Apply the golden rule of mechanics

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The "Golden Rule of Mechanics" was formulated by Galileo Galilei, an Italian scientist, and reads: "What you save in strength, you have to put in the way". You can apply this principle in physics to calculations within mechanics.

Use the golden rule of mechanics for lifting work
Use the golden rule of mechanics for lifting work © Lisa Eiling-Wilke / Pixelio

What you need:

  • calculator

How to explain the golden rule

  • If you lift an object or move it on the ground, you are doing some work. All of these activities have the common feature that a force is overcome along a distance.
  • Note that in the physics only the physical work is calculated.
  • The "golden rule of mechanics"means that the work gets bigger, the bigger the force is which has to overcome the resistance along the way.
  • Remember that the longer the path over which the resistance is overcome, the greater the work. Therefore, you calculate the work as the product of the force component F.s and the distance s.
  • To apply the "golden rule of mechanics" you need the formula W = Fs * s.
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  • The variable W means work. You use the unit Newton meter (Nm) or Joule (J).
  • Note that Fs is the force component in the direction of travel and has the unit Newton (N).
  • The variable s is the path and is measured in meters.
  • Note that the work 1 J is done when an object is lifted 1 m with a weight of 1 N.
  • Apply the "golden rule of mechanics" to a force whose direction coincides with the path angle includes α, this is the force component falling in the direction of travel. The formula is then Fs = F * cos α.

How to apply the principle of mechanics

  • You can apply the "golden rule of mechanics" to lifting work. The force F becomes the weight FG and from the distance s the height h. The weight FG In your calculations, multiplying the mass m by the acceleration due to gravity g = 9.81 ms-2
  • You calculate the lifting work WHub with the formula WHub = FG * H.
  • Practice with this task to apply the "golden rule of mechanics": A goods quantity of 2.5 t should be raised by 3.7 m. How big is the lifting work?
  • First, calculate FG. Convert 2.5 t to kg so you get 2500 kg. F.G calculate by multiplying m by g = 2500 kg * 9.81 ms-2= 24525 N.
  • Put the calculated value in the formula WHub= FG * h a. W.Hub = 24525 N * 3.7 m = 90742.5 J = 90.7 kJ.
  • The "golden rules of mechanics" can also be used to calculate the acceleration work. For this purpose, the formula WAcceleration = 1/2 * m * v2 worked. For example, if a car with the mass m = 1.5 t = 1500 kg accelerates from a standstill to 60 km / h = 16.67 m / s, the acceleration work is 208,416.68 kg m2 s-2 = 208.4 kJ, because you put the following values ​​in the formula: WAcceleration = 1/2 * 1500 kg * (16.67 m / s)2.
  • Remember that when you move an object on the floor you do not have the necessary force the force of weight, but only the force to overcome the friction between the object and the ground is.
  • Use the "golden rule of mechanics" and the following formula to determine the work of friction or displacement: WR. = FR. * s = μ * F.N * s where μ is the coefficient of sliding friction.
  • Practice with this exercise to determine the work of friction: A cardboard box with a weight of 15 N is pushed 4 m over a straight ramp. The coefficient of sliding friction is μ = 0.6. How much is the friction work?
  • First calculate the frictional force: FR. = μ * F.G = 0,6 * 15 N = 9 N
  • You calculate with the formula WR. = FR. * s the frictional force: WR. = 9 N * 4 m = 36 Nm = 36 J

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