In the experiment investigating a block sliding down an inclined plane the relationships studied are

• Surface area contact
• Types of material or surfaces in contact
• Mass of block

Since the experiment was done qualitatively (no numbers or measurements), of the three variables it appeared that only type of material effected the ability of the block to slide down an inclined plane. Both surface area and mass did not change the angle of repose.

In the second experiment, with the same block will be pulled on a horizontal surface. In the class experiment the force required to overcome static friction and the force required to overcome kinetic friction (& keep the block) moving will be measured for four different masses. Mass must be changed to force in the calculations and graphings.
The starting force required to just get the block moving is related to static friction and the force to keep the block moving is related to kinetic friction is to be plotted against the different masses (F_g) and the slope of the line is to be determined. This slope is the coefficient of friction. The slope will be non zero and usually less than 1. There is no units to this slope.

In the third experiment the coefficient of Sliding Friction will be determined.
This relates directly to the diagram above seen here as a thumbnail.

Work and Force

• Work is the energy required to cause an object to move. Work is done when an object is moved a given distance. If the object does not move then no work is done, even though energy is applied. An example of this is you pushing on a wall, just because you apply a force, the wall does not move hence no work is done.
• Another way of saying the same thing: a force when applied to an object may or may not cause the object to undergo an acceleration. If an onject undergoes a change in motion i.e. it is accelerated then work is done on the object. Remember Newton's First Law: An ojbject in motion will stay in motion unless acted upon by a force. On Earth this force is usually friction which acts in the opposite direction of the motion.
• The units for work is the joule. This is the same unit as for energy.
• Work is mathematically calculated by multiplying the force times the distance the object moves. The force and the direction of the motion must be in the same direction. Pushing an object acoss a floor will not cause it to be lifted.
• The mathematical is W = Fd
• This equation is key to understanding why a machine makes a job or "work" easier. Machines can change the value of the applied force making the effort involved easier. For example it is easier to push an heavy load up a ramp than to lift it directly upward. A screwjack easily will lift a car, something you could not do without a machine.
• Important: machines change or alter forces not work
  Since work is applied energy, it cannot be created, but you can alter the effort required to do that work. Explination via examples to follow in class

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

Homework from the text book
   Page 65 # 7
   Page 66 #9, 10
   Page 68 #13, 14
   Force & Motion work sheet; requires motion equations to complete all the questions.

Hints when working with motion equations

These problems tend to be layered, that is multiple steps are required, several formulae are to be used in conjunction with one another.
A few common sence points

• problem analysis is an absolute must!
• rest means that the velocity is 0.00 m/s. An object can start from rest v₁ = 0.00 m/s or it may come to rest, it is stopping, therefore v₂ = 0.00 m/s.
• A positive force will cause the acceleration to be in the direction of the motion and either keep the object moving at a constant speed or cause the object to speed up.
• A negative force will cause the acceleration to be in the opposite direction of the motion. This will cause the object to slow down and eventually come to rest or stop.
• Vector diagrams or free-body diagrams will assist you in sorting out the forces acting on an object. Accurately drawn diagrams will enable you to sove problems without using triginometry (Laws of Sines and Cosines)
• Subtracting the second or final velocity (v₂) from the first or initial velocity (v₁) and dividing by the time it takes the object to change velocity will yield the acceleration (Units are m/s²)
  These are the equations that you must be familiar with. For a set of homework questions Click the Leaf
• Remember that the mass can be changed into a force by multiplying the mass by 9.80. Please note that this force only acts in the downward direction or [S] in a vector diagram. A normal force will always be equal to this but opposite in direction.

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

Machines

Fundamental Types of Machines

The six (seven) simple machines can be catorgized into two modes:

1. the lever which include the pulley, wheel and axle and gears
2. the inclined plane which include ramps, the wedge, and screw

• Machines are devices can be used to transform energy from one form to another such as an car engine turns chemical energy stored in gasoline into mechanical energy.
• Machines are also used to transfer energy from one place to another.
  Remember, a machine cannot create energy or work
  A bicycle sprocket and chain transfers energy from the pedals to the back wheel.
• Another use for machines is to multiply force. In any system energy must be conserved, however, force may be manipulated
• Machines are used to change the direction of a force, which may make the task easier for a person to preform. For example, sometimes its easier to pull than to push.
• Machines make a human chore easier or in some cases possible, for example you cannot lift a car up to change a tire with the use of a machine.

Moments or Torque

The turning effect produced by a force acting on an object free to rotate about a point of support is called its moment about that point or torque. The magnitude of this moment depends on two factors : the magnitude of the applied force (load or effort) and its distance from the point of support. This means that the torque or moment about a point is the product of magnitude and distance: Torque = F x d . This torque may be in either a clockwise or counterclockwise direction. The units for torque is the newton-meter (N-m).
Torque will occur on both sides of the fulcrum of a lever, but in opposite directions. Motion will occur on the side with the greatest torque and if the torque is equivalent on both sides of the fulcrum motion will not occur and all forces will be balanced or in equilibrium.

Mechanical Advantage

The force applied to a machine is understood to be the force the the operator applies to make the machine work. This force is frequently called the effort.
The force moved at the "other end " of the machine is refered to as the load or resistance. Remember, a mass when moved becomes a force (F = ma)
During the operation of a machine both the applied force, effort, and the load are displaced. The ideal mechanical advantage of a machine is the ratio of the distance that the effort moves to the distance theat the load moves. Since friction always occurs from the contact of moving parts,the actual mechanical advantage is somewhat less than the ideal mechanical advantage and can be determined as the ratio of the load to the applied
force F_L to F_E.

Efficiency of Machines

The fundamental purpose of any machine is to do useful work. In order ot do work the machine must be supplied with energy. If all this energy is converted into useful work this would be an ideal machine with an efficiency rating of 1 or 100%. Since energy is always lost in a machine to other nonuseful forms of energy such as sound, heat, or friction, no machine actually converts all its inputed energy or work to useful or actual work done. The efficiency of a machine is evaluated as the ratio of useful work done by the machine to the work or energy supplied to operate the machine. There are several versions of efficiency equations which will be discussed in the lesson.
Efficiency may be determined as the ratio of actual mechanical advantage to ideal mechanical advantage.