Lesson 5A: An Engineering Introduction to Machines–ALTERNATE, Inclined Plane (January 9, 2018)

This SUPPLEMENTAL assignment is for ONLY the students who have more than one engineering class with this teacher.

Objectives: (1) To introduce students to the basic concepts of machines, as used by engineers; (2) to build on basic principles previously learned about the inclined plane.

This is the third assignment1 relating to the inclined plane,  It explores some slightly more advanced aspects of the subject.

Please read the article below.  Then complete the Assignment in the blue box.

The Inclined Plane:2

  • Basic Principles of simple machines:
    • Work = Force X Distance
  • The Law of Conservation of Energy states that energy cannot be created or destroyed.
    • So the work done by a machine cannot be greater than the work done on the machine.
    • work input = work output
    • OR, input force X distance = output force X distance
    • So when the distance is increased, the input force decreases.
  • Machines do NOT decrease the amount of work you have to do, but change the way a force is applied.
  • They make work easier by allowing a force to be applied over a greater distance or by changing the direction of the input force.
  • There is a trade-off for less input force–the force is exerted over a greater distance.
  • In an inclined plane the trade-off is distance.  In order to use less effort by using the ramp, you need to travel a longer distance.

    Ramps (inclined planes)
    Ramps (inclined planes) — click on image to enlarge.

Consult the diagram above.  Assume an ideal machine (ignore friction)

  • Questions 1, 2, and 3.  Draw the figure above, with no ramp, Ramp #1 and Ramp #2.
  • Question 4 of 10 (write the question and answer)  Which ramp is shorter?
  • Question 5 of 10 (write the question and answer)  Which ramp is longer?
  • Question 6 of 10 (write the question and answer)  Which ramp would take less effort (force) to  push an object up up?
  • Question 7 of 10 (write the question and answer)  Which ramp requires more WORK?

Gravitational Force and Inclined Planes:3

Every object has a center of gravity. The center of gravity is the point at which the entire weight of a body may be considered to be concentrated; if supported at this point, the body would remain in equilibrium in any position.

The force of gravity acting on an object is directed through this center of gravity and toward the center of the Earth. The object’s weight, W, can be represented by a vector directed down (along the line the object would fall if it were dropped). When this object is resting on a level surface, its weight acts perpendicularly to the surface and will be equal to the normal force, which is the force keeping the object from falling through the floor. The normal force is always perpendicular to the surface; when the surface is not level, the normal force will be equal to some subset of the weight. This is seen in the image below, which shows a box on an inclined plane.

Box on an inclined plane.

The weight of the box acts through the center of gravity and directly towards the center of the Earth. The weight vector in the sketch is red and labeled W.  The normal force acts perpendicular to the surface of the inclined plane to keep the box from falling through the plane. The force of the box on the plane is equal to the normal force. Since the normal force and the force of the box acting on the plane are the same, we can reference the force against the plane as the normal force. That force, FN, is purple in the image above. In addition, there is a force acting on the box parallel to the surface of the plane and pushing the box down the plane. This force is drawn in blue and is called the parallel force. The normal force and the parallel force add to give the weight.

The triangle of the black inclined plane and the yellow triangle are similar triangles; the corresponding sides are mutually perpendicular. Therefore, the angle at the top of the yellow triangle is also 30°. For a right triangle, if we know one other angle (the 30° angle) and one side (the weight), we can calculate the other two sides. Therefore, we can calculate the parallel force pushing the box down the incline.

Consult the diagram above.  Assume an ideal machine (ignore friction)

  • Questions 8 of 10.  (Incorporate the question in your answer):  Define “Weight” in the context of an inclined plane.
  • Questions 9 of 10.  (Incorporate the question in your answer):  Define “Normal Force” in the context of an inclined plane.
  • Questions 10 of 10.  (Incorporate the question in your answer):  Explain what the  “Parallel Force” represents in the diagram above.

FOOTNOTES

  1.   See also Alternate Lesson 4A on December 14, 2018, and Lesson 5 on January 8, 2019
  2.   Sources:  VANDERBILT STUDENT VOLUNTEERS FOR SCIENCE, “Inclined Plane,” Fall 2013 (https://www.vanderbilt.edu/cso/Inclined_Plane.pdf), viewed January 8, 2018); CK-12 website, Gravitional Force and Inclined Planes,  (https://www.ck12.org/physics/gravitational-force-and-inclined-planes/lesson/Gravitational-Force-and-Inclined-Plane-PHYS/), viewed 1-8-2019
  3.   CK-12 website, Gravitional Force and Inclined Planes,  (https://www.ck12.org/physics/gravitational-force-and-inclined-planes/lesson/Gravitational-Force-and-Inclined-Plane-PHYS/), viewed 1-8-2019