Force is that action which causes or tends to cause motion or a change of motion of an object. To describe a force completely, its direction of action, magnitude, and point of application must be known. What is commonly referred to as a "force" is really two forces, as forces are never present singly, but always in pairs. The two parts are called action and reaction. They are always of equal magnitude, but in opposite directions. In this text, the weight of an object will be considered a force. Forces are commonly measured in units of ounces (oz), pounds (lb), and tons (ton).
Pressure is the amount of force or thrust exerted over a given area. Pressure is the combination of two units, force and area. Therefore the common units for pressure will be a combination of these two, lb/in2, oz/in2, lb/ft2, etc.
The concept of time has its root in the natural cycles of the earth. One very visible cycle is the ocean tides. The words time and tide both come from the same root. The current idea of time is as a measure of an interval of duration. Time may be better described as an accounting technique for relating events. The common units for time are seconds (sec), minutes (min), and hours (hr).
Velocity, speed, is the time rate of movement. Velocity is also a combined unit. It is the combination of distance and time. The common units of velocity are ft/min, mi/hr, etc.
Power is the rate of doing work. Work (W) is the result of a force acting (or moving) through a distance. Written as an equation:
A numerical value for work may be obtained by multiplying the value of a force by the displacement.
Problem: If a force of 100.0 lb displaces 12.0 ft, how much work has been performed?
In this situation 1,200 ft-lb of work was completed. Notice that according to this definition, unless both distance and force are present, no work is being accomplished.
Problem: A loaded wagon weighing 10,000.0 lb requires 400.0 lb of force to pull it along a horizontal surface. How much work is done if the wagon is pulled for 100.0 ft?
In this problem, the 400.0 lb of force is not related to the weight of the wagon. It is the force required to pull it.
Written as an equation Power =- because work equals distance times
Time force. Then:
Distance x Force W D
Time T T
Because D/T equals velocity (speed), power is the force times the velocity. This demonstrates that power is a combination of distance, force, and time.
Problem: How much power is developed when a force of 100.0 lb moves through a distance of 12.0 ft in 2.0 min?
Notice that the unit associated with power is a combination of the individual units for the variables. In this case, the answer is read as "600 foot-pounds per minute." This is the "time-rate" at which work is being done. Remember; always write down the units that are associated with a number.
Problem: A person loads a 60.0-lb bale onto a truckplatform4.0 ft high in 0.50 min. How much power is being developed?
Up to this point we have used easy-to-understand values with units of feet for distance, pounds for force, and minutes for time. Suppose that in the previous problem the individual could load three 60.0-lb bales in 0.50 min. In this example it is easy to make a mistake in determining a value for the force. The solution to this problem is:
3 bales 60.0 lb
0.50 min 0.50 min min
Here the average power produced is 1,400 ft-lb/min because the weight moved in 0.50 min is the weight of all three bales (3 x 60 lb).
This problem illustrates a principle of power. If three times the amount of work is done in the same amount of time, the power will be increased three times. What is the impact on the power produced if the distance changes, or if the time changes?
Problem: If a person could load three 60.0-lb bales onto the 4.0 ft platform in 10.0 sec, instead of 0.50 min, how would this change the power produced?
T 10.0 sec sec sec
The amount of power changed, but this answer cannot be compared to the previous one because the units are different. You might ask, is foot-pounds per second an acceptable unit of measure for power? Yes, but to compare this value for power to the previous one the units must be converted. This can be accomplished in more than one way. When the desired units are ft-lb/min, a conversion value can be added to the equation. To change the unit of time from seconds to minutes:
Now the two values can be compared. It should be obvious that it takes a greater amount of power to complete the same amount of work in less time. A similar relationship is true for the distance moved. The power requirement will change as the distance moved changes, assuming that the force and the time remain the same.
In summary, power is directly proportional to distance and force, and is inversely proportional to time.
In working with agricultural machinery, speed is usually measured in miles per hour (mph). When this is the case, the units must be changed. Otherwise the answer will be incorrect. Study the following statements: If Power is equal to work divided by time, then:
This can be changed to:
and because D/T (distance/time) is speed, if D/T is in miles/hour, it must be converted to feet/minute. The common conversion factor for speed is: 1 mph = 88 ft/min. This factor is obtained as follows:
min 1 mi 60 min 1 hr
Therefore power can also be found by:
where F = force (lb); S = Speed (mi/hr); 88 = Units conversion value.
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