Mechanical systems is the study of forces and the application of forces

Mechanical Systems Overall Expectations
By the end of this course, students will:

• describe and apply concepts related to forces, Newton’s laws of motion, static and kinetic friction, simple machines, torques, and mechanical advantage;
• design and carry out experiments to investigate forces, coefficients of friction, and the operation of simple machines;
• identify and analyse applications of applied forces, friction, and simple machines in real-world machines and in the human body.

The focus of this strand are forces and the application of forces via simple machines. The main headings of study are as follows:

1. To start the program I will spent the openning sessions reviewing elementary math skills. Without these skills it will constantly be a struggle to achieve high marks! You will be expected to complete and hand worksheets provided and from this site.
2. Review of the simple elements of motion and its components. A quick look at vectors. A board presentation.
   For a set of homework questions. This is a hand in homework assignment Physics Problems for College Bound Students
   Click the Leaf for assignment   Due date is September 7 2008 or Feburary 6 2009
   The homework section is divided into colour sections (blue, green,& pink). If you need addition help come at 8:00.
   A short list of definitions and a formula page may be found at

   For addition information view Div 1

3. Force's and Newton's Three Laws; emphasis on the Second Law
   Free body diagrams
4. Friction and the Inclined Plane
5. Identifying simple machines: ramp, lever, pulley will be studied in some detail
6. Torques, Force and Displacement; how they are related to each other
7. The Law of the Lever
8. Simple machines and Mechanical Advantage; single, double and moveable pulley systems
9. End-of-Unit Task: Construct a Compound Machine; eg a block and tackle

Forces in General

When we say that there is a force on an object we mean that there is a push or a pull on the object. Some outside agent is placing this push or pull on the object.

In the metric system forces are measured in units of Newtons. This unit is named after Isaac Newton. In the English system forces are measured in units of pounds. A Newton of force is much smaller than a pound of force. It takes about 4.5 Newtons to equal a force of one pound. So, if you usually state your weight in pounds, then you could figure your weight in the Newtons by multiplying those pounds by 4.5.

Forces are vectors. That is, they are quantities that have both size and direction. Forces can be symbolized with arrows, as can all vectors. The arrow in the picture below is meant to show a force with the size of 15 Newtons directed toward the left.

One must understand vectors to understand forces.

Why is "Net Force" Important?

"Net force" is a central idea of dynamics. Here's why:

Newton's Laws are the big deal in dynamics. Newton's First Law can be stated:

If the net force on an object is zero, its acceleration will be zero.

You will soon find out that Newton's Second Law says:

where F_net means "net force".

In order to use Newton's Laws, the first thing you need to know is "What is the net force".

Finding the Net Force:

In Physics 1, you will need to be able to calculate the net force on an object in the five situations shown below.

	If no forces act on an object, the net force on the object is zero. Although this happens in physics problems, it is very unlikely in practice that an object will have no forces at all acting on it.
	If there is just one force on an object, then that force is the net force. In the diagram at left, the net force is 5 Newtons to the right. For example in free fall, the net force on an object equals its weight - the one force pulling on it.
	If 2 forces push or pull on an object in opposite directions, and the two forces cancel each other exactly, the net force is zero.
	If two forces act on an object in opposite directions and they don't exactly cancel, what is left over is the net force (the difference in the forces). In the diagram at left, the net force is 2 Newtons to the right.
	If two(or more) forces act on an object in the same direction, the net force is the sum of the forces. In the diagram at left, the net force is 10 Newtons to the right.

1.Mechanics & Forces; Working with Net Forces Click here to view

2. Vectors in 4 parts; Introduction, Finding Components, Visualizing Components, & Component Method for Adding Vectors Click here to view

Newton's First Law of Motion

Inertia is defined as that property of matter that resists changes to its state of motion or when it is at rest. Inertia is a resistance to a change in motion, whereas friction is a resistance to that motion. Remember a body at rest will stay at rest, a body in motion will stay in motion, unless acted upon by some external force. This is not extremely obvious on Earth because all motion is subject to some from of friction which is an external force an will act in opposition to any appllied force or motion. The above statment is essentially Newton's First Law of Motion.

