0.19 Phy1170: energy -- work  (Page 4/7)

The special name and notation are used because this patternoccurs often in physics and mathematics.

Units of work

The SI unit of work (and energy) is the newton-meter (N*m), which is given the name joule (symbol: J), after the English physicist James Prescott Joule. One joule is equivalent to onenewton of force causing a displacement of one meter.

A stubborn dog

Pretend that you have a dog that is very stubborn and just wants to sleep. You pull on the dog's leash and cause the dog to slide 2 meters across thefloor. In this case, the displacement is horizontal and you are pulling at an angle of 30 degrees above the horizontal.

The work done on the dog would be the product of the horizontal component of the force that you exert on the leash (F*cos(theta)) and thedisplacement distance of 2 meters. If you were pulling with a constant horizontal force component of 3 newtons, then you would have done 2*3=6 joulesof work.

A stubborn pig

A very large pig has escaped from its pen. You have a rope tied around the pig's neck and you are trying to pull the pig back into the pen. The rope is horizontal andyou pull with a steady force of 3 newtons.

While you are pulling, however, the pig is backing up (actually pulling you forward away from the pen), and travels 2 meters in the direction opposite thedirection that you are pulling.

In this case, the angle between the line of action of the force that you are exerting and the direction of the pig's displacement is 180 degrees. Since thecosine of 180 degrees is -1, the product of the force, displacement, and cosine of 180 degrees would be -6. Therefore, your efforts to move the pig toward thepen are unsuccessful and you have done -6 joules of work on the pig.

Therefore, work can be either positive or negative.

More on that stubborn pig

The very large pig has decided to lay down on a hydraulic lift on the back of a truck and someone accidentally flipped the switch causing the hydraulic liftto start moving up.

You still have a rope tied around the pig's neck and you attempt to pull the pig off the lift to prevent it from getting hurt. You pull as hard as you can onthe rope but the pig doesn't budge. The lift goes up two meters to the height of the truck bed and turns itself off automatically with the pig still laying onthe lift.

The angle is 90 degrees

In this case, the angle between the line of action of the force that you exert and the direction of displacement of the pig is 90 degrees. The cosine of90 degrees is 0. Therefore, the product of the force, the displacement, and the cosine of 90 degrees would be 0.

While you might be ready for a rest after exerting all of that effort trying to pull the pig off the lift, you actually haven't done any work on the pig.

Therefore, work can even be zero if the line of action of the force is perpendicular to the displacement of the object. In this case, work did get doneto raise the pig 2 meters off the ground, but you didn't contribute anything to that work. The work was done by the mechanical system that operates thehydraulic lift on the truck.