Lesson 5: An Engineering Introduction to Machines–Inclined Planes (January 8 and 9)

Objectives: (1) To introduce students to the basic concepts of machines, as used by engineers; and (2) to specifically learn the most basic principles of the INCLINED PLANE.

INSTRUCTIONS:

  • Read the article below.
  • Answer the questions in the blue boxes. PLEASE NOTE: There are 20 questions in blue boxes inserted throughout the article.

Based on Mr. Tunon’s notes and powerpoint1

REVIEW:

Types of machines
Types of machines

In Engineering, there are five main types of simple machines:

    • levers,
    • wheels and axles (which count as one),
    • pulleys,
    • Incline planes, and
    • screws.

REVIEW:

Question 1 of 20  (incorporate the question in your answer):  Explain what a lever is and how it works.

Question 2 of 20  (incorporate the question in your answer): Give 2 examples of a lever being used.

Question 3 of 20  (incorporate the question in your answer): Explain what a wheel and axle is and how it works.

Question 4 of 20  (incorporate the question in your answer): Give 2 examples of a wheel and axle being used.

Question 5 of 20  (incorporate the question in your answer): Explain what a gear is and how it works.

Question 6 of 20  (incorporate the question in your answer):  Give 2 examples of  gears being used.

Question 7 of 20  (incorporate the question in your answer): Explain what a pulley is and how it works.

Question 8 of 20  (incorporate the question in your answer): Give 2 examples of a pulley being used.

A machine is an object or mechanical device that receives an input amount of work and transfers the energy to an output amount of work. For an ideal machine, the input work and output work are always the same. Remember that work is force times distance; even though the work input and output are equal, the input force does not necessarily equal the output force, nor does the input distance necessarily equal the output distance.2

Question 9 of 20  (incorporate the question in your answer):  Does “work in” generally equal “work out” in an ideal simple machine?

Question 10 of 20  (incorporate the question in your answer):   Explain why (or why not) the main point of a simple machine is often to make the output force different than the input force.

INCLINED PLANES

  • Inclined plane: a simple machine consisting of a sloping surface, whose purpose is to reduce the force that must be applied to raise a load.
Inclined plane
  • To raise a body vertically a force must be applied that is equal to the weight of the body.
  • The amount of work done (i.e., energy expended) in raising the body is equal to its weight times the distance through which it is raised.

Question 11 of 20  (incorporate the question in your answer): Explain what a inclined plane is and how it works.

Question 12 of 20  (incorporate the question in your answer): Give 2 examples of an inclined plane being used.

  • By means of an inclined plane a force smaller than the weight of the body can be exerted over a distance greater than the direct vertical distance, doing work equal to the product of the force and the distance through which it acts.
  • If friction is ignored, the work done using the inclined plane will be exactly equal to the work done in lifting the body directly.
  • To calculate the mechanical advantage of an inclined plane, divide the length of the ramp by the height of the ramp. M.A=Length of the sloping surface / Height of the plane.
  • An inclined plane in an ideal system whose sloping length is 5 m and whose vertical rise is 1 m has a mechanical advantage of 5; a 300-newton load can be moved up such a plane by a 60-newton force.

Calculating the mechanical advantage of an inclined plane:

Question 13 of 20  (show your calculations): You want to use an inclined plane to lift a 100 pound object 10 feet, with a  mechanical advantage of at least 5.  How long must the ramp be?

Question 14 of 20  (show your calculations): You want to use an inclined plane to lift a one ton object 10 feet, with a  mechanical advantage of at least 5.  How long must the ramp be?

Example 1:  The Great Pyramid (completed about 2560 BC)3

The Great Pyramid of Giza is the oldest monument on the list of the Seven Wonders of the Ancient World. And it is the only one left standing. It is a marvel of human engineering and construction. Its size and scale rivals any modern structure.

The Great Pyramid of Giza was built for the Fourth Dynasty Pharaoh Khufu (or Cheops), and was completed around 2560 BC. Scholars have long debated how it was built. There is no shortage of theories. Some evidence suggests up to 20,000 workers over the course of 20 years built it–perhaps by slaves, or maybe by paid workers.

When completed, the Great Pyramid, was faced in gleeming white Tura limestone.  I was a spectacular sight in the Egyptian desert, at 481 feet high (it has since lost its top and is currently 25 feet less tall) and covering 13.1 acres. It is estimated that 2.3 million stone blocks were used, weighing between 2 and 15 tons each.

Some theories suggest teams of men maneuvered each block over a ramp that encircled the structure as it rose, or that they moved each stone up long ramps that got higher and longer as the pyramid got taller, or even that scaffolding was used. Many reject these theories for various reasons. For example wood that could have been used for scaffolding or ramps would have been at a premium. Using  mud brick for those purposes would not have held under the enormous weight of each massive block.

However, recent archaeological discoveries may have solved the mystery of the system used to haul massive stone blocks into place some 4,500 years ago.  Archaeologists discovered the remains of this system at an ancient quarry in the Eastern Desert of Egypt. According to the archaeologists working at the site,4 this process could have moved massive stones up a steep ramp.

The system they suggest, would have been composed of a central ramp flanked by two staircases with numerous post holes. According to this theory, a sled carried a stone block and was attached with ropes to these wooden posts. This enabled ancient Egyptians to pull the gigantic blocks out of the quarry on very steep slopes of 20 percent or more.

Question 15 of 20  (Write the question and the correct answer):  What is noteworthy about the Great Pyramid of Giza.

Question 16 of 20 (Write the question and the correct answer):   Explain how inclined planes may have been used to build the Great Pyramid of Giza.

Question 17 of 20  (incorporate the question in your answer):  During the construction of  the Great Pyramid of Giza, would you expect a longer ramp would have been necessary for heavier blocks of stone?  Explain your answer.

Question 18 of 20 (incorporate the question in your answer):   During the construction of  the Great Pyramid of Giza, would you expect a longer ramp would have been necessary for the upper blocks of stone–that is near the top of the pyramid?  Explain your answer.

Question 19 of 20 (incorporate the question in your answer):   According to the above article, explain in your own words how post holes could have helped in using inclined planes during construction of of  the Great Pyramid of Giza.

Question 20 of 20 (incorporate the question in your answer):   If the  the Great Pyramid of Giza was built today, with modern techniques and equipment, explain why (or why not) you would expect modern engineers to use ramps.

 

  1.   John Tunon J. P. Taravella High School
  2. CK-12 website (https://www.ck12.org/physics/simple-machines-1501903848.65/lesson/Simple-Machines-PHYS/)
  3. Sources:  LiveScience, “This 4,500-Year-Old Ramp Contraption May Have Been Used to Build Egypt’s Great Pyramid,”  Owen Jarus, Live Science Contributor, 10/31/2018 (https://www.livescience.com/63978-great-pyramid-ramp-discovered.html);  Ancient History Encyclopedia, The Great Pyramid of Giza: Last Remaining Wonder of the Ancient,” publ. 1/18/ 2012 (https://www.ancient.eu/article/124/the-great-pyramid-of-giza-last-remaining-wonder-of/
  4. From the Institut français d’archéologie orientale (French Institute for Oriental Archaeology)