Newton's Second Law of Motion

When a force acts on an object, this object will accelerate in the direction of the applied force. As long as the force is applied the object will accelerate. A bullet fired from a rifle will accelerate down the barrel of the rifle. Once it leaves the barrel, the applied force of the chemical explosion is not longer present and the bullet will now gradually slow down due to air resistance. Actually the bullet will either strike some object or fall to the ground long before air resistance will stop its motion. Gravity will act on the bullets vertical motion but will not effect its horizontal motion.
The mass of an object is also part of the equation. Throw a baseball then try to throw a bowling ball. Which can you throw farther? The applied force which cames from you arm muscles is the same in both cases. The baseball will achieve a greater acceleration and travel further. The only difference if the mass of each ball.
Newton's Second Law is stated on page 108 of the text, and so is the equation theat relates the three variables; mass, acceleration, and force. F = ma. Remember that F is actually the net force acting on the object.
Another example of this concept is the difference between mass and weight.

The Law itself is simple and straight forward to use. Additions to a problem include

• determining the net force acting on the object
• resolving a force in the horizontal and vertical directions
• when masses and forces are know, these can now be used with the seven equations of motion to determine velocity and distance of an object

Newton's Third Law of Motion

Forces always occur in pairs. The action force and the reaction force. Whenever one object exerts a force on another or second object, the second object exerts a force on the first object will an equal magnitude but in the opposite direction. So who wins this apparent pushing contest? Lets look at a couple of examples.

• Take a slap shot with a hockey stick; what moves?
• With skates on stand at the boards and push on them; what moves?
• A rocket engine is ignited and rapidly expanding gases are thrust out the nozzle; both the gaes and rocket move, but in opposite directions
• While sitting in a canoe, you paddle. The paddle pushes backwards and the canoe move forward; equal forces but opposite direction

First we must look at what is called a Free Body Diagram representing all the forces acting on an object. Please note that all forces are vectors. This will be dealt with accordingly.

An object, either in motion or at rest on a horizonatal plane has four forces acting on it.

• F_g is the force of gravity acting on the object in a downward direction.
• F_m is the force of motion acting on this object and causing it to move with a given velocity in the same direction as the force. The object may or may not be accelerating.
• F_f is the force of friction acting between the object and the surface it is resting on. This force is always opposite to the force of motion but can never cause the object to move in a backwards direction even though it may have a value that can exceed F_m.
• F_n is the so called normal force. This is the force of the plane or surface acting upward on the block and if the object is not moving in the vertical plane, will equal the force of gravity of F_g. The normal force is always perpendicular to the surface. If the surface is horizontal F_n will equal F_g. If the surface is tilted then F_n will not equal F_g and always be less than F_g.

Situations relating these four forces:

• If F_g = F_n the object will niether move up or down.
• If F_g > F_n the object will fall downward. Such an example would occur if placed your book on a piece of paper .
• If F_g < F_n cannot occur because F_n is a reaction force and can never be greater than F_g Note, however, that if F_g is increased F_n will also increase.
  

  ---

• If F_m = F_f the object will either be at rest or moving at a constant velocity. Note: at rest means the v = 0.0 m/s. In both cases there will be no acceleration.
• If F_m > F_f the object will be accelerating in the direction of this force. When this situation occurs the horizontal force are considered to be unbalanced and the object moves in the direction of the greater force.
• If F_m < F_f the object will definitely be at rest or slowing down if the object was origonal in motion. F_f will be studied on its own under the concepts of coefficient of friction.

Coefficient of Friction

1. The force of friction appears to be approximately the same different low speeds.
2. The force of friction does not depend strongly on the area of contact between clean uniforn surfaces.
3. The force of friction is directly proportional to the perpendicular force (the normal) pressing the two surfaces together.
4. Starting friction is somewhat greater than moving friction. Remember that inertia must be overcome to start an object moving.

If the plane is not in the horizontal position but is inclined then the acting forces on the object interact with each other in a more complex manner.
In this situation the force of gravity F_g will influence the motion of the object down the inclined plane.
Here's a diagram of the forces acting on an object sitting on an inclined plane.

