the window causes thepressure just outside to be much less than the pressure inside, where the air is still.

The difference in force pushes the windows outward, and hence explodes. If youknow that a hurricane is coming it is therefore better to open as many windows as

possible, to equalize the pressure inside and out.

http://home.earthlink.net/~mmc1919/venturi.html

2.5 Inertial and Non-inertial Frames of Reference

Inertial Frame of Reference: A frame in which the law of inertia is valid.

e.g. A ball resting on the floor of a moving bus. Relative to the bus moving at aconstant velocity, the ball stays at rest, as if is there is no net force acting on it.

(Newton’s first law: Resting bodies will remain at rest unless a net force acts uponit).

Non-inertial Frame of Reference: a frame in which the law of inertia is not valid.

e.g. When the brakes are applied, the bus decelerates, but the ball continues movingat a constant velocity, relative to the ground. Relative to the bus, it appears that theball is accelerating forward. It appears as if there is a net force acting on the ball,

when there is none.

Newton’s 3rd Law: For every force, there is a reaction force equal inmagnitude but opposite in direction.



chapter 2 forces

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