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Educating the Net Generation - LearnWith.Tech
Educating the Net Generation . Educational Leadership, Feb. 1999, Vol. 56, No. 5, pp. 6-11. http://www.ascd.org/readingroom/edlead/abstracts/feb99.html.

The first equation used to calculate work is W Fd This equation, however, holds only for constant forces exerted in the direction of motion What happens if the force is exerted perpendicular to the direction of motion An everyday example of this is the motion of a planet around the Sun, as shown in Figure 10-2 If the orbit is circular, then the force is always perpendicular to the direction of motion Recall from 6 that a perpendicular force does not change the speed of an object, only its direction Consequently, the speed of the planet doesn t change Therefore, its kinetic energy also is constant Using the equation W KE, you can see that when KE is constant, KE 0 and thus, W 0 This means that if F and d are at right angles, then W 0 Because the work done on an object equals the change in energy, work also is measured in joules One joule of work is done when a force of 1 N acts on an object over a displacement of 1 m An apple weighs about 1 N Thus, when you lift an apple a distance of 1 m, you do 1 J of work on it Constant force exerted at an angle You ve learned that a force exerted in the direction of motion does an amount of work given by W Fd A force exerted perpendicular to the motion does no work What work does a force exerted at an angle do For example, what work does the person pushing the car in Figure 10-3a do You know that any force can be replaced by its components If the coordinate system shown in Figure 10-3b is used, the 125-N force, F, exerted in the direction of the person s arm, has two components The magnitude of the horizontal component, Fx, is related to the magnitude of the force, F, by a cosine function: cos 250 Fx/F By solving for Fx , you obtain Fx F cos 250 (125 N)(cos 250 ) 113 N Using the same method, the vertical component Fy F sin 250 (125 N)(sin 250 ) 528 N, where the negative sign shows that the force is downward Because the displacement is in the x direction, only the x-component does work The y-component does no work.



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And given the proper imports and error handling, what is the result A Compilation succeeds B Compilation fails due to multiple errors C Compilation fails due only to an error on line 14 D Compilation fails due only to an error on line 15 E Compilation fails due only to an error on line 16 F Compilation fails due only to an error on line 17 50 Given:

(Courtesy of Kay Elementrics)

Figure 10-3 If a force is applied to a car at an angle, the net force doing the work is the component that acts in the direction of the displacement





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The work you do when you exert a force on an object, at an angle to the direction of motion, is equal to the component of the force in the direction of the displacement, multiplied by the distance moved The magnitude of the component force acting in the direction of displacement is found by multiplying the magnitude of force, F, by the cosine of the angle between F and the direction of the displacement: Fx F cos Thus, the work done is represented by the following equation Work (Angle Between Force and Displacement) W Fd cos

Work is equal to the product of force and displacement, times the cosine of the angle between the force and the direction of the displacement

2 import javautil*; 3 public class GIS { 4 public static void main(String[] args) { 5 TreeMap<String, String> m1 = new TreeMap<String, String>(); 6 m1put("a", "amy"); m1put("f", "frank"); 7 NavigableMap<String, String> m2 = m1descendingMap(); 8 try { 9 m1put("j", "john"); 10 m2put("m", "mary"); 11 } 12 catch (Exception e) { Systemoutprint("ex "); } 13 m1pollFirstEntry(); 14 Systemoutprintln(m1 + " " + m2); 15 } }

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Other agents exert forces on the pushed car as well Which of these agents do work Earth s gravity acts downward, the ground exerts a normal force upward, and friction exerts a horizontal force opposite the direction of motion The upward and downward forces are perpendicular to the direction of motion and do no work For these forces, 90 , which makes cos 0, and thus, W 0 The work done by friction acts in the direction opposite that of motion at an angle of 180 Because cos 180 1, the work done by friction is negative Negative work done by a force exerted by something in the external world reduces the kinetic energy of the system If the person in Figure 10-3a were to stop pushing, the car would quickly stop moving its energy of motion would be reduced Positive work done by a force increases the energy, while negative work decreases it Use the problemsolving strategies below when you solve problems related to work

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