The dynamics of this object will be a function of the angle of inclination, the surfaces in contact with each other as measured by the coefficient of friction, the mass of the object, that is F_g and any applied force, F_m. These relations will be discussed in class, with an appropriate board note.
If the object is just about to move the angle θ is called the angle of repose
Information relating to our experiments

A third hand in homework assignment   Due date : September 28 or February 25

Section 2

Machines, Work, & Mechanical Advantage

A machine is a device designed to make "work" easier or in some cases possible for a preson to do. If you have a flat tire you cannot lift your car, however using a car-jack or screwjack enables you to raise the car and change the flat. Also, you cannot remove the wheel nuts without a tire wrench. These are examples of machines. Here are pictures of 6 simple machines.

Some machines change one force into another, others transfer force from one place to another or cause an applied force to have its direction changed. Machines can amplify a force or decrease its size. You should and remember examples of each of these different machines.
One thing a machine cannot do: make energy. Machines change amplify but do not produce more energy than what can be inputed.
How is work and force related?

The Inclined Plane or Ramp

The inclined plane is a simple machine that allows large objects to be raised against the force of gravity, with less work than needed to directly lift the object.
An experiment will be done to confirm this concept. A mass will be lifted a given distance and the work calculated to do so. The same mass will be pulled up a ramp and the work required determined. The two values will be compared.
This leads to the concept of mechanical advantage. In each case the amount of energy is the same, however the force or effort can be manipulated. This is what a machine does best. The actual mechanical advantage of any machine is the ratio of the magnitude of the force required to lift the load vertically (the load force) to the magnitude of the force necessary to move the object by the machine doing the work.
Determining the efficiency of a machine, use the formula

               load force          Fg
       MA    =   ----------   =     -------
               applied force        Fa
        

Levers and Pulleys

A lever consists of a rigid bar that can rotate about a fixed point called a fulcrum There are three classes of levers which depent on the position of the load to applied force to fulcrum. Make sure you can define each. Pictures are shown below

The turning effect of a force on a lever is called Torque. It is defined to be the product of the force and the perpendicular distance from the axis of rotation to the application of the applied force or the load. This perpendicular distance is called the lever arm (l) . Torques has units of newton-meters but is not really considered to be work. The torque applied to one side of a lever must equal the torque on the other side of the lever. Since torque equals F x l, determing an applied force for a lever can be computed. Problems to be done in class.

Pulleys are another of the simple machines. Pulleys trade distance for effort so as to make lifting a heavy object easy that is, the applied force can be reduced. Examples of pulley systems are shown below.

For You: determine the mechanical advantage of each of these systems

A simple lab activity is carried out, in which you build the pulley system and compare the effort force to the load and the distance the load is raised to the distance pulled by the effort. Machanical advantage can then be determined.

DIV 1

Homework Assignment #3

DIV 5

The Lever and Mechanical Advantage

A lever consists of a rigid bar that can rotate about a fixed point called a fulcrum. There are three classes of levers depending upon where the load, effort and fulcrum are positioned relative to each other. (See above diagrams and those sketched in class).
In this picture the effort is on the left and the load is on the right. Note the various ratios of effort to load, distance ratios and arc length ratios.

The turning effect of a force on a lever is called torque. When a lever is in the balanced position, the clockwise torque will equal the counterclockwise torque. This is called the law of the lever.
The magnitude of the torque symbol τ is calculated by multiplying the force applied (either load or effort) by the perpendicular distance of the force from the fulcrum. The perpendicular distance is called the lever arm l. The unit for torque are newton-meters (N-m)
Experiments are to be done in class to verify this law and to measure the Mechanical Advantage MA of a lever system.

There are two types of mechanical advantage:

• Ideal mechanical advantage which ignores friction and is based on distances.
• Actual mechanical advantage which incorporates friction, based on the forces used, ie, effort and load.

Which one do you use: read the problem, it will tell you. Sometimes you calculate IMA and then calculate AMA
Both IMA or AMA are the ratio of the load force to the applied force or F_g to F_a.

The efficiency of a machine is the ratio of useful work done to actual work done. In most machines incolving motion effort muct be applied to overcome friction. This causes the machine's useful work to be less than the applied work. In the example of pushing a crate up a ramp the ramp makes the effort easier but frictional forces require extra effort.

For more information go to DIV 6

DIV 6